Effects of Scarcity, Climate Variability, and Risk Management Policy on Cropland Allocation, Water Use, and Technology Adoption on the U.S. West Coast

Jian Shi, Oregon State University, [email protected] Junjie Wu, Oregon State University, [email protected]

Selected Paper prepared for presentation at the 2019 Agricultural & Applied Economics Association Annual Meeting, Atlanta, GA, July 21 – July 23

Copyright 2019 by [authors]. All rights reserved. Readers may make verbatim copies of this document for non-commercial purposes by any means, provided that this copyright notice appears on all such copies.

Abstract: This paper analyzes how water availability, water supply institutions, and climate affect producers’ land and water use decisions. We first construct a theoretical model to characterize farmers’ behavior, subject to climate risks and uncertainties in water supply. From the model, we derive the conditions for optimal production decisions and identify key parameters affecting land allocation, water application rate, and irrigation technology adoption. We then estimate a system of equations jointly to investigate how farmers adapt to different climate and water conditions with detailed irrigation and climate data for the states of California, Oregon and Washington. We also specify policy alternatives to simulate potential changes in water supply institutions, water pricing policies, and extreme weather and climate scenarios. We demonstrate how to assess the effect of risk management policy and future climate change on producers’ adaption strategies.

Keywords: , climate variability, water use, irrigation, water conservation

I. Introduction

Agriculture is a major water user on the U.S. West Coast, accounting for over 90% of human water consumption (USDA 2017). Water scarcity and extreme weather cause substantial economic losses to agricultural producers in the region. For example, the 2014 Central Valley drought reduced surface water availability by 6.6 million acre-feet in California, resulting in $2.2 billion economic losses to (Howitt et al. 2014). Water scarcity and extreme weather also impose significant stress on the environment and ecosystems on the West Coast, which in turn reduces agricultural productivity (Hoekstra 2014; IPCC 2014; Li et al. 2018). For example, to cope with demand for irrigation during the 2014 Central Valley drought, groundwater extraction increased by 5 million acre-feet, which lowered groundwater level, deteriorated groundwater quality, and increased risk of land sinking. In addition, a deadly salmon parasite thrived in the drought and infected nearly all the juvenile Chinook salmon in the Klamath River in Northern California before they migrate to the ocean. The economic and environmental damages from drought and other extreme weather are anticipated to be more severe and frequent in the current context of climate change (Bates et al. 2008; Howitt et al. 2014).

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Population increase, economic growth, and physical limit to water supply will lead to reduced per capita on the West Coast. The influence of increasing population on water shortage is four times as important as the influence of water availability due to long-term climatic change (Kummu et al. 2010). Both over allocation of surface water and overdraft of groundwater contribute to uncertainty in water supply. California has allocated five times more surface water than the average annual streamflow (Grantham and Viers 2014), causing disputes over water ownership during times of water scarcity. Before the Sustainable Groundwater

Management Act (SGMA) was passed in 2014, groundwater in California was an unregulated open access resource subject to the tragedy of the commons (Hardin 1968). NASA’s GRACE satellite mission data shows that water reserves have significantly declined since 2003 in twenty- one of the thirty-seven largest aquifers in the world, mainly in the most prolific agricultural regions, such as the Central Valley of California (Richey et al. 2015).

Climate change intensifies water scarcity in a variety of ways and complicates the challenges faced by western agricultural producers. Changing patterns of precipitation and rising temperature are expected to decrease snowpack, cause earlier snowmelt runoff, increase the risk of winter flooding, and reduce spring and summer stream inflows on the U.S. West Coast, which will impact surface water availability (Hayhoe et al. 2004). In 2017, California had record level of precipitation after over five years of drought, with April snowpack approaching 200% of the normal level (NASA 2017). Agriculture is a climate-sensitive industry. Climate change and associated changes in water supply can affect the quantity (i.e. yield) and quality of agriculture products and alter agricultural landscape. For example, warmer temperature may shift ripening of wine grapes in California 1-2 months earlier, generating degraded quality and lower market value (Hayhoe et al. 2004; Jackson et al. 2011). Irrigated cropland decreased by about 0.8 million

2 acres in the US from 2007 to 2012, with most of the decline occurring in the western states due to drought (USDA 2017).

Adapting irrigation management is one of the primary mechanisms for the society to cope with water scarcity and climate change (Howden 2007). Farmers are exposed to uncertainties and risks associated with water, climate and price variability. To maintain profitability, they are incentivized to conserve water and alter production practices. Irrigated agricultural producers could respond to risks and policies in several major ways: (1) changing water application rates,

(2) adjusting irrigated acres, (3) adopting more efficient irrigation technology, and (4) altering crop mix. Nowadays, many policy options are available to cope with production risks and attain sustainable agricultural development, such as water pricing policy, institutional reforms, market- based mechanisms, and water use regulations. Some of them are complements. For example, appropriate legal setting regarding water rights and flexible institutional arrangements may enhance participation in water trading (Libecap 2011; Li et al. 2018; Regnacq et al. 2016;

Rosegrant and Bingswanger 1994). Some options are substitutable. For example, irrigation technology adoption can be a substitute of changing water price or water quota rates to reach similar level of water conservation (Dinar and Yaron 1990).

Improving water management policy design necessitates a deeper theoretical understanding and credible empirical measurement of the impacts of water scarcity and climate variability on adaptive production decisions connected with agricultural water use. This paper attempts to fulfill this need by addressing the following questions: a) what are the main economic, climate and institutional factors influencing a farmer’s cropland allocation, water use and irrigation technology adoption for major crops on the West Coast (California, Oregon and

Washington)? and b) What is the impact of alternative policy options for water conservation and

3 irrigation technology adoption?

To address these questions, we first construct a farm-level theoretical model to characterize producers’ behavior under water and climate risks at both the extensive margin

(adjustments to irrigated share of cropland) and intensive margin (adjustments to water application rate). In particular, we capture production risks associated with extreme weather, such as drought, frost, and extreme heat. A formula of sufficient statistics representing optimal production decisions and key parameters in the adaptation strategies are derived. The conceptual framework informs empirical estimation and generates fresh insights into how farmers in irrigated agricultural production systems would respond to water scarcity and climate change.

Based on the theoretical model, we then conduct an empirical analysis to measure the relative importance of various economic, climate, and institutional factors influencing famers’ adaptations for five major categories of crops in this region (orchard/vineyard, rice, potato, wheat, and forage). This study combines irrigation data from the Farm and Ranch Irrigation

Survey (FRIS) developed by the USDA in 2008 and 2013, with climate data developed by the

PRISM Climate Group at Oregon State University. With the unique crop-specific and growing- season-specific data of key water and climate variables, we estimate a farm-level modelling system. The estimation results add to our understanding of producers’ adaptation to water scarcity, climate variability and institutional changes, and contributes to improving water resource management. Building on the empirical analysis, we evaluate irrigated agricultural performance under various scenarios. We first identify alternative policy options for managing water scarcity and climate variability, e.g., price increase under water scarcity, surface water supply curtailment, institutional adjustments, changes in type or frequency of extreme weather, etc. We then apply the modelling system to assess the effect of the policy options and climate

4 patterns on crop choices, water conservation, and irrigation technology adoption on the West

Coast. This policy evaluation presents a framework to identify the challenges and options for adaptive agricultural management in irrigated production systems.

