Rebound Effects of New Irrigation Technologies: The Role of Water Rights
November 2016
Haoyang Li
Department of Economics; Environmental Science and Policy Program
Michigan State University
[email protected]
Jinhua Zhao ∗
Department of Economics; Dept. of Ag, Food and Res. Econ
Environmental Science and Policy Program
Michigan State University
[email protected]
∗
We thank Bruno Basso, Erin Haacker, Joe Herriges, Dave Hyndman, Anthony Kendall, and Jeff
Wooldridge for many helpful discussions, and Dustin Fross for assistance in obtaining and cleaning the
WIMAS data. We also thank Lisa Pfeiffer and Cynthia Lin for pointing us to the WIMAS database. Part
of the research is supported by NSF WSC #1039180 and USDA NIFA 2015:68007-23133.
Abstract
We study the role of imperfectly enforced water rights in restricting water use and limiting the rebound
effects of Low Energy Precise Application (LEPA) irrigation technology, as well as farmer incentives to
preserve their water rights. Using data from the Ogallala-High Plains Aquifer region of Kansas, we find
that restricting water rights can reduce water extraction even when ex post the water rights are not
binding, and these effects are more pronounced after the adoption of LEPA, thereby reducing the
technology’s rebound effects of raising water extraction. The rebound effects arise from LEPA adopters
switching to more water intensive crops as well as irrigating more intensively. Larger water right holders
extract more water because they irrigate larger fields and also because they irrigate more intensively.
Farmers have incentive to preserve their water rights in response to the use-it-or-lose-it clause of the
water right system, but the associated water waste is insignificant.
JEL: Q15, Q25
Keywords: rebound effect, LEPA irrigation, water rights, Ogallala-High Plains Aquifer
1
1. Introduction
Irrigation is a major factor influencing modern agriculture’s capacity to adapt to global climate change.
Facing higher average temperature, greater variability in rainfall and increased likelihood and severity of
droughts, production agriculture will be more dependent on irrigation to meet the increasing global food
demand (Zilberman, Zhao and Heiman, 2012). Over 60% of the world’s consumption of water is used for
irrigation, making agriculture the largest consumer of water (Wada and Bierkens 2014, FAO 2016).
However, irrigation as an adaptation strategy is limited by the worldwide depletion of surface and
groundwater resources. The recent California drought has resulted in increased irrigation using
groundwater, leading to substantial depletion of groundwater resources in the Central Valley (Famiglietti
et al. 2011). In the High Plains region, irrigation water use since 1930s has depleted over half of the
aquifer capacity in the southern part of the Ogallala-High Plains aquifer (henceforth HPA) that overlies
Texas and New Mexico (McGuire 2009; Haacker, Kendall, and Hyndman 2015). Consequently, new
irrigation technologies such as Low Energy Precise Application (LEPA) irrigation and drip irrigation
have been called upon to improve irrigation efficiency, thereby reducing water needs while maintaining
or raising agricultural outputs (Schoengold and Zilberman 2007; Zilberman, Zhao and Heiman 2012).
However, more efficient irrigation technologies do not always reduce water use. Ward and
Pulido-Velazquez (2008) finds that adoption of water conservation technologies may raise total water use
due to the conversion of more land into production agriculture. Pfeiffer and Lin (2014a) find statistically
significant rebound effects of LEPA in HPA: water use increased after farmers switched from central
pivot to LEPA, and the increase occurred both at the intensive margin (i.e., water use per acre of irrigated
field) and at the extensive margin (i.e., size of field irrigated). Such rebound effects limit the potential of
new technologies in promoting agricultural adaptation and sustainability.
Economists have long recognized the limitations of purely technological responses to external
changes, and argued that resilient and effective institutions can be effective adaptation strategies
(Zilberman, Zhao and Heiman 2012). Examples of such institutions include property rights over both
surface water and groundwater, water markets and trading, and water use organizations that help regulate
water use. At least theoretically, effective institutions can not only promote the adoption and diffusion of
efficient technologies but also limit or even eliminate undesirable rebound effects of these technologies.
In this paper, we study the interacting impacts of institutions and new technologies by
investigating the role of water rights in reducing water use, promoting the adoption of LEPA, and limiting
the rebound effects of LEPA in the HPA region of the state of Kansas. Using a panel data set that includes
well level water use and water rights during 1991 – 2010, we show that a large part of LEPA’s effect of
raising water use is moderated by the associated water rights, indicating that reducing water rights can
significantly limit LEPA’s rebound effects, even when the water rights are not strictly binding. Kansas
2
follows a prior appropriation water right system with a three-year use-it-or-lose-it (UIOLI) clause. We
find that farmers have an incentive to apply a small amount of water in order to preserve their water rights
even when irrigation is not profit maximizing, and this incentive is slightly higher after LEPA is adopted.
The potential water savings if UIOLI is removed, however, are rather small.
As shown in Pfeiffer and Lin (2014a), increases in water use due to LEPA can occur on the
extensive margin through acres irrigated and on the intensive margin through crop choices and irrigation
intensity decisions. Extending Pfeiffer and Lin (2014a), we compare the channels through which water
rights and LEPA affect water use. We show that a large part of LEPA’s effect on water use is mediated by
crop choices, while the majority of water rights’ effect on water use is mediated by irrigated acreages.
That is, LEPA’s rebound effect mainly operates through farmers switching to more water intensive crops
such as corn, while larger water rights lead to more water use mainly through farmers with more rights
irrigating larger areas of their fields.
There is a sizable literature on the effects of new irrigation technologies on water use in general
(Ward and Pulido-Velazquez 2008; Whittlesey and Huffaker 1995; Ellis, Lacewell and Reneau 1985;
Scheierling, Young and Cardon 2006; Khanna, Isik and Zilberman 2002; and Hanak et al 2010) and in the
HPA region of Kansas in particular (Pfeiffer and Lin 2012, 2013, 2014a, 2014b; Hendricks and Peterson
2012; Peterson and Ding 2005). Our work is closest to Pfeiffer and Lin (2014a), which finds and
decomposes the rebound effects of LEPA. Our innovations include explicitly modeling water rights and
farmer incentives to preserve water rights, identifying the moderating effects of water rights on LEPA,
and quantifying the channels through which the rebound effects arise by estimating the role of such
mediators as crop choices and irrigated acreages. Further, our data span a longer time period (1991 – 2010
in our paper vs. 1996 – 2005 in Pfeiffer and Lin (2014a)), and we test the endogeneity of LEPA using a
different instrument variable for LEPA adoption based on neighbor influences.
2. High Plains Aquifer and Water Rights in Kansas
Our study area is the HPA region of the state of Kansas, which relies heavily on irrigation water
withdrawal from HPA. Widely considered the breadbasket of the US, the High Plains Region is facing the
double threat of declining water table of the HPA and climate change. HPA is also the largest freshwater
aquifer in the world (Miller and Appel, 1997) and has variable recharge rates from the north to the south.
In most of Kansas HPA, the aquifer has a low recharge rate, and irrigation is essentially equivalent to
mining a nonrenewable resource.
Kansas has a prior appropriation water right system (Peck 1995, 2007), with each water right
specifying the maximum amount of water that can be extracted from the HPA in a given year. The
relationship between water rights and the points of diversion (i.e., irrigation wells) can be classified into
3
four types: a single well assigned with a single water right (Type 1), a single well assigned with multiple
water rights (Type 2), multiple wells sharing a single water right (Type 3), and multiple wells sharing
multiple water rights (Type 4). We focus on Type 1 wells, which account for about 80% of the wells that
reported use of certain types of irrigation technologies during our study period.
Seniority of a water right is determined by the time when the water right application was recorded.
Among the Type 1 wells in our sample, most of the application dates are in 1970s. There is effectively a
moratorium on new water right applications after 1990s (Peck 1995). Figure 1 shows the distribution of
Type 1 wells by application dates. In principle, when water availability cannot satisfy the demand, a well
with a more senior water right can block wells with junior water rights from extracting water from HPA.
So far this type of blocking has never occurred in Kansas.
FIGURE 1 HERE
Water rights in Kansas are not always strictly binding. First, water use is self-reported by farmers.
Although water pumping is metered, it is possible that farmers misreport their actual water use. Second,
farmers are allowed to go beyond the water right limits in drought years. Each year in our sample, about
10% of the wells reported water use above their water rights. However, as shown in Figure 2, this
percentage has been going down, especially after 2002.
FIGURE 2 HERE
The water right system in Kansas has a three-year use-it-or-lose-it (UIOLI) clause, implying that the
water rights of a well without water use for three consecutive years are subject to cancellation. Under the
Kansas Administrative Procedure Act (KAPA), a farmer can appeal to the Kansas Department of Water
Resources to keep the water rights if he/she can establish a “due and sufficient cause for non-use” (Peck
1995). Such cause includes sufficient rainfall, enough surface water as diversion sources, soil and water
conservation such as CRP, etc. Among the Type 1 wells in our sample period, about 10% experienced
three consecutive years of no water use, and among these wells, about 32% successfully kept their water
rights.
Although farmers can appeal against the UIOLI clause, the burden of proof for establishing the due
and sufficient cause for non-use lies with the farmer. Given the transaction costs involved, farmers might
have incentive to use a small amount of water when irrigation is not needed in order to preserve their
water rights. We will test this hypothesis and evaluate its impact on water use.