II. Background

In this section, we provide some background information for the analysis, including a summary of water conservation practices, a brief review of previous studies that examine the effect of the water scarcity and climate change on irrigated agricultural systems, and a discussion of our contributions to literature.

Policy Options for Water Conservation

As the West Coast moves into the age of increasingly limited and costly water supply, some policy options have been proposed to promote agricultural water conservation and to increase water use efficiency. Such policy options fall into several main categories. a) Water pricing policy

In the long run, the price elasticity of irrigation water demand is estimated to be larger

than 0.48 in the U.S. (Scheierling et al. 2006). This high responsiveness indicates that water

pricing policy is an effective instrument to induce water conservation. Even though water

pricing has long been recognized as an efficient water allocation tool, there is no consensus

among decision makers and economists on how to derive an optimal water-pricing policy

(Johansson et al. 2002; Kim and Schaible 2000). In theory, an efficient water pricing policy

equates the marginal benefits and marginal cost of water use. However, there are such

distortionary constraints as water being a public good, water pricing entailing

implementation costs, and information asymmetry influencing the efficiency and equity of

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water pricing policies. In practice, a variety of methods are available for irrigation water

pricing, including volumetric pricing (i.e., charging irrigation water based on the quantities

of water consumed), non-volumetric pricing (i.e., charging irrigation water based on a per

output/input/area basis or land values), quotas, and water markets (Bandaragoda 1998; Dinar

2000; Renzetti 2000; Tsur 2000; Johansson et al. 2002). Getting water price right under

institutional and physical constraints requires more investigation into different pricing

structures. For example, an alternative is to examine the effect of switching from “a fixed fee

for a fixed amount of water” to setting a positive marginal price of water, which imposes a

variable charge for additional water supply (Moore 1999). b) Water institutional reforms

Policymakers consider institutional arrangements to change water allocation policy,

such as changing federal water provision by the US Bureau of Reclamation, or

implementing surface water curtailment to control water use (Moore and Negri 1992). Under

the prior appropriation doctrine, allocative priority of water rights and water scarcity cause

heterogeneous effect on irrigated land use activities among farmers. Currently the majority

of western U.S. adopt a priority-based sharing system to distribute water, following the

chronological order in which water rights are established. Such arrangements redistribute the

risk of water shortages. They tend to benefit senior water right holders, while exposing

junior holders to more water-supply risks. Water right holders with senior priorities have an

advantage to access water over junior holders. They can irrigate more acreage of land and

are less likely to have curtailed allotment. Whereas junior water right holders who are more

vulnerable to future climate change and predominantly bear the costs associated with

droughts are put at a greater disadvantage because of less secured water supplies (Brent

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2017; Burness and Quirk 1979; Hutchins 1968, 1977; Libecap 2011; Li et al. 2017, 2018;

Schlenker et al. 2007; Xu and Li 2016). As such, it is necessary to introduce reforms to the

existing institutional water management, such as building up a risk-sharing mechanism to

upgrade the current priority level of junior groups and promote overall social welfare. c) Development of water markets

This policy option focuses on market-based efforts to improve water trading, including

short-term water transactions and long-term water rights transfers. At times of drought, a

well-developed water market is necessary to reduce water application on marginal land,

move water to higher-value uses and achieve efficient water re-distribution with relatively

low cost and high flexibility (Hanak 2015; Howitt et al. 2014; Rosegrant 1990). Water

trading can bring about some unexpected consequences though, such as expanding irrigated

landscape, increasing the reliance of local economy on irrigation, and adversely affect local

water supply sustainability (Fleskens et al. 2013). For over three decades, most of the

world’s water market mechanisms are concentrated in the western U.S. and Australia

(Bjornlund and McKay 2002; Hadjigeorgalis 2009; Regnacq et al. 2016). In the western

U.S., formal water transfers are conducted mainly through water banks, bulletin board

markets, options markets and water trusts. Water banks have been outperforming other

transfer mechanisms and moving considerable amount of water without significant third-

party impacts. For example, the California Drought Water Bank facilitated the reallocation

of 389,970 acre-feet of water in 1991 under emergent drought conditions (Howitt et al. 1992;

Israel and Lund 1995).

In spite of the success in some market mechanism, water market is generally immature

compared with the strong institutional governance in this region, i.e., priority-based water

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sharing arrangements (Hadjigeorgalis 2009; Xu and Li 2016). Concerns arise over managing

negative externalities on groundwater use and the environment, dependency on supporting

institutional framework, defining property rights and incorporating transaction costs, and

equity issues. In the western U.S., private water markets have failed in protecting the

interests of the poor and led to inequitable distribution of water (Meinzen-Dick and Ringler

2006). A primary hurdle to establish a well-developed water market is that water trading may

be incompatible with the fundamental rules of water arrangements (Rosegrant and

Bingswanger 1994). For example, famers may violate the beneficial-use principle if they sell

unused water. Their water rights might be taken by state administrators or judicial systems in

this case. Hence, employing market approaches to improve water use efficiency and ease

water stress requires eliminating such legal obstacles. Moreover, uncertainty in searching for

trading partners and high transfer costs hinder short-term water trading in California

(Regnacq et al. 2016). In this case, a state-level system that collects and handles trading

information can facilitate searching process and encourage market participation. A preceding

successful example is the online platform operated in Murray-Darling Basin in Australia

(Culp et al. 2014). d) Water use regulation

Lastly, there are state and federal regulations regarding agricultural water consumption.

Increasing groundwater extraction has been an adaptation strategy to attenuate the negative

impact of surface water reduction. Farmers can choose between paying a higher premium for

more expensive water resources and bearing potential crop loss. However, if not managed

properly, long-term groundwater sustainability will be impaired (Hornbeck and Keskin

2014). State-wide regulations for groundwater rights in California have been absent until

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recently. SGMA of 2014 improves groundwater management in California by motivating

producers to change land use practices and sustainably use groundwater resources.

Groundwater basins are regulated under a Groundwater Sustainability Plan, compatible with

the criteria developed by the California Department of Water Resources (Olen et al. 2016).