3. Model Specification
The irrigation scheduling literature recognizes that a farmer typically irrigates a field multiple times
during a single growing season, and the “optimal” intra-season scheduling depends on the stages of crop
growth, soil characteristics, and irrigation technology (Yaron and Dinar 1982; Scheierling, Cardon and
4
Young 1997; Shani et al. 2009). During early stages of the growing season, the farmer might not know for
sure how much irrigation water is needed for the reminder of the season due to weather uncertainties and
future crop/energy prices. Facing the constraint imposed by water rights, the farmer may decide to limit
the amount of water applied during the early season to leave more options open in order to meet possible
high water needs during the later season. Therefore, water rights can affect the total irrigation water use of
the entire growing season even when ex post the farmer ends up using less water than the water right cap.
There is a fixed cost of irrigation, arising from the minimum pressure required in order for the
irrigation equipment to start. LEPA reduces the required water pressure – a reduction from 75 PSI for
Center Pivot to 18 PSI for LEPA (Delano, Williams and O’Brien 1997). As a result, farmers tend to
irrigate more frequently under LEPA than under central pivot. This tendency might lead farmers to
irrigate more intensively, contributing to LEPA’s rebound effects. These effects can be limited by water
rights, especially during early periods of the growing season if the farmer expects a high level of
irrigation in later season under LEPA. These considerations and the existence of UIOLI clause lead to two
hypotheses that we will test:
Hypothesis 1: The rebound effects of LEPA on water use are partly attributable to increased
irrigation intensity, and can be ameliorated by reducing the associated water rights.
Hypothesis 2: Farmers have incentives to preserve water rights under UIOLI, and the incentives are
stronger as future irrigation profitability rises and the associated water rights are larger.
A Dynamic Joint Estimation Framework
We first develop and estimate a joint estimation model of water use and water right preservation
to test the above hypotheses simultaneously. We focus on the effects of LEPA replacing central pivot,
limiting ourselves to wells that have only used one or both technologies during our sample period. Our
basic unit of analysis is wells, with each well treated as representing a single farmer. Let 𝑦𝑦𝑖𝑖𝑖𝑖 be the
observed water extraction of well i in year t. Farmers first decide whether to use water from the well in
the current year and then decide how much water to use. Let 𝑦𝑦𝑖𝑖𝑖𝑖∗ be the latent variable representing the
profit maximizing water extraction level without considering the fixed cost of irrigation. In reduced form,
𝑦𝑦𝑖𝑖𝑖𝑖∗ depends on the field characteristics, weather conditions, management practices, irrigation technology
and water rights. Under a linear specification, we have
yit* =Ri β1 + Ri2 β 2 + AC it β3 + LEPAit β 4 + ( LEPAit * Ri ) β5 + si β 6
+ dtwit β 7 + wit β8 + Gg + ϕt + ci + ε it
5
.
(1)
In (1), 𝑅𝑅𝑖𝑖 is the time-invariant annual authorized maximum water extraction amount specified by the
water right. We include its square term 𝑅𝑅𝑖𝑖2 to capture possible nonlinear effects of water rights. 𝑨𝑨𝑨𝑨𝒊𝒊𝒊𝒊 is a
vector of acres of various crops irrigated by well i in year t. 𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝑖𝑖𝑖𝑖 is a dummy variable that equals 1 if
the irrigation technology is LEPA and 0 if the technology is central pivot. We include the interaction of
LEPA and Ri to test part of Hypothesis 1, and coefficient 𝛽𝛽5 captures the moderation effect of water right
𝑅𝑅𝑖𝑖 on LEPA’s impact on water use. 𝑠𝑠𝑖𝑖 is a time invariant vector of soil characteristics of the field
irrigated by well i. 𝑑𝑑𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖 is the well’s depth to groundwater, which affects the energy needed to extract
the groundwater for irrigation. 1 𝑤𝑤𝑖𝑖𝑖𝑖 is a vector of weather conditions, and 𝐺𝐺𝑔𝑔 and 𝜑𝜑𝑡𝑡 capture the fixed
effect of the groundwater management district well i belongs to and time fixed effect. 𝜀𝜀𝑖𝑖𝑖𝑖 is iid error term
across wells and years and 𝑐𝑐𝑖𝑖 is a well specific unobserved heterogeneity.
The dynamics of water use arises from the incentive to preserve one’s water rights, which
depends on the irrigation needs in future periods. Let 𝑧𝑧𝑖𝑖𝑖𝑖∗ be the latent variable describing the farmer’s
incentive to use water at all from well i in year t. In reduced form, 𝑧𝑧𝑖𝑖𝑖𝑖∗ is specified as:
zit* =
rci + 1( yit +1 > 0 ) α1 + xityα 2 + ηit
(2)
Two sets of factors affect this incentive: the need to irrigate in the current period, and the need to preserve
𝑦𝑦
the water right due to the UIOLI clause. In (2), 𝑥𝑥𝑖𝑖𝑖𝑖 includes all variables used in the extraction equation
(1) except for crop acres and 𝑐𝑐𝑖𝑖 , and captures the current period need to irrigate. The response to the
UIOLI clause is captured by the need to irrigate next year 𝑦𝑦𝑖𝑖𝑖𝑖+1: if the farmer expects that he will use
water next year, his incentive to use water now would be higher because doing so helps preserve his water
rights. Following Wooldridge (2000) and Biewen (2009), the coefficient 𝑟𝑟 on 𝑐𝑐𝑖𝑖 in (2) allows the
unobserved heterogeneity to affect 𝑦𝑦𝑖𝑖𝑖𝑖∗ and 𝑧𝑧𝑖𝑖𝑖𝑖∗ differently.
Let 𝑆𝑆̅ be a water extraction threshold such that, because of the fixed cost of irrigation, it is
∗
∗
profitable to irrigate if and only if yit > S . Otherwise, if the water need yit is lower than S , the
additional profit from irrigation cannot compensate for the fixed cost, and the farmer should not irrigate
for the purpose of maximizing the current period profit. The observed water extraction then satisfies
1
The depth to water measures the distance from soil surface to the top of the underground aquifer. It is related to a
well’s saturated thickness, which measures the depth or thickness of water in the aquifer, i.e., the distance between
the top and bottom of the aquifer. Saturated thickness affects the pump’s water flow – more water is pumped per
unit of time when there is more water underground, i.e., when the saturated thickness is larger. The sum of depth to
water and saturated thickness equals the distance from the surface of ground to the bottom of the aquifer, and
remains unchanged through time. Since water right Ri is also time invariant, only one of the depth to water and
saturated thickness can be included in (1) to avoid perfect collinearity.
6
= 𝑦𝑦𝑖𝑖𝑖𝑖∗ ,
𝑦𝑦𝑖𝑖𝑖𝑖 �∈ (0, 𝑆𝑆̅],
= 0,
if
𝑦𝑦𝑖𝑖𝑖𝑖∗ > 𝑆𝑆̅, 𝑧𝑧𝑖𝑖𝑖𝑖∗ > 0
𝑦𝑦𝑖𝑖𝑖𝑖∗ ≤ 𝑆𝑆̅, 𝑧𝑧𝑖𝑖𝑖𝑖∗ > 0
𝑧𝑧𝑖𝑖𝑖𝑖∗ ≤ 0
(𝒄𝒄𝒄𝒄)
(𝒄𝒄𝒄𝒄)
(𝒄𝒄𝒄𝒄)
(3)
If 𝑧𝑧𝑖𝑖𝑖𝑖∗ ≤ 0, the farmer does not have any incentive to use water from well i and yit = 0 (case (c3)). If 𝑧𝑧𝑖𝑖𝑖𝑖∗ >
∗
0, the farmer has incentive to use water either because it is profitable to irrigate so that yit = yit (case
(c1)), or because he wishes to preserve his water rights (case (c2)). The former scenario occurs when the
∗
∗
optimal water use yit exceeds S , while the latter occurs when yit ≤ S . In case (c2), the farmer would
apply a small amount of water in order to preserve the water rights, and the observed water use 𝑦𝑦𝑖𝑖𝑖𝑖 ∈
(0, 𝑆𝑆̅]. In our estimation, we set 𝑆𝑆̅ to be 5 AF, in contrast to the mean extraction of 144 AF. We also
conduct a series of robustness checks by varying S to show that our estimates are not sensitive to the
specific levels of S .
The remaining issue is to model individual heterogeneity 𝑐𝑐𝑖𝑖 . Since the water rights as well as soil
characteristics are time invariant for a specific well, we use a random effects rather than fixed effects
specification at the well level in order to identify the coefficients of the time-invariant variables. We
adopt the correlated random effect (CRE) framework of the Chamberlain-Mundlak Device suggested by
Wooldridge (2010) that makes the following distributional assumption for 𝑐𝑐𝑖𝑖 :
ci =
γ 0 + AC i γ1 + LEPAiγ 2 + LEPAi * Riγ 3 + dtwit γ 4 + wiγ 5 + yT γ 6 + ai = ci + ai
where 𝑎𝑎𝑖𝑖 ~
𝑁𝑁(0, 𝜎𝜎𝑎𝑎2 )
(4)
and is independent of the explanatory variables. The bars over variables indicate
time averages of time-varying variables across all sample periods for a well. By including these averages,
we allow correlation between 𝑐𝑐𝑖𝑖 and the time-varying variables in (1) and (2), which is analogous to that
of a fixed effect specification. Because the joint estimation model is dynamic, the “end condition” 𝑦𝑦𝑇𝑇 is
included to capture the potential correlation between 𝑦𝑦𝑇𝑇 and 𝑐𝑐𝑖𝑖 . This “end condition” is analogous to the
“initial condition” used in the dynamic panel estimation approach proposed by Wooldridge (2010). The
only difference is that the dynamics in our model “goes backward” (i.e. 𝑦𝑦𝑖𝑖𝑖𝑖+1 influences 𝑦𝑦𝑖𝑖𝑖𝑖 but not the
other way around) so that an “end condition” rather than an “initial condition” is included. The maximum
likelihood estimation of the CRE specification in a dynamic setting gives consistent estimates of the
model parameters, as shown in Wooldridge (2010).
Equations (1) - (4) describe a forward-looking dynamic system in which decisions are
characterized by double hurdles (at values of yit at 0 and S ) with two latent variables. The likelihood
function is derived in Appendix A1. Our model structure goes beyond the commonly used dynamic panel
model in Wooldridge (2010), which are either linear or Probit/Tobit models. Most double hurdle models
7
are applied to the analysis of cross-sectional data (e.g. Yen, 1993; Newman, Henchion and Matthews,
2003), and the few applications of double hurdle models to panel data, such as Dong and Kaiser (2008),
Dong, Chung and Kaiser (2001), and Ricker-Gibert, Jayne and Chirwa (2011), have much simpler
dynamic structures. For example, Dong and Kaiser (2008) assumes that each agent only makes
participation decision once over the study period, though purchasing quantity decisions are made every
year. In Dong, Chung and Kaiser (2001), the dynamic structure is represented by autocorrelations in one
of the error terms, whereas in our model the influence of 𝑦𝑦𝑖𝑖𝑖𝑖+1 on 𝑦𝑦𝑖𝑖𝑖𝑖 is introduced explicitly. There are
no dynamic decisions in Ricker-Gibert, Jayne and Chirwa (2011).
Separate Estimation of (1) and (2)
The dynamic joint estimation of (1) and (2) is consistent and efficient, but suffers from two
limitations. First, we need to establish causality of LEPA on water use but the econometric literature has
not developed an effective methodology to test and correct for the endogeneity of explanatory variables in
such a nonlinear dynamic model with unobserved heterogeneities. Second, it is difficult to calculate the
∗
∗
marginal effects of key variables. Since zit is a function of yit +1 and the value of yit depends on zit ,
𝐸𝐸(𝑦𝑦𝑖𝑖𝑖𝑖 |𝑐𝑐𝑖𝑖 ) is a complex function of 𝑦𝑦𝑖𝑖𝑖𝑖+1 . Specifically, when we take the derivative of 𝐸𝐸(𝑦𝑦𝑖𝑖𝑖𝑖 |𝑐𝑐𝑖𝑖 ) with
respect to a particular 𝑥𝑥𝑖𝑖𝑖𝑖 , we also need to calculate the derivative of 𝑧𝑧𝑖𝑖𝑖𝑖∗ with respect to 𝑦𝑦𝑖𝑖𝑖𝑖+1 in (2).
∗
∗
and 𝑧𝑧𝑖𝑖𝑖𝑖+1
. The marginal effects involve evaluating a
However, 𝑦𝑦𝑖𝑖𝑖𝑖+1 again depends nonlinearly on 𝑦𝑦𝑖𝑖𝑖𝑖+1
nonlinear chain of derivatives. The computation burden is further increased since we have to integrate 𝑐𝑐𝑖𝑖
out of the marginal effects. Finally, since the marginal effects are highly nonlinear, we will have to rely
on bootstrap methods instead of the delta method to calculate the standard errors of the marginal effects.
Bootstrapping is essentially impossible given the computation burdens involved.
To address these limitations, we also estimate the two decisions in (1) and (2) separately, and use
the separate models to test the endogeneity of LEPA adoption and to evaluate the marginal effects of key
variables. In (2), yit +1 is treated as an exogenous variable. Since separate estimations are biased and less
efficient, we compare estimates of the joint dynamic model with those of separate estimation to assess the
magnitude of the bias and the efficiency loss. We find that the two sets of estimates are extremely close.
We use the correlated random effect (CRE) Tobit method to estimate (1), with (4) replaced by
�������𝑖𝑖 𝜃𝜃2 + �������
𝑨𝑨𝑨𝑨𝒊𝒊 𝜽𝜽𝟏𝟏 + 𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿
𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝑖𝑖 ∗ 𝑅𝑅𝑖𝑖 𝜃𝜃3 + �����
𝑑𝑑𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖 𝜃𝜃4 + 𝑤𝑤
� 𝑖𝑖 𝜃𝜃5 + 𝑎𝑎𝑖𝑖𝑢𝑢 = ����
𝑐𝑐𝚤𝚤𝚤𝚤 + 𝑎𝑎𝑖𝑖𝑢𝑢
𝑐𝑐𝑖𝑖 = 𝜃𝜃0 + ����
which excludes 𝑦𝑦𝑇𝑇 because (1) by itself is a static model, so that the ending period condition is not
needed. In estimating (2), we use di to represent the unobserved heterogeneity:
8
zit* =
di + 1( yit +1 > 0 ) α1 + xityα 2 + ηit
�������𝑖𝑖 𝜑𝜑1 + �������
with 𝑑𝑑𝑖𝑖 = 𝜑𝜑0 + 𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿
𝐿𝐿𝐿𝐿𝐿𝐿𝐴𝐴𝑖𝑖 ∗ 𝑅𝑅𝑖𝑖 𝜑𝜑2 + �����
𝑑𝑑𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖 𝜑𝜑3 + 𝑤𝑤
� 𝑖𝑖 𝜑𝜑4 + 𝑧𝑧𝑇𝑇 𝜑𝜑5 +
(5)
𝑎𝑎𝑖𝑖𝑧𝑧
1 if zit* > 0 or equivalently 𝑦𝑦𝑖𝑖𝑖𝑖 > 0, and 𝑧𝑧𝑖𝑖𝑖𝑖 = 0 otherwise, (5) is equivalent to
= ����
𝑑𝑑𝚤𝚤𝚤𝚤 +
𝑎𝑎𝑖𝑖𝑧𝑧 .
Defining 𝑧𝑧𝑖𝑖𝑖𝑖 =
zit* =
di + zit +1α1 + xityα 2 + ηit
(6)
which will be estimated by standard correlated random effect dynamic Probit methods.
Mediation Effect – Intensive and Extensive Margins
Pfeiffer and Cynthia (2014a) showed that LEPA adoption can raise water extraction through both
the intensive and extensive margins. To more formally study the channels through which LEPA and water
rights affect water use, we adopt the three step procedure of a mediation effect model with two mediators,
crop choices and irrigated acreage. Specifically, in step 1, we regress water use on LEPA and water rights
without the mediators, i.e., we estimate the model in (1) without the crop acreages. In step 2, we regress
the mediators on LEPA and water rights, and in step 3, we estimate the model in (1), which includes the
mediators.
Since the estimation model in (1) is nonlinear, we cannot rely on the Sobel test to estimate the
magnitude of the mediation effects as in, for example, Hendrics and Peterson (2012), which conducts a
Sobel test to evaluate the effects of water price on water demand. Instead, we adopt the general rule that
mediation effects are present if LEPA and water rights are significant in Step 1, but their magnitudes
and/or significance levels are reduced in Step 3, and they are significant in Step 2. The logic is that the
independent variables (LEPA and Water Rights) affect the mediators (crop choices and irrigated acreage),
which in turn affect the dependent variable (water use). We compare the changes in the marginal effects
on water extraction of LEPA and water rights, with and without the mediators (i.e., in steps 1 and 3). The
reduction in their marginal effects when the mediating variables are included show how much of their
effects manifest through the mediators.
Endogeneity Test of LEPA Irrigation
The adoption of LEPA might be endogenous in water use equation (1) – it is possible that
unobserved factors raise water use as well as promote LEPA adoption 2. Pfeiffer and Lin (2014a) use
county level subsidies for LEPA adoption as instruments and show that correcting for endogeneity of
LEPA makes a small but statistically significant difference. In this paper, we use a different instrument:
2 One
may argue that the depth to water (DTW) is also endogenous as DTW is greater in areas that have extracted
more water in the past. However, regression analysis shows that an individual well’s water extraction has little effect
on annual DTW changes – the larger influence comes from the aggregate water extraction of all neighbor wells.
Thus we treat DTW as exogenous, similar to Pfeiffer & Lin (2014a).
9
the adoption of LEPA by one’s neighbors in the previous year. The large literature on herd behavior and
information cascades has demonstrated the existence of neighbor influences in technology adoption
decisions, including adoption of agriculture production technologies (Zhao 2007). The influence is mainly
through learning about the performance of the new technology, but can also arise due to network
externalities, e.g., when marketing services are established after a large number of farmers have adopted
the technology.