Previous Studies on the Economics of Agricultural Water Resources

This analysis builds on previous research on agricultural water use and climate change impacts. The existing irrigation technology adoption literature is both extensive and well developed (Connor et al. 2009; Dinar and Zilberman 1991; Green et al. 1996; Green and Sunding

1997; Lichtenberg 1989; Schuck and Green 2001; Shrestha and Gopalakrishnan 1993; Xu et al.

2018). Farmers make irrigation decisions out of economic and physical considerations (Carey and Zilberman 2002; Caswell and Zilberman 1986; Li et al. 2018). It is recognized that variable climate conditions (e.g. temperature and precipitation) are associated with different technical efficiency, which critically affect producers’ irrigation technology choices (Dinar and Yaron

1990; Finkel and Nir 1983; Frisvold and Deva 2013; Negri and Brooks 1990). Nevertheless, there is a dearth of information for understanding how water use and irrigation decisions respond to climate change, especially the risk of extreme weather events. Two noticeable exceptions are

Olen et al. (2016) and Schuck et al. (2005), which examine how farmers change irrigation decisions to mitigate crop damage from water scarcity and climate change. This paper complements the previous studies by examining extreme weather events that are closely related to the volatility of water supplies and responsible for crop failure.

Apart from irrigation decisions, many studies focus on how water availability and climate determine agricultural land use and crop mix. Expected climate and water supply fluctuations alter land values (Mendelsohn et al. 1994; Schuck et al. 2005). Previous studies also suggest that

9 water scarcity reduces cropland allocated to relatively low-value and water-intensive crops

(Manning et al. 2017; Moore and Negri 1992; Moore et al. 1994; Sunding et al. 2002). Famers make land and water use decisions jointly (Howitt et al. 2014, 2015; Moreno and Sunding 2005;

Sunding et al. 2002; Pfeiffer and Lin 2014). It is yet to be known how the uncertainties of water availability and climate affect land allocation and irrigation decisions simultaneously.

Contributions

This study has several desirable features compared with existing literature. First, it is a farm-level, crop-specific analysis. The West Coast is one of the ten USDA Farm Production

Regions, with significant spatial and temporal variations. There are many microclimates even within a small area due to the complex topography. Extensive literature has primarily focused on the effect of water supply uncertainties and climate risks on crop yield or output, as well as water management from the perspective of administrative agency at the macroscale (Deschenes and

Greenstone 2007; Fischhendler and Heikkila 2010; Rosegrant and Binswanger 1994; Saleth and

Dina 2000; Saleth 2004; Schlenker and Roberts 2009). The effect of climate risks on an individual farmer’s land and water use decisions has received much less attention, due to lack of detailed farm-level data. Our micro-level modelling system attempts to explore how individual farmers with heterogeneous portfolios adapt to production risks. The crop-specific specification captures susceptibility of individual crops to alternative extreme weather events. For example, fruit blossoms can be damaged by spring freeze, making freeze risk one of the top drivers of crop loss for orchard/vineyards. As such, variation of freeze dates is a significant determinant of fruit tree growers’ responses, since irrigation can be used to mitigate freeze damage. Furthermore, this system models the impacts of water scarcity and climate variability on cropland allocation, water use and irrigation technology adoption decisions simultaneously. This approach presents a

10 holistic framework to investigate individual famer’s adaptation mechanisms and assess the magnitude of water scarcity and climate change effects. Estimation results provide valuable implications to promote development of efficient agricultural policies.

Second, the model explicitly distinguishes whether the decisions involved is a short-run or long-run response. Some of farmers’ adaptations are short-run decisions, while others involve long-run investment. For example, in the short run, farmers can adjust water application rates or irrigated acres during the growing season in response to observed weather and water conditions.

An array of climate statistics is developed for each month and season to represent observed variations of the agricultural growing season. However, it often entails long-run, quasi- irreversible capital investment to change irrigation technology or to convert from an annual crop to a perennial crop. Long-run decisions are more likely to respond to climate and water scarcity expectations, which can be represented by long-run averages for an array of climate statistics.

Third, this analysis differentiates annual crop and perennial crop. A perennial crop will be non-bearing or non-mature in the first several years, which may result in variations in water use.

To deal with the perennial nature of some crops, we include a set of variables characterizing the age structure of perennial crops and estimate how they affect farmers’ responses to climate and water variability.

Lastly, this study examines specialty crop producers’ behavior under risks and uncertainties. Specialty crops are a major source of farm income, especially on the West Coast.

But they are not as well analyzed as field crops in literature. Also, there may be unique risks for growing specialty crops. For example, many specialty crops are perishable, making them susceptible to placement risk (Schieffer and Vassalos 2015). Finally, the 2014 Farm Bill authorizes the Risk Management Agency (RMA) to expand crop insurance to more specialty

11 crops and more counties. Liability of specialty crops grew from around $7 billion in 2000 to almost $15 billion in 2014, accounting for 13.6% of total crop insurance liability in 2014 (FCIC

2015). More research about the impact of water supply uncertainties and climate risks on specialty crop producers’ behavior can promote development of efficient agricultural policies.

III. Methodology

Theoretical Model

This section outlines the model setup; more details are provided in Appendix.

To illustrate the basic structure of the model, consider a multioutput producer, who makes production decisions, including crop mix, input use, and irrigation technology adoption, to maximize his expected utility, subject a land use constraint, a water availability constraint, and a physical constraint for the adoption rate of a risk-reducing irrigation technology:

(1) max 퐸[푈(휋|휃, 휀)], 퐿푗,푟푗,푎푗,푧푗 s.t. ∑푗 퐿푗 ≤ 퐿,

∑푗 푟푗퐿푗 ≤ 퐸[푊̅ |휀],

0 ≤ 푎푗 ≤ 1,

(2) 푈(휋|휃, 휀) = −푒−훼휋,

(3) 휋 = ∑푗[푃푗퐿푗푓푗(∙) − 푐(휀)푟푗퐿푗 − 휔푧푗퐿푗 − 푡푎푗],

훽푗 훾푗 휃 (4) 푓푗(∙) = 푓(푟푗훿푎푗, 푧푗, 휃) = (푟푗훿푎푗) 푧푗 푒 , where

푗 = an index of crop;

퐿푗 = land allocated to crop 푗;

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퐿 = total cropland;

푟푗 = crop-specific per-acre water application rate;

푊̅ = an exogenous water use constraint;

푎푗 = crop-specific share of cropland adopting water-saving irrigation technology;

훼 = Arrow-Pratt measure of risk aversion;

푃푗 = output price;

푐 = water price;

휔 = price of non-water input;

푧푗 = crop-specific per-acre non-water input use;

푡 = unit equipment cost of the water-saving irrigation system;

훿 = efficiency of the water-saving irrigation technology.

According to equation (3), profit is a summation of crop revenue (푃푗퐿푗푓푗(∙)) minus costs from water use (푐(휀)푟푗퐿푗), non-water input use (휔푧푗퐿푗), and the equipment and installation of the water-saving irrigation system (푡푎푗), which is independent of land allocated to the crop. Assume price-taking behavior and no uncertainty in output price. Equation (4) gives a Cobb-Douglas production function. 훽푗 + 훾푗 is assumed to be positive but smaller than 1 to guarantee decreasing returns to scale in agricultural production. The distribution of production risk associated with climate change is specified as 휃~푁(0, 휎2). Let 푐(휀) = 푐 + 휀2, where 퐸(휀) =

2 0 and 푉푎푟(휀) = 휎휀 . There is no assumption imposed on the distributional form of 휀, which creates flexibility for the model as it proceeds. This specification implies that water scarcity increases expected water price.

By setting up a Lagrangian function, the necessary first order conditions for the optimal solutions can be derived. The conditions are informative. For example, the optimal acreage

13 allocated to a specific crop is such that the shadow price of the land availability constraint equals the net marginal benefit of land, where the net marginal benefit is measured by the difference between expected value of marginal product of land and extra cost of water and non-water input, extra risk premium. The optimal per-acre water use of a specific crop is determined at the level where the shadow price of the water availability constraint equals the per-acre net marginal benefit of water. The net marginal benefit is similarly defined as the difference between expected value of per-acre marginal product of water and extra cost of intensive-margin water use, extra per-acre risk premium. The optimal share of the efficient irrigation technology is at the level where the net marginal benefit is equal to its shadow price.

Theoretical Results

Comparative static analysis can be conducted to examine how water scarcity and water cost affect the optimal decisions. Some of the preliminary findings are presented as follows.

First, crop-specific water application rates are negatively associated with water scarcity.

Intensified water scarcity increases expected water price. Consistent with law of demand, producers would cut the volume of water applied in response to predicted price increase.

Second, a comparison between risk-averse and risk-neutral producers’ behavior suggests that the water-saving irrigation technology is a risk-decreasing input. It can improve the relative efficiency of water use, mitigate the effects of production risks from climate change (e.g. uncertain rainfall), and reduce the implicit cost of risks. In addition, as producer becomes more risk averse, he can manage risk exposure by increasing the risk-reducing technology adoption rate. Climate change and water scarcity have opposite impact on technology adoption rates. For producers with low adoption rates, more climate risks or reduced water scarcity discourage technology adoption. While producers with high water use efficiency respond reversely.

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Lastly, the impact of climate change and water scarcity on land allocations corresponds to the impact on irrigation decisions. Higher technology adoption rate is associated with more planted acreage for a specific crop. Comparably, when the scale of production is sufficiently large, an extra unit of land cannot bring high marginal benefit. Producers tend to reduce planted acreage of the crop given anticipation of intensified water scarcity. In contrast, when the net marginal benefit of land is high, producers would expand production given reduced climate risks or more uncertainties in water availability.

Empirical Estimation

A system of equations will be estimated simultaneously to identify how farmers adapt to different climate and water resource conditions. The equation system captures the spatial and temporal variations in farmers’ responses (including share of cropland allocated to a specific crop with a certain technology, and water application rate) and key determinants (including water supply institutions, water availability, climate and weather conditions, land characteristics, and farmer demographics). A general specification can be written as

푗푘 푗푘 (5) 푆푖푡 = 푓 (퐼푖푡, 푆푖푡, 퐶푖푡, 퐿푖푡, 퐷푖푡),

푗푘 푗푘 (6) 푊푖푡 = 푔 (퐼푖푡, 푆푖푡, 퐶푖푡, 퐿푖푡, 퐷푖푡), where

푖 = an index of farm;

푗 = an index of crop or crop type;

푡 = year;

푘 = irrigation technology (gravity, sprinkler, or drip);

푗푘 푆푖푡 = share of cropland allocated to crop 푗 irrigated using technology 푘 in farm 푖

15 and year 푡;

푗푘 푊푖푡 = amount of water applied to crop 푗 irrigated using technology 푘 in farm 푖 and year 푡;

퐼푖푡 = water supply institutions;

푆푖푡 = economic and physical indicators of water availability;

퐶푖푡 = climate and weather conditions;

퐿푖푡 = land characteristics;

퐷푖푡 = demographic features.

A notable feature of this analysis is that land allocation, water use, and irrigation technology adoption decisions are made jointly. Besides, alternative specifications and methods will be tested and compared. For example, land allocation is formulated as a share. To estimate equation (5), there are several approaches available, such as fractional logit model (Papke and

Wooldridge 1996), multinomial logit model (Lichtenberg 1989), latent class logit model

(Claassen et al. 2017). While water application rates can be estimated with Heckman or Tobit method due to truncation.

Analysis of Policy Responses

The empirical model links farmers’ cropland allocation, water use and irrigation technology adoption decisions to water supply institutions, economic and physical indicators of water availability, climate and weather conditions, land characteristics, and demographic features. We consider the projections under different climate scenarios and water supply variations following Schlenker et al. (2007) and Xu and Li (2016). Major scenarios are identified as follows.

16 a) Water supply institutions

Currently, farms can receive water from federal agencies (e.g. the U.S. Bureau of

Reclamation, U.S. Army Corps of Engineers, and others), or different institutions that only

supply surface water or groundwater. In the empirical model, we construct variables

reflecting the nature of contracts between farms and government agencies. Assume there is

an institutional adjustment that restricts surface water use. We will estimate its impact by

changing the variables representing surface water supply and predicting farmers’ responses. b) Water pricing policy

Corresponding to different water supply institutions, there are three major price

structures. Farms pay a fixed fee for a fixed amount of water if they choose federal water

supply. There is a variable unit cost for additional water applied if farms only receive surface

water. If farms only have groundwater supply, water price depends on groundwater pumping

cost, which is affected by well depth, pump capacity, energy price, and other factors (Moore

et al. 1994). We expect a price increase under water scarcity. To examine farmers’ cost

responsiveness, we will change the variables representing federal water fee, surface water

cost, or well depth. We also include some interaction terms to check how institutional

adjustments influence farmers’ response to water scarcity when making irrigation decisions. c) Extreme weather and climate scenarios

Specific scenarios involve changing the type and frequency of extreme weather events

that are closely related to specific crops. For example, we include variables indicating

whether a farm produces in an arid region with frequent drought. This specification enables

measuring how the expectation of frequent drought affects water use and technology

adoption. Similarly, the effect of extreme heat or frost will be identified by changing the

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variables for whether irrigation is used to reduce heat stress or prevent frost damage. Lastly,

we analyze the impact of climate change-induced warming patterns. We follow the

temperature projection of Mote and Salathé (2010), who anticipate an increase in the

temperature range by 1.1-2.9°C in western U.S. by the end of the 21st century. Projected

range of standard deviation can be -0.5°C to 1°C for the temperature extremes (IPCC 2007).