The instrument variable we adopt is the number of wells that used LEPA in the previous year
among a particular well’s 11th closest to its 30th closest neighbor wells (i.e., 20 wells in total). We exclude
the ten closest neighboring wells to rule out the wells owned by the same farmer; a farmer owns four to
six wells on average in our sample. The adoption of LEPA by one’s neighbors in the previous year is not
likely to influence the well’s own water use due to the time lag and the fact that we are controlling for a
rich set of weather and soil characteristics.3
A major difficulty in conducting the endogeneity test is that both the first and second stages of the
test are nonlinear (Probit for the first stage and Tobit for the second stage). Although the control function
approach can be used for nonlinear models in the main estimation, nonlinearity of both equations poses
particular challenges. We follow Papke and Wooldridge (2008) and use the generalized residual of the
first stage Probit regression in the second stage Tobit regression. 4
4. Data
The data used for our estimation are drawn from multiple sources. Information about points of diversions
(i.e. wells) is from the Water Information Management and Analysis System (WIMAS) maintained by the
Kansas Water Office. As indicated earlier, there are four types of wells depending on how they are related
to their water rights. We focus on Type 1 wells for two reasons: (i) the relationship between each well and
its water rights is straightforward, and (ii) little information will be lost due to the high proportion of Type
1 wells in our sample. After deleting wells that have no irrigation technologies reported during the study
period (1991-2010), we are left with 16,187 wells in total, among which 12,503 wells are of Type 1
3
One possible concern about the exogeneity of our IV is that neighbor wells might have similar soil and weather
conditions, so that their water uses and thus incentives to adopt LEPA are correlated with the water extraction of
well i. However, we already control for a rich set of soil and weather characteristics in the regression. To address
possible correlation of unobserved characteristics across farmers that might affect water use and LEPA adoption, we
perform robustness check in Appendix A2 by varying the distances of neighbors included in the IV strategy. The
results fail to reject the null hypothesis that LEPA is exogenous and are not sensitive to the selection of neighbors.
4
The generalized residual formula of the Probit regression of dependent variable y on independent variable x is
given by
𝜙𝜙(𝑥𝑥𝑥𝑥)
Φ(𝑥𝑥𝑥𝑥)[1−Φ(𝑥𝑥𝑥𝑥)]
[𝑦𝑦 − Φ(𝑥𝑥𝑥𝑥)].We employ pooled Probit and pooled Tobit models with time averages of time-
varying variables included to perform the endogeneity test as suggested by Papke and Wooldridge (2008). We do
not use the random effect panel models because generalized residuals are defined for cross-sectional analysis only.
10
defined above, accounting for 77% of all wells.
Similar to Pfeiffer and Lin (2014a), we remove outlier wells by excluding those that use more
than 500 AF of water in any year and those with the maximum irrigated acres in the study period greater
than 640 or lower than 60 acres. The remaining sample contains 10,891 wells. We delete a small number
of wells for which the reported water extraction is positive but no planted crops are reported. To form a
balanced panel, we also delete wells that have records of flood irrigation during the study period, 5 those
that are abandoned before the end of the study period (year 2010) and those that are outside of the HPA
area, leaving 4,321 wells in our final sample. Since most applications for water rights occurred in 1970s
and all water rights in our sample have application dates that are at least five years earlier than the
beginning of our sample period (cf. Figure 1), we take the water rights as exogenous in our estimations.
Spatially explicit soil characteristics are obtained from SSURGO soil survey on the website of USDA
Natural Resources Conservation Service. These characteristics include detailed soil information about
slope, Available Water Capcity, Irrigated Capacity Class and Saturated Hydraulic Conductivity. Data on
Depth To Water are obtained from the output files of Haacker, Kendall & Hyndman (2015). Weather data
are obtained from North America Land Data Assimilation System (NLDAS) maintained by NASA that
reports geo-referenced information about annual precipitation and potential evapotranspiration.
Finally, the well and water right data obtained from WIMAS are matched to soil and weather data
using the spatial join function in ArcGIS. Table 1 presents the summary statistics of the variables used in
our estimation.
TABLE 1 HERE
5. Estimation Results
Table 2 presents the dynamic joint estimation and separate estimation results for water extraction ( yit )
and incentive to use water ( zit ). The estimated coefficients and the significance levels of most variables
are similar across the two estimation approaches, and this is particularly true for the main variables of
interest, namely LEPA, Water Right, and their interaction term. The only noticeable difference between
the two approaches lies in the coefficients of the crop acreages in the water use equations: those of the
separate estimation roughly equal those of the joint dynamic estimation plus 0.30 for all crops. One
possible reason is that the total acreage of planted crops is almost perfectly correlated with the incentive
to use water, and in joint estimation the indicator variable of using water 1( yit +1 > 0) partly captures the
5
Wells using only Center Pivot and/or LEPA irrigation account for more than 80% of the full sample during the
study period.
11
crop acreage effect. Overall, the bias about the main effects of LEPA and Water Right from separately
estimating the two equations instead of estimating them jointly is limited. We will rely on the separate
estimation results in subsequent discussions and analyses.
TABLE 2 HERE
Water Extraction Decisions
The Tobit estimation results of the water extraction equation (1) are reported in the second
column of Table 2. The estimated coefficients of most variables have expected signs. Water extraction
goes up as the irrigated crop acreages rise, and this effect is the most significant for water intensive crops
including corn, soybean and alfalfa. Water use also rises in potential evapotranspiration (a higher value of
which represents a higher demand for water by crops), in saturated hydraulic conductivity (which
measures how easy water flows through soil and thus the water flow out of pumps), and in slope of the
land (since more sloped land requires more water to irrigate due to more runoff). On the other hand, water
extraction decreases in precipitation, in depth to water (since more depth means more energy expenditure
needed to extract water to the land surface), and in available water capacity (a higher value of which
indicates more water is stored in a crop’s root zone for crop needs).
Consistent with Pfeiffer and Lin (2014a), we find a statistically significant rebound effect of
LEPA: compared with central pivot, LEPA raises the annual water extraction per well by 3.32 AF, and
this “marginal” effect is statistically significant.6 Although this amount is equivalent to only 2.25%
increase in annual water extraction per well, the rebound effect is still economically significant given the
fact that LEPA has a higher irrigation efficiency and is expected to reduce rather than to raise water use.
Further, the annual net effect of LEPA adoption on groundwater level is likely to be higher than 3.32 AF
per well because the return percolation of extracted water back to the aquifer is lower under LEPA than
under central pivot, due to LEPA’s higher precision of water application.
More importantly, our results indicate that LEPA’s rebound effect can be reduced by restricting
water rights: the interaction term of LEPA with water right is positive and significant, thereby confirming
part of Hypothesis 1. This observation highlights an important approach to ameliorating the rebound
effects of LEPA, namely by reducing the water rights allocated to the existing wells. For example, a 10%
reduction of water rights across all wells will reduce the rebound effect of LEPA by 13.5%. 7 This result is
6
Our estimated marginal effect of LEPA (3.32 AF) is similar to that obtained in Pfeiffer and Lin (2014a). Under a
range of model specifications, their estimated marginal effect ranges from 3.60 to 5.07, with 3.60 being from their
most preferred specification.
7
The 10% reduction of water rights equals 23.58 AF per well on average. Such a reduction decreases LEPA’s
rebound effect by 0.019*23.58=0.448 AF, or by 0.448/3.32=13.5%.
12
striking given that water rights are not always binding and are not always strictly enforced. As discussed
earlier, one possible reason is that farmers, facing water right constraints and crop price and weather
uncertainties, restrict water use during early growing season in order to leave more options open to
increase water use during later season. As water right decreases, water use in early season goes down,
leading to lower water use even if ex post the water right is not binding. Such incentives are also reflected
by the nonlinearity of the effects of water rights on water use. The coefficient on the square term of water
right is negative, indicating that tightening water rights has larger impacts on wells with lower water
rights. These wells have less flexibility in allocating water use within the growing season to start with,
and further reduction in their water rights will push down water use in early season even more, since
doing so helps preserve water use flexibility in later parts of the season.
To investigate the channels through which LEPA and water rights affect water extraction, we
conduct the three step regressions used in formal mediation tests with two possible mediators, acres
irrigated and crop choices (Tables 3 – 5). Tables 3 and 4 show that the two independent variables, LEPA
and water rights, do affect the two mediators. In Table 3, the coefficient of Water Right is positive and
statistically significant, and the marginal effects of Water Right and LEPA on acres irrigated are
significant. Other variables also have expected signs. In Table 4, LEPA raises the acreage of corn and
soybean, two water intensive crops, while higher Water Rights raise the acreage of corn and corn-soybean
rotation.
TABLES 3 – 5 HERE
In Table 5, the first column reports the regression results when both mediators are excluded from
the regression; the second column contains results when one of the mediator, acres irrigated per well, is
added as an explanatory variable; and the third column repeats the separate estimation results in column
two of Table 2, which contain all the mediators. 8 The bottom rows of Table 5 present the marginal effects
of Water Right and LEPA. When Acres Irrigated is added to the explanatory variables (comparing
between the first and second columns), the marginal effect of Water Right on water extraction decreases
by 50%, while that of LEPA only decreases slightly. However, when crop choices are added (comparing
between the second and third columns), the marginal effect of Water Right decreases slightly, but that of
LEPA goes down by 23%. These results indicate that roughly half of the effect of Water Right on water
extraction operates through irrigated acreage, while about a quarter of the effects of LEPA operates
through crop choices. That is, a well with higher water rights tends to irrigate more land, while a well
with LEPA tends to irrigate more water intensive crops, and these channels are major contributors to the
8
Instead of adding the irrigated acreage and the crop choices (excluding a default crop) as separate variables, the
third column simply contains the irrigated acreage of all crops. The results of the two approaches are equivalent.