IV. Data

This analysis uses farm-level cross-sectional data on water and climate for the states of

California, Oregon and Washington. The data is obtained from two main sources. First, the

USDA Farm and Ranch Irrigation Survey (FRIS) is the primary data for characterizing the variability in water availability, water supply institutions, farmer demographics, water use, and irrigation technology adoption across farms on the West Coast. This essay generates a representative sample of farms on the West Coast with data in production years 2008 and 2013.

The West Coast is one of the ten USDA Farm Production Regions. The FRIS provides the most comprehensive profile of irrigation in the U.S. because it is delivered to all irrigated farms as a supplement to the Census of Agriculture. It contains detailed farm-level data on water sources (e.g., groundwater and surface water), water supply institutions, farm characteristics, farmer demographics, and a variety of irrigation management practices, including technology adoption, water use, water recycling and reclamation, and whether irrigation was used to mitigate damage from extreme weather such as freeze and heat stress. Water availability is measured by both physical and economic variables. The physical variables include: a) surface water and groundwater use; b) depth to groundwater; c) groundwater saturated thickness; d) pump capacity for irrigation technology (i.e., well water discharge rate); and e) how groundwater well depth has

18 changed in the last five years. The economic variables measuring water availability include: a) whether a fee is paid for surface water; b) cost of off-farm surface water; c) cost of new groundwater well construction or deepening wells; and d) cost of construction or improvement of permanent water storage and distribution systems.

The second major source of data is crop-specific climate data developed from the PRISM system, capturing both spatial and temporal variations of important climate variables on the West

Coast. PRISM datasets are recognized world-wide as the highest-quality spatial climate datasets currently available and provide the USDA with their official 30-year digital climate maps (Daly

2006; Daly et al. 2012; 2008; 2002; Daly et al. 1994). The PRISM system produces continuous, digital grid estimates of daily, monthly, yearly, and event-based climatic parameters.

The climate variables developed from PRISM database are specific to crops. It is an important feature because different crops are sensitive to different types of extreme weather.

Some crops are more sensitive to heat, while others are more sensitive to freeze or moisture stress. For example, the variation of spring and fall freeze dates may be an important determinant of water use and irrigation technology decisions for tree crops because irrigation is used to mitigate crop freeze damage. Moreover, the climate data are unique in that they reflect both expected climate and observed weather conditions. Long-term climate expectations can affect long-term investment, such as technology adoption and production decisions regarding perennial crops. To represent long-term expectations, recent 30-year averages will be developed for an array of climate statistics for each month of the year for California, Oregon, and Washington.

Short-term water use and land allocation are more likely to respond to observed weather. To represent short-term observations, an array of climate statistics will be developed for each month and season.

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V. Expected Results

The modelling system of land allocation, water use and irrigation technology adoption will be estimated with the detailed irrigation and climate data. Empirical results will indicate the major economic, climate and institutional factors influencing producer behavior. An estimation of farmers’ response to proposed risk management policies and climate variability generates some policy implications regarding technology adoption and agricultural water use.

Focusing on the theoretical framework of the analysis, my presentation is expected to generate some discussion over the background, setup, intuition, and application of the model.

Comments will add to our understanding of producers’ adaptation to water scarcity, climate variability and institutional changes, which provides insights into improving theoretical model design and conducting empirical analysis.

20

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Appendix

A1. Conceptual Framework

The General Case

This paper constructs a microeconomic model of a multioutput producer. The following equations are used to characterize an optimization under climate risks and water supply uncertainty:

(A1-1) max 퐸[푈(휋|휃, 휀)], 풙

(A1-2) 휋 = 풑푓(풙, 휃) − 푣(풗, 휀)풙, where

풙 = a vector of inputs;

풑 = a vector of output prices;

풗 = a vector of input prices;

푓(∙) = a stochastic production function;

휃 = a random variable reflecting production uncertainty associated with climate change;

휀 = a random variable reflecting uncertainty in input price associated with water scarcity.

In this setup, a private producer chooses inputs to maximize expected utility from profits, subject to climate risks and uncertainty in water supply. The producer has

28 information about the distribution of the random variables 휃 and 휀. Applying the chain rule, the necessary first order conditions for the optimal choice are:

휕푓(풙,휃) (A1-3) 퐸 [푈′ ∙ (풑 − 푣(풗, 휀))] = 0 ∀푥 ∈ 풙, or 휕푥

′ ′ 휕푓(∙) 휕푓(풙,휃) 푐표푣(푈 ,푣(∙))−푐표푣(푈 ,풑 ) (A1-4) 퐸 [풑 ] − 퐸[푣(풗, 휀)] = 휕푥 ∀푥 ∈ 풙. 휕푥 퐸[푈′] The certainty equivalent is formulated as:

(A1-5) 퐶퐸 = 퐸[풑푓(풙, 휃) − 푣(풗, 휀)풙] − 푅(풙), where 푅(풙) represents the Arrow-Pratt risk premium. If the producer is risk averse,

푅(풙) > 0. If the producer is risk neutral, 푅(풙) = 0. The producer is indifferent between a sure amount of money 퐶퐸 and a risky profit 휋. Assume 푈′ > 0. The expected utility maximization problem is equivalent to maximizing the certainty equivalent 퐶퐸. The necessary first order conditions for the optimal input choice are:

휕푓(풙,휃) 휕푅(풙) (A1-6) 퐸 [풑 ] − 퐸[푣(풗, 휀)] = ∀푥 ∈ 풙, 휕푥 휕푥

휕푅(풙) where represents the marginal risk premium. A comparison of the right-hand side 휕푥 휕푓(∙) 푐표푣(푈′,푣(∙))−푐표푣(푈′,풑 ) of equation (A1-4) and (A1-6) shows that 휕푥 indicates the impact of 퐸[푈′] input choice on the implicit cost of risk bearing. Assume diminishing marginal

휕푓2(풙) productivity < 0. For a risk-averse producer and a risk-decreasing input, the 휕푥2

휕푅(풙) marginal risk premium is negative < 0. The producer has an incentive to use more 휕푥 of this input than a risk-neutral producer (푅 = 푅′ = 0). This can be demonstrated by the following graph. As shown in Figure 1, a risk-averse producer has higher demand for the risk-reducing input, due to lower implicit cost of risks. Alternatively, a risk-averse

29 producer would use less of a risk-increasing input than a risk-neutral producer.