13
increased water use when the water rights are higher and after LEPA is adopted. The results also confirms
part of Hypothesis 1: even after expanded irrigation acreage and more water intensive crop choices are
accounted for, about 75% of LEPA’s rebound effect is attributable to farmers simply irrigating more
intensively under LEPA than under central pivot. One possible reason is that LEPA requires lower water
pressures to operate and thus lower energy expenditure to pump water out of the aquifer, thereby reducing
the cost of irrigation.
As discussed earlier, one might argue that the adoption of LEPA is potentially endogenous since
farmers with larger water demands will more likely adopt the more efficient irrigation technology. In
Appendix A2, we use a control function approach to show that we fail to reject the null hypothesis that
the adoption of LEPA is exogenous. Our finding is largely consistent with Pfeiffer and Lin (2014a),
which controlled for the potential endogeneity of LEPA adoption using 2SLS; the coefficients of LEPA in
their fixed effect models with and without the instrument variable are close to each other.
The first stage regression in the endogeneity test is a pooled Probit model of LEPA adoption. As
shown in the second column of Table A1, the coefficient of Water Right is negative and significant,
indicating that farmers with smaller water rights are more likely to adopt LEPA. This is intuitive since
these farmers face stricter constraints in water availability and thus are more likely to adopt LEPA which
raises the water use efficiency. This explanation is also supported by comparing the ratio of water
extraction to water rights under LEPA and central pivot for different water right levels, as shown in Table
6. Wells with annual water rights less than 100 AF tend to use water exceeding their water rights with an
average water use/water right ratio of 1.09, while the ratio decreases as the water rights rise. Further, for
these “small water right” wells, the ratio decreases from 1.12 for those using central pivot to 1.07 for
those using LEPA, while the ratio does not change much across irrigation technologies for the “large
water right” wells. These results are also consistent with the earlier findings that reducing water rights
decreases water use.
TABLE 6 HERE
Decisions to Preserve Water Rights
The fourth column of Table 2 reports the panel Probit regression results of the decision to use
water (equation (2)). Confirming part of Hypothesis 2 that farmers’ decisions are influenced by
expectations about future water use, the coefficient of the indicator variable of water use in the next
period ( yit +1 > 0 ) is positive and significant. That is, farmers have more incentive to preserve their water
rights in the current period if they expect that they will again irrigate the next year.
14
LEPA has a positive and significant influence on the incentive to preserve water rights, although
the effect is not large. Specifically, the marginal effect of LEPA on the water use probability is 0.007,
implying that on average a farmer is 0.7% more likely to preserve his water rights if LEPA has been
adopted than if central pivot is still used. The intuition is that LEPA is more profitable than central pivot
and adoption of LEPA involves sunk costs. The coefficient of water rights is not significant, possibly
because we have controlled for a large number of covariates in the estimation and because farmers view
water rights as providing irrigation services instead of having values over and above the irrigation
services. In other words, once the irrigation demand is controlled for, the size of the water rights itself
does not contribute a large enough value to the farmer’s payoffs and thus do not significantly affect their
incentives to preserve the water rights.
Robustness Checks
In estimating the water extraction decisions in (1) and (3), we introduced the water extraction
threshold S to interpret whether observed water use is for irrigation in the current period or for
preserving water rights. We set S = 5 AF in our estimation, but this threshold could be at other values.
We re-estimate (1) and (3) using different values of S (at 5, 10, and 20 AF). The results, reported in
Table 7, show that the estimated coefficients and the marginal effects of key variables remain largely
unchanged, establishing that our estimates are robust to different values of S .
TABLE 7 HERE
Since water right applications occurred much earlier than our study period (cf. Figure 1), water
rights are treated as being exogenous in our regression analysis. One might argue that farmers with higher
water demands applied for larger water rights, and serial correlation in water demands could cause water
rights to be endogenous. However, we control for a wide range of factors affecting water demand,
including soil and weather characteristics, crops and depth to water, as well as time fixed effects.
Nevertheless, to test whether any unobserved variables are correlated with water rights, we conduct a
robustness check in which only wells with water right application dates prior to 1980 are included. The
estimation results, reported in the last column of Table 7, are similar to those based on the entire sample.
6. Policy Simulations of Changing Water Governing Institutions
While it is important to recognize the existence of the rebound effects of more efficient technologies such
as LEPA, it is perhaps even more important to investigate what can be done in response to such rebound
effects. The previous discussions highlight the importance of water governing institutions: reducing (even
imperfectly enforced) water rights can help limit the rebound effects. Further, farmers do respond to the
15
use-it-or-lose-it clause by using water in order to preserve their water rights. If water is used only to
preserve the water rights instead of for profitable irrigation, removing the UIOLI clause might help save
water. In this section, we conduct a series of counterfactual simulations to evaluate how water use will be
affected as the water rights are reduced and as the UIOLI clause is removed.
Figure 3 shows the percentage reductions in expected water extraction and the associated 95%
confidence intervals as the water rights for all wells are reduced by 5%, 10% and 15% respectively. The
top panel illustrates the results for year 2010, the last year in our sample, while the bottom panel is for the
entire sample period of 1991-2010. Each panel includes the results for wells using central pivot, for those
using LEPA, and for both technologies pooled together. Roughly speaking, a 10% reduction in water
rights leads to about 5-6% reduction in water extraction, and this relationship is about linear within the
range of our policy simulations. The reduction in water extraction is more pronounced for wells using
LEPA than those using central pivot, consistent with the earlier finding that reducing water rights helps
limit the rebound effects of LEPA.
FIGURE 3 HERE
Water is wasted when it is not profitable to irrigate but water is nevertheless extracted in order to
preserve the water rights, i.e., when 𝑦𝑦𝑖𝑖𝑖𝑖∗ < 𝑆𝑆̅ and 𝑧𝑧𝑖𝑖𝑖𝑖∗ > 0. The actual waste equals a small amount not
higher than 𝑆𝑆̅. If we assume that the waste is at the upper bound of 𝑆𝑆̅, then the expected water waste per
well equals
Prob( yit∗ < S , zit∗ > 0) × S
(7)
Since the error terms of 𝑦𝑦𝑖𝑖𝑖𝑖∗ and 𝑧𝑧𝑖𝑖𝑖𝑖∗ (i.e. 𝜀𝜀𝑖𝑖𝑖𝑖 + 𝑎𝑎𝑖𝑖𝑢𝑢 and 𝜂𝜂𝑖𝑖𝑖𝑖 + 𝑎𝑎𝑖𝑖𝑧𝑧 ) specified in equations (1) and (3) are both
normally distributed, the join probability in (7) could be calculated as long as we know the correlation
coefficient of 𝜀𝜀𝑖𝑖𝑖𝑖 + 𝑎𝑎𝑖𝑖𝑢𝑢 and 𝜂𝜂𝑖𝑖𝑖𝑖 + 𝑎𝑎𝑖𝑖𝑢𝑢 . 9 We calculate the expected waste in (7) and bootstrap its standard
errors using -1, 0.5, 0, 0.5 and 1 as the correlation coefficients. Figure 4 shows the annual expected water
waste per well for these correlation coefficients. The top panel shows the wastes for year 2009, 10 while
the bottom panel is for all years. Again, the expected water waste is calculated for wells using central
pivot, wells using LEPA, and for all wells.
FIGURE 4 HERE
9
The correlation coefficient could be estimated through joint dynamic estimation of the water extraction and water
use incentive equations while allowing for the error terms to be correlated. However, since the standard errors can
only be estimated through bootstrapping, the computation time involved is prohibitively long.
10
Since water use incentives are dynamically determined through forward looking behavior, the last sample year for
which the counterfactual can be conducted is 2009 instead of 2010.
16
Figure 4 shows that the expected water waste is rather small, at about 0.1-0.25 AF per year for
each well, and this result is not sensitive to the correlation coefficients. This amount is insignificant
compared with the average annual water extraction of 146.3 AF. Even if the amount applied each time is
higher, say, at 10 (or 20) AF, the resulting annual waste of 0.2-0.5 (or 0.4-1) AF is still small. We
therefore conclude that the UIOLI clause has not resulted in significant water waste.
7. Conclusions
In this paper we study the role of water rights in limiting the rebound effects of LEPA and farmer
incentives to preserve their water rights in the HPA region of Kansas. We find that, although water
extraction moderately increases after central pivot is replaced by LEPA, this rebound effect can be
ameliorated by reducing the water rights. Specifically, a 10% reduction of water rights can reduce
LEPA’s rebound effect by 13.5%. We also find that limiting water rights raises farmer incentives to adopt
LEPA. Thus, institutional changes such as reducing water rights can limit the undesirable rebound effects
of new technologies such as LEPA without hurting incentives to adopt them.
We also find that about a quarter of the effects of LEPA in raising water extraction arises from
the channel of crop choices: farmers using LEPA are more likely to grow water intensive crops such as
corn, soybean and alfalfa compared with those using central pivot. Adoption of LEPA does not lead
farmers to irrigate more land, and the remaining three quarters of LEPA’s rebound effect is attributable to
more intensive irrigation. The lower water pressure required for LEPA irrigation to operate implies that it
is less costly for farmers to apply additional rounds of irrigation.