$ 휕푓(∙) 휕푓(∙) 퐸[풑 ] 퐸 ቈ풑 ቉ − 푅′ 휕푥 휕푥

퐸[푣]

푥푅푁 푥푅퐴 푥

Figure A1-1: A comparison of risk-reducing input use between RN and RA producers

A Special Case

To address the research question, this paper introduces specific functional forms and makes a few assumptions. Consider a multioutput producer, who makes production decisions, including crop mix, input use, and irrigation technology adoption, to maximize his expected utility, subject a land use constraint, a water availability constraint, and a physical constraint for the adoption rate of a risk-reducing irrigation technology:

(A1-7) max 퐸[푈(휋|휃, 휀)], 퐿푗,푟푗,푎푗,푧푗 s.t. ∑푗 퐿푗 ≤ 퐿,

∑푗 푟푗퐿푗 ≤ 퐸[푊̅ |휀], 30

0 ≤ 푎푗 ≤ 1,

(A1-8) 푈(휋|휃, 휀) = −푒−훼휋,

(A1-9) 휋 = ∑푗[푃푗퐿푗푓푗(∙) − 푐(휀)푟푗퐿푗 − 휔푧푗퐿푗 − 푡푎푗],

훽푗 훾푗 휃 (A1-10) 푓푗(∙) = 푓(푟푗훿푎푗, 푧푗, 휃) = (푟푗훿푎푗) 푧푗 푒 , where

푗 = an index of crop;

퐿푗 = land allocated to crop 푗;

퐿 = total cropland;

푟푗 = crop-specific per-acre water application rate;

푊̅ = an exogenous water use constraint;

푎푗 = crop-specific share of cropland adopting water-saving irrigation technology;

훼 = Arrow-Pratt measure of risk aversion;

푃푗 = output price;

푐 = water price;

휔 = price of non-water input;

푧푗 = crop-specific per-acre non-water input use;

푡 = unit equipment cost of the water-saving irrigation system;

훿 = efficiency of the water-saving irrigation technology.

According to equation (A1-9), profit is a summation of crop revenue (푃푗퐿푗푓푗(∙)) minus

31 costs from water use (푐(휀)푟푗퐿푗), non-water input use (휔푧푗퐿푗), and the equipment and installation of the water-saving irrigation system (푡푎푗), which is independent of land allocated to the crop. Assume price-taking behavior and no uncertainty in output price.

Equation (A1-10) gives a Cobb-Douglas production function. 훽푗 + 훾푗 is assumed to be positive but smaller than 1 to guarantee decreasing returns to scale in agricultural production. The distribution of production risk associated with climate change is

2 2 2 specified as 휃~푁(0, 휎 ). Let 푐(휀) = 푐 + 휀 , where 퐸(휀) = 0 and 푉푎푟(휀) = 휎휀 .

There is no assumption imposed on the distributional form of 휀, which creates flexibility for the model as it proceeds. This specification implies that water scarcity increases expected water price.

Assume 휋 is normally distributed with mean 퐸[휋] and variance 푉푎푟[휋].1

They can be derived from the distribution of 휃:

훽 1 2 푗 훾푗 휎 2 (A1-11) 퐸[휋] = ∑푗[푃푗퐿푗(푟푗훿푎푗) 푧푗 푒2 − (푐 + 휎휀 )푟푗퐿푗 − 휔푧푗퐿푗 − 푡푎푗],

2 2 훽 휎 휎 푗 훾푗 2 2 (A1-12) 푉푎푟[휋] = 푒 (푒 − 1) ∑푗[푃푗퐿푗(푟푗훿푎푗) 푧푗 ] .

The expected utility function can be expressed as an increasing function of 퐸[휋] −

1 훼푉푎푟[휋]: 2

1 −훼(퐸[휋]− 훼푉푎푟[휋]) (A1-13) 퐸[푈(휋|휃, 휀)] = −푒 2 .

1 According to equation (A1-5), the risk premium is 푅 = 훼푉푎푟[휋]. 2

A Lagrangian function, denoted 퐿퐴, states the optimization problem as:

1 The joint distribution of (휃, 휀) can be derived. The conditional distribution of 휀 can also be derived. 2 The covariance of revenue from different crops are assumed to be zero for simplicity. 32

(A1-14) 퐿퐴 = 퐸[푈(휋)] + 휆(퐿 − ∑푗 퐿푗) + 휂(퐸[푊̅ |휀] − ∑푗 푟푗퐿푗) + 휏(1 − 푎푗), where 휆, 휂, and 휏 are the shadow prices assigned to the land, water supply and share constraint, respectively. Similar to equation (A1-6), the necessary first order conditions for the optimal solutions are:

훽 1 2 2 2 2훽 푗 훾푗 휎 2 휎 휎 2 푗 2훾푗 (A1-15) 푃푗(푟푗훿푎푗) 푧푗 푒2 − (푐 + 휎휀 )푟푗 − 휔푧푗 − 휆 − 휂푟푗 = 훼푒 (푒 − 1)푃푗 퐿푗(푟푗훿푎푗) 푧푗 ,

훽 1 2 2 2 2훽 푗 훽푗−1 훾푗 휎 2 휎 휎 2 푗 2훽푗−1 2훾푗 (A1-16) 훽푗푃푗(훿푎푗) 푟푗 푧푗 푒2 − (푐 + 휎휀 ) − 휂 = 훼푒 (푒 − 1)훽푗푃푗 퐿푗(훿푎푗) 푟푗 푧푗 ,

훽 1 2 2 2 2훽 푗 훾푗−1 휎 휎 휎 2 푗 2훾푗−1 (A1-17) 훾푗푃푗(푟푗훿푎푗) 푧푗 푒2 − 휔 = 훼푒 (푒 − 1)훾푗푃푗 퐿푗(푟푗훿푎푗) 푧푗 ,

훽 1 2 2 2 2훽 푗 훽푗−1 훾푗 휎 휎 휎 2 2 푗 2훽푗−1 2훾푗 (A1-18) 훽푗푃푗퐿푗(훿푟푗) 푎푗 푧푗 푒2 − 푡 − 휏 = 훼푒 (푒 − 1)훽푗푃푗 퐿푗 (훿푟푗) 푎푗 푧푗 ∀푗.

These conditions are informative. Equation (A1-15) states that the optimal

∗ acreage allocated to a crop 퐿푗 is such that the shadow price of the land availability constraint 휆 equals the net marginal benefit of land. The net marginal benefit is defined as the difference between expected value of marginal product of land

훽 1 2 푗 훾푗 휎 2 (푃푗(푟푗훿푎푗) 푧푗 푒2 ) and extra cost of water ((푐 + 휎휀 )푟푗 + 휂푟푗), extra cost of non-water

2 2 2훽 휎 휎 2 푗 2훾푗 input (휔푧푗), extra risk premium (훼푒 (푒 − 1)푃푗 퐿푗(푟푗훿푎푗) 푧푗 ). Equation (A1-16)

∗ states that the optimal per-acre water use of a crop 푟푗 is determined at the level where the shadow price of the water availability constraint 휂 equals the per-acre net marginal benefit of water. The net marginal benefit is similarly defined as the difference between

훽 1 2 푗 훽푗−1 훾푗 휎 expected value of per-acre marginal product of water (훽푗푃푗(훿푎푗) 푟푗 푧푗 푒2 ) and

2 extra cost of intensive-margin water use (푐 + 휎휀 ), extra per-acre risk premium

2 2 2훽 휎 휎 2 푗 2훽푗−1 2훾푗 (훼푒 (푒 − 1)훽푗푃푗 퐿푗(훿푎푗) 푟푗 푧푗 ). Equation (A1-18) states that the optimal

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∗ share of the efficient irrigation technology 푎푗 is at the level where the net marginal benefit is equal to its shadow price (휏).