In contrast, about half of the effects of water rights on water extraction operate through irrigated
acreage: famers with higher water rights will irrigate larger areas of their fields. The remaining half of the
effects are attributable to more intensive irrigation by farmers with larger water rights. Further, a 10%
reduction in water rights across all wells can reduce the average water extraction by 5-6%.
We find that farmers have incentive to preserve their water rights even when no irrigation is
needed, in response to the use-it-or-lose-it clause of the water right system. This incentive is higher if the
farmer expects to irrigate in the next period. Intuitively, such incentive will result in waste of water.
However, we find that the waste is insignificant, at about 0.1-0.25 AF per well each year, relative to the
annual water extraction of 146.3 AF.
Our findings about the role of water rights are significant partly because water extraction is selfreported, and water rights are not strictly enforced. One can only expect the effects of water rights to be
more significant when they are more strictly enforced.
17
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Figures
Figure 1. Distribution of Type 1 Wells by Application Time
Figure 2. Annual Percentage of Wells Extracting Beyond Their Water Rights (1992-2009)
22
Figure 3. Counterfactual Policy Simulation: Reducing Water Rights
23
Figure 4. Counterfactual Policy Simulation: Water Waste due to UIOLI
24
Tables
Table 1. Summary Statistics*
Variables (units)
Water Extraction (AF)
Balanced Panel 1991-2010 (4321 wells)
Definition
Mean
Std.D
Min
Max
Annual water extraction from a
148.59
75.75
0
498.08
well
Water Right (AF)
Cap on annual water extraction
235.83
106.18
0
1280
Acres Irrigated (Acres)
Annual acres irrigated by a well
134.80
48.92
0
633
Extraction per acre
Ratio of Water Extraction to
1.12
0.48
0
9.62
(AF/Acre)
Acres Irrigated
LEPA
=1 if LEPA is used; 0 otherwise 0.59
0.49
0
1
Precipitation (in)
Annual rainfall
25.23
5.93
10.96
50.05
Depth to Water (ft)
Distance from land surface to
92.81
70.56
0
415.19
top of aquifer
Slope (% of distance)
Ground surface gradient
2.55
2.86
0
19
Potential Evapotranspiration
Water loss via evaporation and
113.76
9.64
91.09
134.58
(in)**
transpiration
Saturated Hydroconductivity
Rate of water moving in
31.01
34.19
0.21
92
(𝜇𝜇m/sec)
saturated soil
Available Water Capacity
Soil’s ability to retain water
0.16
0.045
0
0.25
Irrigated Capability Class
=1 if soil is suitable for
0.39
0.49
0
1
(dummy)
Irrigation; 0 otherwise
(cm/cm)
Percent of wells planting
certain crops
Corn
44.81%
Soybeans
8.54
Alfalfa
7.86
Corn and Wheat
4.04
Corn and Soy
3.76
Wheat
3.56
Sorghum
2.12
25
Fallow/Dryland Crop
1.13
Other Crops***
24.18
* The summary statistics is based on a balanced panel of 4321 wells over 20 years (1991-2010), resulting in a
sample size of 86,420.
** Potential evapotranspiration is determined by multiple factors including temperature, wind, solar radiation, and
humidity. The calculation of Potential Evapotranspiration is alfalfa-based in our data source.
*** In our dataset, some irrigated fields are planted with multiple crops, without information about the planted acres
for each crop. We lump these as well as crops with extremely low percentages into the “Other Crops” category.
26
Table 2 Dynamic Joint Estimation and Separate Estimation Results
Variables
Water Extraction (𝑦𝑦𝑖𝑖𝑖𝑖 )
Dynamic Joint
Separate
1( yit +1 > 0)
Water Right
Incentive to Use Water (𝑧𝑧𝑖𝑖𝑖𝑖 )
Dynamic Joint
Separate
1.74***
1.29***
(0.039)
(0.058)
0.15***
0.22***
4.60e-5
3.60e-4
(0.015)
(0.017)
(0.000)
(0.000)
-1.22e-4***
-1.90e-4***
(0.000)
(0.000)
-1.85*
-1.06
0.014
0.13
(1.09)
(1.07)
(0.061)
(0.097)
0.020***
0.019***
0.001**
4.21e-4
(0.004)
(0.004)
(0.000)
(0.000)
-1.70***
-1.64***
-0.003
-0.018**
(0.082)
(0.081)
(0.003)
(0.007)
-0.49***
-0.47***
-0.004***
-0.005**
(0.025)
(0.023)
(0.000)
(0.002)
0.73***
1.37***
-0.001
0.003
(0.17)
(0.20)
(0.006)
(0.008)
Potential
1.55***
1.57***
0.010***
0.007
Evapotranspiration
(0.073)
(0.072)
(0.001)
(0.006)
Saturated Hydroconductivity
0.022
0.054**
5.00e-5
4.66e-4
(0.022)
(0.025)
(0.000)
(0.001)
-109.07***
-114.37***
0.68
-0.19
(16.92)
(19.39)
(0.56)
(0.81)
-0.27
-0.20
0.028
0.022
(0.92)
(1.06)
(0.031)
(0.042)
0.48***
0.78***
(0.009)
(0.007)
0.43***
0.73***
(0.010)
(0.008)
0.44***
0.74***
(0.010)
(0.009)
Water Right 2
LEPA
Water Right*LEPA
Precipitation
Depth to Water
Slope
Available Water Capacity
Irrigated Capacity Class
Corn Acres
Soybeans Acres
Alfalfa Acres
27
Corn-Wheat Acres
Corn-Soybeans Acres
Wheat Acres
Sorghum Acres
Other Crop Acres
r
0.41***
0.67***
(0.009)
(0.008)
0.47***
0.75***
(0.011)
(0.010)
-0.002
0.30***
(0.011)
(0.010)
0.24***
0.54***
(0.012)
(0.011)
0.37***
0.65***
(0.008)
(0.007)
0.81***
0.81***
(0.045)
(0.045)
Marginal Effects
Water Right (Overall)
Water Right (@ LEPA = 1)
0.14***
1.69e-5
(0.012)
(0.000)
0.15***
(0.012)
Water Right (@ LEPA = 0)
0.13***
(0.012)
LEPA
3.32***
0.007***
(0.57)
(0.001)
1(𝑦𝑦𝑖𝑖𝑖𝑖+1 > 0)
0.118***
(0.011)
Time Fixed Effect
Yes
Yes
Yes
Yes
GMD Fixed Effect
Yes
Yes
Yes
Yes
N
82099
86420
82099
82099
*** 1% significance level, ** 5% significance level, * 10% significance level.
Standard errors are reported in parentheses in the first three columns. The last column reports cluster robust standard
errors (clustered at the well level).
28
Table 3. Mediation Test: Effect of LEPA and Water Rights on Acres Irrigated (Panel Tobit)
Variables
Acres Irrigated
Water Right
0.41***
(0.019)
Water Right 2
-2.09e-4***
LEPA
0.15
(0.000)
(0.60)
WR*LEPA
0.003
(0.002)
Precipitation
-0.12***
(0.046)
Slope
-0.58**
(0.24)
Depth to Water
-0.079***
(0.013)
Potential Evapotranspiration
-0.027
(0.041)
Saturated Hydro-Conductivity
-0.041
(0.030)
Available Water Capacity
31.76
(23.53)
Irrigated Capacity Class
-1.41
(1.29)
Marginal Effects
Water Right
0.30***
(Overall)
(0.014)
Water Right
0.30***
(@ LEPA=1)
(0.014)
Water Right
0.29***
(@ LEPA = 0)
(0.014)
LEPA
0.78**
(0.33)
29
*** 1% significance level, ** 5% significance level, * 10% significance level.
Standard errors are reported in parentheses.
Table 4. Mediation Test: Effect of LEPA and Water Rights on Crop Choices (Linear Random
Effects Model)
Water Rights
Water Rights
(@ LEPA = 1)
(@ LEPA = 0)
5.03***
0.073***
0.063***
(0.97)
(0.020)
(0.018)
0.80*
-0.007
0.003
(0.42)
(0.005)
(0.005)
0.34
-0.007
-0.010
(0.52)
(0.008)
(0.007)
0.34
0.081***
0.089***
(0.70)
(0.021)
(0.018)
-0.62
0.024***
0.012**
(0.45)
(0.006)
(0.005)
-0.72*
-0.019***
-0.016***
(0.39)
(0.006)
(0.005)
-0.38
-0.008**
-0.005
(0.27)
(0.003)
(0.003)
-4.05***
0.16***
0.16***
(1.05)
(0.038)
(0.035)
Marginal Effects
LEPA
Corn Acres
Soybeans Acres
Alfalfa Acres
Corn & Wheat Acres
Corn & Soy Acres
Wheat Acres
Sorghum Acres
Others Acres
*** 1% significance level, ** 5% significance level, * 10% significance level.
Clustered robust standard errors are reported in parentheses (clustered at well level).
30
Table 5. Mediation Test: Comparison of Estimates with and without Mediators (Panel Tobit)
Variables
Water Extraction Estimation With/Without Mediators
No Mediators
With Acres Irrigated
With Crop Acres
0.55***
0.310***
0.22***
(0.022)
(0.020)
(0.017)
Water Right 2
-4.40e-4***
-3.00e-4***
-1.90e-4***
(0.000)
(0.000)
(0.000)
LEPA
-0.79
-0.78
-1.06
(1.16)
(1.10)
(1.07)
0.023***
0.022***
0.019***
(0.004)
(0.004)
(0.004)
-1.74***
-1.68***
-1.64***
(0.088)
(0.084)
(0.081)
-0.53***
-0.49***
-0.47***
(0.025)
(0.024)
(0.023)
1.32***
1.69***
1.37***
(0.28)
(0.24)
(0.20)
Potential
1.52***
1.54***
1.57***
Evapotranspiration
(0.078)
(0.075)
(0.072)
Saturated
0.020
0.044
0.054**
Hydroconductivity
(0.034)
(0.030)
(0.025)
Available Water Capacity
-145.20***
-164.84***
-114.37***
(26.81)
(22.95)
(19.39)
-0.66
0.26
-0.20
(1.47)
(1.26)
(1.06)
Water Right
WR*LEPA
Precipitation
Depth to Water
Slope
Irrigated Capability Class
Acres Irrigated
0.669***
(0.007)
Corn Acres
0.78***
(0.007)
Soybeans Acres
0.73***
(0.008)
Alfalfa Acres
0.74***
(0.009)
31
Corn-Wheat Acres
0.67***
(0.008)
Corn-Soybeans Acre
0.75***
(0.010)
Wheat Acres
0.30***
(0.010)
Sorghum Acres
0.54***
(0.011)
Other Crop Acres
0.65***
(0.007)
Marginal Effects
Water Right (Overall)
0.35***
0.17***
0.14***
(0.016)
(0.014)
(0.012)
Water Right
0.36***
0.18***
0.15***
(@ LEPA=1)
(0.016)
(0.014)
(0.012)
Water Right
0.33***
0.16***
0.13***
(@ LEPA = 0)
(0.015)
(0.014)
(0.012)
LEPA
4.65***
4.29***
3.32***
(0.62)
(0.59)
(0.57)
*** 1% significance level, ** 5% significance level, * 10% significance level;
Standard errors are reported in parentheses.
32
Table 6. Ratio of Annual Water Extraction to Water Rights
Level of Water Rights (Acre Feet)
Technologies
<100
[100, 200]
>200
Both Technologies
1.09 (100%)
0.74 (100%)
0.59 (100%)
Center Pivot
1.12 (37%)
0.73 (43%)
0.61 (39%)
LEPA
1.07 (63%)
0.74 (57%)
0.59 (61%)
The sample shares of the technology-water right combinations are reported in parenthesis.
33
� and Samples (Panel Tobit)
Table 7. Robustness Check: Estimating (1) for Different Values of 𝑺𝑺
Variables
Water Extraction (𝒚𝒚𝒊𝒊𝒊𝒊 )
𝑆𝑆̅ = 5
𝑆𝑆̅ = 10
Sample = all
Sample = all
𝑆𝑆̅ = 20
Sample = all
𝑆𝑆̅ = 5
Sample =
Before 1980
Water Right
0.22***
0.23***
0.23***
0.21***
(0.017)
(0.017)
(0.017)
(0.018)
Water Right 2
-1.90e-4***
-1.90e-4***
-1.90e-4***
-1.80e-4***
(0.000)
(0.000)
(0.000)
(0.000)
LEPA
-1.06
-0.96
-0.82
-0.061
(1.07)
(1.07)
(1.08)
(1.18)
0.019***
0.018***
0.018***
0.016***
(0.004)
(0.004)
(0.004)
(0.004)
-1.64***
-1.65***
-1.66***
-1.65***
(0.081)
(0.082)
(0.082)
(0.090)
1.37***
1.36***
1.36***
1.06***
(0.20)
(0.20)
(0.20)
(0.23)
-0.47***
-0.47***
-0.47***
-0.48***
(0.023)
(0.023)
(0.023)
(0.026)
Potential
1.57***
1.58***
1.59***
1.58***
Evapotranspiration
(0.072)
(0.073)
(0.073)
(0.080)
Saturated Hydro
0.054**
0.054**
0.054**
0.091***
Conductivity
(0.025)
(0.025)
(0.025)
(0.028)
Available Water Capacity
-114.37***
-115.03***
-115.43***
-91.95***
(19.39)
(19.43)
(19.52)
(21.41)
-0.20
-0.20
-0.27
-0.35
(1.06)
(1.06)
(1.06)
(1.15)
0.78***
0.77***
0.75***
0.78***
(0.007)
(0.007)
(0.007)
(0.008)
0.73***
0.72***
0.70***
0.73***
(0.008)
(0.009)
(0.009)
(0.009)
0.74***
0.73***
0.71***
0.75***
(0.009)
(0.009)
(0.009)
(0.010)
Water Right*LEPA
Precipitation
Slope
Depth to Water
Irrigated Capacity Class
Corn Acres
Soybeans Acres
Alfalfa Acres
34
Corn-Wheat Acres
0.67***
0.67***
0.65***
0.67***
(0.008)
(0.008)
(0.008)
(0.008)
0.75***
0.74***
0.73***
0.75***
(0.010)
(0.010)
(0.010)
(0.010)
0.30***
0.28***
0.26***
0.30***
(0.010)
(0.010)
(0.010)
(0.010)
0.54***
0.53***
0.51***
0.53***
(0.011)
(0.011)
(0.012)
(0.012)
0.65***
0.64***
0.62***
0.65***
(0.007)
(0.007)
(0.007)
(0.007)
0.14***
0.14***
0.14***
0.13***
(0.012)
(0.012)
(0.012)
(0.012)
Water Right (@ LEPA =
0.15***
0.14***
0.14***
0.14***
1)
(0.012)
(0.012)
(0.012)
(0.013)
Water Right (@ LEPA =
0.13***
0.13***
0.13***
0.12***
0)
(0.012)
(0.012)
(0.012)
(0.012)
LEPA
3.32***
3.32***
3.31***
3.84***
(0.57)
(0.57)
(0.57)
(0.63)
Corn-Soybeans Acre
Wheat Acres
Sorghum Acres
Other Crop Acres
Marginal Effects
Water Right (Overall)
*** 1% significance level, ** 5% significance level, * 10% significance level
Standard errors are reported in parentheses.
35
Appendix
A1. Maximum Likelihood Estimation of the Dynamic Model
Assuming that 𝜀𝜀𝑖𝑖𝑖𝑖 ~ 𝑖𝑖𝑖𝑖𝑖𝑖 𝑁𝑁(0, 𝜎𝜎𝜀𝜀2 ), 𝜂𝜂𝑖𝑖𝑖𝑖 ~ 𝑖𝑖𝑖𝑖𝑖𝑖 𝑁𝑁(0,1), and 𝑐𝑐𝑐𝑐𝑐𝑐(𝜀𝜀𝑖𝑖𝑖𝑖 , 𝜂𝜂𝑖𝑖𝑖𝑖 ) = 0, 11 we know the period t density
function for 𝑦𝑦𝑖𝑖𝑖𝑖 has three possible cases. Under condition (c1),
𝑦𝑦
𝑓𝑓𝑐𝑐1 �𝑦𝑦𝑖𝑖𝑖𝑖 |𝑦𝑦𝑖𝑖𝑖𝑖+1 , 𝑐𝑐𝑖𝑖 , 𝑥𝑥𝑖𝑖𝑖𝑖 �
Under condition (c2):
𝑦𝑦
𝑓𝑓𝑐𝑐2 �𝑦𝑦𝑖𝑖𝑖𝑖 |𝑦𝑦𝑖𝑖𝑖𝑖+1 , 𝑐𝑐𝑖𝑖 , 𝑥𝑥𝑖𝑖𝑖𝑖 �
Under condition (c3):
𝑦𝑦
𝑦𝑦
1 𝑦𝑦𝑖𝑖𝑖𝑖 − 𝑐𝑐𝑖𝑖 − 𝑥𝑥𝑖𝑖𝑖𝑖 𝛽𝛽
𝑟𝑟𝑐𝑐𝑖𝑖 + 1(𝑦𝑦𝑖𝑖𝑖𝑖+1 > 0)𝛼𝛼1 + 𝑥𝑥𝑖𝑖𝑖𝑖 𝛼𝛼2
= 𝜙𝜙(
) ∗ Φ(
)
𝜎𝜎𝜀𝜀
𝜎𝜎𝜂𝜂
𝜎𝜎𝜀𝜀
𝑦𝑦
𝑦𝑦
𝑐𝑐𝑖𝑖 + 𝑥𝑥𝑖𝑖𝑖𝑖 𝛽𝛽 − 𝑆𝑆̅
𝑟𝑟𝑐𝑐𝑖𝑖 + 1(𝑦𝑦𝑖𝑖𝑖𝑖+1 > 0)𝛼𝛼1 + 𝑥𝑥𝑖𝑖𝑖𝑖 𝛼𝛼2
= [1 − Φ �
)
�] ∗ Φ(
𝜎𝜎𝜀𝜀
𝜎𝜎𝜂𝜂
𝑓𝑓𝑐𝑐3 (𝑦𝑦𝑖𝑖𝑖𝑖 |𝑦𝑦𝑖𝑖𝑖𝑖+1 , 𝑐𝑐𝑖𝑖 , 𝑥𝑥𝑖𝑖𝑖𝑖 ) = 1 − Φ �
𝑦𝑦
𝑟𝑟𝑐𝑐𝑖𝑖 + 1�𝑦𝑦𝑖𝑖𝑖𝑖+1 > 0�𝛼𝛼1 + 𝑥𝑥𝑖𝑖𝑖𝑖 𝛼𝛼2
𝜎𝜎𝜂𝜂
Together, the likelihood function for a particular well i in specific year t is:
𝑦𝑦
𝑓𝑓�𝑦𝑦𝑖𝑖𝑖𝑖 |𝑦𝑦𝑖𝑖𝑖𝑖+1 , 𝑐𝑐𝑖𝑖 , 𝑥𝑥𝑖𝑖𝑖𝑖 �
𝑦𝑦
𝑦𝑦
�
𝑦𝑦
= [𝑓𝑓𝑐𝑐1 �𝑦𝑦𝑖𝑖𝑖𝑖 |𝑦𝑦𝑖𝑖𝑖𝑖+1 , 𝑐𝑐𝑖𝑖 , 𝑥𝑥𝑖𝑖𝑖𝑖 �]1(𝑦𝑦𝑖𝑖𝑖𝑖>𝑆𝑆̅) [𝑓𝑓𝑐𝑐2 �𝑦𝑦𝑖𝑖𝑖𝑖 |𝑦𝑦𝑖𝑖𝑖𝑖+1 , 𝑐𝑐𝑖𝑖 , 𝑥𝑥𝑖𝑖𝑖𝑖 �]1(0<𝑦𝑦𝑖𝑖𝑖𝑖 ≤𝑆𝑆̅) [𝑓𝑓𝑐𝑐3 �𝑦𝑦𝑖𝑖𝑖𝑖 |𝑦𝑦𝑖𝑖𝑖𝑖+1 , 𝑐𝑐𝑖𝑖 , 𝑥𝑥𝑖𝑖𝑡𝑡 �]1(𝑦𝑦𝑖𝑖𝑖𝑖 =0)
Note that, due to the dynamic structure in (2), the likelihood function in period t depends on yit +1 .