The conditions generate the optimal solutions:

∗ 훽푗훾푗 (A1-19) 푟푗 = 2 , (1−훽푗−훾푗)(푐+휎휀 +휂)

∗ 휆훾푗 (A1-20) 푧푗 = , 휔(1−훽푗−훾푗)

1 2 ∗ 2 2 ∗ 훽푗 ∗훾푗 ∗훽푗 휎 (A1-21) 푎푗 (훼, 훽푗, 훾푗, 휎 , 훿, 푃푗, 푐, 휎휀 , 휔, 푡; 휆, 휂, 휏): 푃푗(푟푗 훿) 푧푗 (1 − 훽 − 훾푗)푎푗 휆훽푗푒2 −

2 ∗ 훽푗 ∗훾푗 ∗2훽푗+1 휎2 휎2 2 [푃푗(푟푗 훿) 푧푗 (1 − 훽푗 − 훾푗)] 푎푗 훼푒 (푒 − 1)(푡 + 휏) = 휆 훽푗,

∗ (1−훽푗−훾푗)(푡+휏) ∗ (A1-22) 퐿푗 = 푎푗 , 휆훽푗

∗ where 푎푗 is characterized by the implicit function in equation (A1-21).

A2. Comparative Analysis

An assessment of the impact of water availability and climate change on production decisions requires a clear and direct measure of risks. In this essay, an increase in risks is reflected by an increase in risk premium. According to the specification, 푅 =

1 1 2 2 훽 훼푉푎푟[휋] = 훼푒휎 (푒휎 − 1) ∑ [푃 퐿 (푟 훿푎 ) 푗푧 훾푗 ]2. Therefore, changes in risks can be 2 2 푗 푗 푗 푗 푗 푗 represented by changes in producers’ risk aversion level (훼), variability of climate risks

2 2 (휎 ), and variability in water supply (휎휀 ). Selected comparative static results are presented as follows.

Impact of Risk Aversion on Adaption Strategies

As discussed in The General Case, the behavior of a risk-averse producer is different 34 from that of a risk-neutral producer. Risk aversion makes a producer willing to pay a positive amount of money to avoid bearing risks. Hence, for a risk-averse person, 푅 > 0,

훼 > 0. Whereas for a risk-neutral person, 푅 = 0, 훼 = 0.

휕푟∗ 휕푧∗ Firstly, 푗 = 푗 = 0, suggesting that risk aversion level doesn’t affect 휕훼 휕훼 producers’ decisions regarding water application rate or non-water input use.

∗ 훽푗 ∗훾푗 Secondly, according to equation (A1-21), when 훼 > 0, 푃푗(푟푗 훿) 푧푗 (1 −

1 2 훽 1 2 ∗훽푗 휎 2 ∗ 푗 ∗훾푗 ∗훽푗 휎 훽푗 − 훾푗)푎푗 휆훽푗푒2 > 휆 훽푗; when 훼 = 0, 푃푗(푟푗 훿) 푧푗 (1 − 훽푗 − 훾푗)푎푗 휆훽푗푒2 =

2 휆 훽푗. Therefore, a risk-averse producer has a higher share of cropland adopting the water- saving irrigation technology than a risk-neutral producer. The irrigation technology is thus a risk-reducing input. It improves the relative efficiency of water use, reduces the effects of climate change (e.g. uncertain rainfall) on production, and reduces the implicit cost of risks.

∗ Furthermore, a comparison of the optimal 푎푗 among risk-averse producers is conducted by taking derivative of equation (A1-21) with respect to 훼. It can be shown that

훽푗 훾 훽 1 2 ∗ ∗ ∗ ∗ 푗 ∗ 푗 2휎 휕푎푗 푎푗(푃푗(푟푗 훿) 푧푗 (1−훽푗−훾푗)푎푗 푒 −휆) (A2-1) = 1 > 0. 훽푗 훾 훽 휎2 휕훼 ∗ ∗ 푗 ∗ 푗 2 훼[휆훽푗+(1+훽푗)(휆−푃푗(푟푗 훿) 푧푗 (1−훽푗−훾푗)푎푗 푒 )]

As the producer becomes more risk-averse, he can manage risk exposure by increasing the share of land using the risk-reducing irrigation system.

Lastly, change in land allocated to a specific crop is proportional to change in the

휕퐿∗ (1−훽 −훾 )(푡+휏) 휕푎∗ optimal technology adoption rate, 푗 = 푗 푗 푗. For a specific crop, if the 휕훼 휆훽푗 휕훼 35 producer decides to adopt the relatively efficient irrigation technology for a higher percentage of cropland, he would also allocate more land to this crop. But the expansion in the scale of production is positively affected by the cost associate with the efficient irrigation technology (푡 + 휏), and limited by returns to scale (훽푗 + 훾푗), shadow price of land 휆, and output elasticity of efficient water use 훽푗 as well.

Impact of Climate Risks on Adaption Strategies

Climate change results in production risks. Of particular interest are the effects of the variability in climate, represented by its variance 휎2, on production behavior. Similarly,

휕푟∗ 휕푧∗ 푗 = 푗 = 0. Zero-effect indicates that producers make both water and non-water input 휕휎2 휕휎2 use decisions regardless of climate change.