Utilizing the property of conditional density functions, the full likelihood function (conditional on 𝑐𝑐𝑖𝑖 ) of
well i over all years is given by the product of per-period likelihood functions:
𝑦𝑦
𝑓𝑓�𝑦𝑦𝑖𝑖 |𝑦𝑦𝑖𝑖𝑖𝑖 , 𝑐𝑐𝑖𝑖 , 𝑥𝑥𝑖𝑖𝑖𝑖 �
𝑇𝑇𝑖𝑖 −1
𝑦𝑦
= � 𝑓𝑓�𝑦𝑦𝑖𝑖𝑖𝑖 |𝑦𝑦𝑖𝑖𝑖𝑖+1 , 𝑐𝑐𝑖𝑖 , 𝑥𝑥𝑖𝑖𝑖𝑖 �
𝑡𝑡=1
Using the distribution of ci in (3), the unconditional likelihood contribution becomes
𝑦𝑦
𝑦𝑦
𝑓𝑓�𝑦𝑦𝑖𝑖 |𝑦𝑦𝑖𝑖𝑖𝑖 , 𝑥𝑥𝑖𝑖𝑖𝑖 � = � 𝑓𝑓�𝑦𝑦𝑖𝑖 |𝑦𝑦𝑖𝑖𝑖𝑖 , 𝑐𝑐𝑖𝑖 , 𝑥𝑥𝑖𝑖𝑖𝑖 � ℎ(𝑐𝑐𝑖𝑖 |𝑥𝑥𝑖𝑖 , 𝑦𝑦𝑇𝑇𝑖𝑖 , 𝜃𝜃)𝑑𝑑𝑐𝑐𝑖𝑖
A2. Endogeneity Test of the Adoption of LEPA
We adopt the control function approach to test the endogeneity of LEPA. First, a pooled Probit model of
LEPA adoption on the IV variable as well as other exogenous variables is performed. Generalized
residuals from this model are calculated and are used as the control function. In the second stage, the
pooled Tobit model of water extraction is estimated with the control function added as an explanatory
11
We also make the typical assumption that 𝜎𝜎𝜂𝜂2 = 1 in order to identify the model.
36
variable. Table A1 reports the results of endogeneity test. The control function in the second stage is
statistically insignificant, failing to reject the null hypothesis that LEPA is exogenous.
Table A1. Endogeneity Test of LEPA (Results of Pooled Tobit)
Endogeneitty Test
First Stage
Independent Variables
(Dep = Water Use)
(Dep = LEPA)
Water Right
0.21***
-0.001***
(0.023)
(0.000)
Water Right 2
-1.89e-4***
4.69e-7**
(0.000)
(0.000)
LEPA
-2.49
(4.95)
Water Right*LEPA
0.029***
(0.010)
Control Function
-2.80
(2.56)
# Neighbors with LEPA LAST YEAR (IV)
0.056***
(0.003)
Precipitation
Depth to Water
Slope
Potential Evapotranspiration
Saturated Hydro-Conductivity
Available Water Capacity
Irrigated Capacity Class
Corn Acres
-1.68***
0.005*
(0.088)
(0.003)
-0.43***
0.003***
(0.048)
(0.001)
1.42***
-0.015***
(0.21)
(0.003)
1.79***
0.003
(0.074)
(0.003)
0.054**
0.001**
(0.024)
(0.000)
-123.26***
1.10***
(20.79)
(0.24)
-0.21
0.032**
(1.07)
(0.013)
0.777***
0.001***
(0.025)
(0.000)
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Soybeans Acres
Alfalfa Acres
Corn-Wheat Acres
Corn-Soybeans Acres
Wheat Acres
Sorghum Acres
Other Crop Acres
0.730***
0.001***
(0.024)
(0.000)
0.736***
0.001**
(0.027)
(0.000)
0.682***
0.000
(0.024)
(0.000)
0.755***
0.000
(0.025)
(0.000)
0.307***
-0.000
(0.025)
(0.000)
0.539***
0.000
(0.028)
(0.000)
0.645***
0.000
(0.024)
(0.000)
0.13***
-1.15e-4***
(0.01)
(0.000)
Marginal Effects
Water Right (Overall)
LEPA
4.30
(4.30)
# Neighbors with LEPA LAST YEAR (IV)
0.013***
(0.001)
Time Fixed Effect
Yes
Yes
GMD Fixed Effect
Yes
Yes
N
82099
82099
*** 1% significance level, ** 5% significance level, * 10% significance level.
Bootstrapped standard errors are reported in parentheses.
Table A2 shows that the endogeneity test is robust to the number of neighbors selected as the IV:
the estimated coefficients of all variables remain largely unchanged as we change the IV to be the 16th40th and 21th-40th nearest neighbors.
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Table A2 Robustness Check – Changing Neighbors used as IV (Pooled Tobit)
Nonlinear Control Function Using Different Neighbor IV
Variables
11 – 30th
16th – 40th
21th – 40th
Water Right
0.21***
0.21***
0.21***
(0.023)
(0.023)
(0.023)
Water Right 2
-1.90e-4***
-1.90e-4***
-1.90e-4***
(0.000)
(0.000)
(0.000)
LEPA
-2.49
-3.74
-7.14
(4.95)
(5.08)
(5.26)
0.029***
0.029***
0.029***
(0.010)
(0.010)
(0.010)
-2.80
-2.11
-0.16
(2.56)
(2.65)
(2.76)
-1.68***
-1.68***
-1.68***
(0.088)
(0.088)
(0.088)
1.42***
1.42***
1.41***
(0.21)
(0.21)
(0.21)
-0.43***
-0.43***
-0.42***
(0.048)
(0.048)
(0.048)
1.79***
1.79***
1.80***
(0.074)
(0.074)
(0.074)
0.054**
0.053**
0.054**
(0.024)
(0.024)
(0.024)
-123.26***
-123.53***
-121.95***
(20.79)
(20.81)
(20.75)
-0.21
-0.23
-0.20
(1.07)
(1.07)
(1.07)
0.777***
0.778***
0.778***
(0.025)
(0.025)
(0.025)
0.730***
0.730***
0.731***
(0.024)
(0.024)
(0.024)
0.736***
0.736***
0.737***
(0.027)
(0.027)
(0.027)
Water Right*LEPA
Control Function
Precipitation
Slope
Depth to Water
Potential Evapotranspiration
Saturated Hydro-Conductivity
Available Water Capacity
Irrigated Capacity Class
Corn Acres
Soybeans Acres
Alfalfa Acres
th
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Corn-Wheat Acres
0.682***
0.682***
0.683***
(0.024)
(0.024)
(0.024)
0.755***
0.755***
0.756***
(0.025)
(0.025)
(0.025)
0.307***
0.307***
0.307***
(0.025)
(0.025)
(0.025)
0.539***
0.539***
0.539***
(0.028)
(0.028)
(0.028)
0.645***
0.645***
0.645***
(0.024)
(0.024)
(0.024)
Time Fixed Effect
Yes
Yes
Yes
GMD Fixed Effect
Yes
Yes
Yes
N
82099
82099
82099
Corn-Soybeans Acres
Wheat Acres
Sorghum Acres
Other Crop Acres
*** 1% significance level, ** 5% significance level, * 10% significance level.
Bootstrapped standard errors are reported in parentheses.
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