The influence on irrigation decision is somewhat complicated. Take derivative of equation (A1-21) with respect to 휎2. It takes the form of

훽 1 2 ∗ 휎2 ∗ 푗 ∗훾푗 ∗훽푗 휎 휎2 ∗ 푎푗[(3푒 −1)(푃푗(푟푗 훿) 푧푗 (1−훽푗−훾푗)푎푗 푒2 −휆)−휆푒 ] 휕푎푗 (A2-2) = 1 . 2 2 훽푗 훾 훽 휎2 휕휎 휎 ∗ ∗ 푗 ∗ 푗 2 2(푒 −1)[휆훽푗+(1+훽푗)(휆−푃푗(푟푗 훿) 푧푗 (1−훽푗−훾푗)푎푗 푒 )]

The sign of this marginal effect is determined by the difference between the adoption rate

1 훾푗 휎2 1−훽 −훾 (4푒 −1)휆 훽푗 휔(1−훽 −훾 ) 훽 푎∗ and a threshold level 푎̅ = 푗 푗 ቈ ቉ [ 푗 푗 ] 푗 (푐 + 휎2 + 푗 푗 휎2 휀 훿훽푗훾푗 (3푒 −1)푃푗(1−훽푗−훾푗) 휆훾푗

휕푎∗ 휕푎∗ 휂). When 푎∗ < 푎̅ , 푗 < 0; otherwise, when 푎∗ > 푎̅ , 푗 > 0. The implication is that 푗 푗 휕휎2 푗 푗 휕휎2 when the technology adoption rate is below a certain level, producers have an incentive to reduce the use of the risk-reducing irrigation technology, subject to an expected 36 increase in climate risks. However, if the adoption rate is already high, above the threshold level, then an increase in climate risks would make producers enhance the use of the efficient irrigation technology. That is, even though climate change doesn’t affect

∗ the crop-specific per-acre water application rate 푟푗 , it can influence production by

∗ ∗ changing the efficient water use level 푟푗 훿푎푗 .

Climate change affects land allocation in a similar manner. The threshold level is

1 훾푗 2 휎2 (1−훽 −훾 ) (4푒 −1)휆 훽푗 휔(1−훽 −훾 ) 훽 defined as 퐿̅ = 푗 푗 ቈ ቉ [ 푗 푗 ] 푗 (푐 + 휎2 + 휂)(푡 + 휏). 푗 2 휎2 휀 휆훿훽푗 훾푗 (3푒 −1)푃푗(1−훽푗−훾푗) 휆훾푗

Above this level, producers increase land allocated to crop 푗 in accordance with the increase in technology adoption rate. Below this level, more uncertainties in climate conditions incentivize producers to reduce both the adoption rate and the acreage of the crop. It is also shown in Appendix A-3 that the threshold level land allocation can be transformed into a level for the shadow price of land constraint 휆̅. In other words, when the shadow price of land is low, producers tend to expand production given an increase in climate risks. Whereas when the marginal benefit of land use is high, producers would reduce planted acreage in the face of more climate risks.

Impact of Water Availability on Adaption Strategies

Reductions in water supply are specified to increase expected water price by a magnitude

∗ 2 휕푟푗 of its variance 휎휀 . 2 < 0, meaning that as the uncertainty in water supply increases, 휕휎휀

37 producers cut the volume of water applied per-acre. This makes intuitive sense. As water becomes more expensive due to reductions in supply, producers have lower demand.

∗ 휕푧푗 Nonetheless, non-water input use remains unaffected ( 2 = 0). 휕휎휀 The influence on irrigation decision also depends on the adoption rate relative to

̅̅̅휀 ∗ 2 a threshold level 푎푗 . The derivative of 푎푗 with respect to 휎휀 takes the form of

훽푗 훽 +1 훾 1 2 2 ∗ ∗ 2 ∗ ∗ 푗 ∗ 푗 2휎 휎 ∗ 휕푎푗 푎푗[휆 훽푗−2훽푗(푟푗 훿) 푎푗 푃푗푧푗 (1−훽푗−훾푗)훼푒 (푒 −1)(푡+휏)] 휕푟푗 (A2-3) = 1 ∙ . 2 훾 휎2 2 훽푗 훽 +1 2 휕휎휀 ∗ ∗ 푗 2 휎 ∗ ∗ 푗 2 휕휎휀 푟푗 [푃푗푧푗 (1−훽푗−훾푗)훼푒 (푒 −1)(푡+휏)(푟푗 훿) 푎푗 (1+2훽푗)−휆 훽푗]

휕푎∗ 휕푎∗ ∗ ̅̅̅휀 푗 푗 If 푎푗 < 푎푗 , 2 > 0; otherwise, 2 < 0. When the technology adoption rate is low, 휕휎휀 휕휎휀 producers would improve water use efficiency by enhancing the use of the water-saving irrigation technology in response to higher water price. Whereas for producers with high adoption rate, their water use efficiency is already high. They are more likely to reduce the use of the technology given water supply uncertainty.

This impact is contrary to the impact of climate risks. In the case of climate risks, water application rate doesn’t change with climate risks. The overall effect of climate change on efficient water use, i.e. decreasing below threshold and increasing above threshold, comes from the effect on adoption rate. Nevertheless, water scarcity not only decreases water application rate, but also changes adoption rate (increasing below threshold and decreasing above threshold). The overall effect of water scarcity on efficient water use depends on which effect dominates.

Water scarcity affects land allocation in a similar way. The threshold level is

(1−훽 −훾 )(푡+휏) ̅휀 푗 푗 ̅̅̅휀 ̅휀 ∗ ̅휀 ̅휀 correspondingly defined as 퐿푗 = 푎푗 , or 휆 = 휆 . When 퐿푗 < 퐿푗 (휆 > 휆 ), 휆훽푗 38 the net benefit of an extra unit of land is high. Hence, producers have an incentive to

∗ ̅휀 expand the production of crop 푗, even with intensified water scarcity. When 퐿푗 > 퐿푗

(휆 < 휆̅휀), the scale of production is sufficiently large. An extra unit of land cannot bring high marginal benefit. Under this circumstance, if producers expect an increase in water price, they would respond by reducing planted acreage, in accordance with decreased water application rate and decreased technology adoption rate.

A3. Conclusion

Climate change and water scarcity are anticipated to affect irrigated agriculture production on the West Coast. In response, producers can adapt by altering land allocations, adjust water application rates and adopt risk-reducing irrigation technologies.

This analysis constructs a theoretical framework to explore multioutput farmers’ adaption strategies and policy responses under uncertainties. Selected comparative statics provide several interesting preliminary findings.

First, crop-specific water application rates are negatively associated with water scarcity. Intensified water scarcity increases expected water price. Consistent with law of demand, producers would cut the volume of water applied in response to predicted price increase.

Second, a comparison between risk-averse and risk-neutral producers’ behavior suggests that the water-saving irrigation technology is a risk-decreasing input. It can

39 improve the relative efficiency of water use and mitigate damage from production risks.

In addition, as producers’ risk-aversion level goes up, the adoption rates become higher.

Climate change and water scarcity have opposite impact on adoption rates. For producers with low adoption rates, more climate risks or reduced water scarcity discourage technology adoption. While producers with high water use efficiency respond reversely.

Lastly, the impact of climate change and water scarcity on land allocations corresponds to the impact on irrigation decisions. Higher technology adoption rate is associated with more planted acreage for a specific crop. Comparably, when the net marginal benefit of land is low, anticipation of more climate risks or less water scarcity incentivizes producers to expand production. In contrast, when the scale of production is relatively small, producers would enlarge planted acreage given reduced climate risks or more uncertainties in water availability.

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