Policy Research Working Paper 9092
Factor Market Failures and the Adoption
of Irrigation in Rwanda
Maria Ruth Jones
Florence Kondylis
John Ashton Loeser
Jeremy Magruder
Development Economics
Development Impact Evaluation Group
December 2019
Policy Research Working Paper 9092
Abstract
This paper examines constraints to adoption of new tech- labor and inputs away from their other plots. Eliminat-
nologies in the context of hillside irrigation schemes in ing this substitution would increase adoption by at least
Rwanda. It leverages a plot-level spatial regression discon- 21 percent. Third, this substitution is largest for smaller
tinuity design to produce 3 key results. First, irrigation households and wealthier households. This result can be
enables dry season horticultural production, which boosts explained by labor market failures in a standard agricultural
on-farm cash profits by 70 percent. Second, adoption is household model.
constrained: access to irrigation causes farmers to substitute
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authors may be contacted at fkondylis@worldbank.org.
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Produced by the Research Support Team
Factor Market Failures and the Adoption of Irrigation in
Rwanda∗
Maria Jones† Florence Kondylis† John Loeser† Jeremy Magruder‡
JEL Classiﬁcation Codes: J43, O12, Q12, Q15
Keywords: Technology adoption, Irrigation, Factor markets
∗
This draft beneﬁted from comments from Chris Barrett, Paul Christian, Alain de Janvry, Simeon
Djankov, Esther Duﬂo, Andrew Foster, Doug Gollin, Saahil Karpe, Elisabeth Sadoulet, John Strauss, Duncan
Thomas, Chris Udry, and seminar audiences at Cornell University, Georgetown University, Michigan State
University, North Carolina State University, World Bank, Northwestern University, University of California,
Berkeley, and University of Southern California. We thank the European Union, the Global Agriculture and
Food Security Program (GAFSP), the World Bank Rwanda Country Management Unit, the World Bank i2i
fund, 3ie, and IGC for generous research funding. Emanuele Brancati, Anna Kasimatis, Roshni Khincha,
Christophe Ndahimana, and Shardul Oza provided excellent research assistance. Finally, we thank the tech-
nical staﬀ at MINAGRI, the staﬀ of the LWH project implementation unit, and the World Bank management
and operational teams in Rwanda for being outstanding research partners. We are particularly indebted to
Esdras Byiringiro, Jolly Dusabe, Hon. Dr. Gerardine Mukeshimana, and Innocent Musabyimana for sharing
their deep knowledge of Rwandan agriculture with us. Magruder acknowledges support from NIFA. The
views expressed in this manuscript do not reﬂect the views of the World Bank. All errors are our own.
†
Development Impact Evaluation, World Bank
‡
UC Berkeley, NBER
Contents
1 Introduction 3
2 Data and context 9
2.1 Irrigation in Rwanda . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.1 Spatial sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.2 Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3 Stylized facts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3 Impacts of irrigation 16
3.1 Empirical strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.1.1 Balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.2 Estimating the eﬀects of irrigation . . . . . . . . . . . . . . . . . . . . . . . . 20
3.2.1 Adoption Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.2.2 Impacts of irrigation . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2.3 Discussion of spillovers . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4 Testing for binding constraint 25
4.1 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.2 A test for separation failures . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.3 Separating constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
5 Separation failures and adoption of irrigation 33
5.1 Empirical strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
5.1.1 Balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
5.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
5.2.1 A test for separation failures . . . . . . . . . . . . . . . . . . . . . . . 35
5.2.2 Impacts of separation failures on adoption of irrigation . . . . . . . . 38
5.2.3 Separating constraints . . . . . . . . . . . . . . . . . . . . . . . . . . 39
6 Experimental evidence 40
6.1 Empirical strategy and results . . . . . . . . . . . . . . . . . . . . . . . . . . 42
7 Conclusions 43
2
1 Introduction
Limited adoption of productive technologies is a prominent explanation of low agricultural
productivity in sub-Saharan Africa (World Bank, 2007). Existing productive technologies are
underutilized due to ineﬃciencies in the markets faced by farmer households (Udry, 1997).
A recent literature has provided robust evidence that these market failures limit technology
adoption, most commonly through experimental manipulation of markets for risk, credit,
and information (De Janvry et al., 2017).
Evidence is thinner on the role of constraints to adoption generated by failures in fac-
tor markets for land and labor. Land and labor markets are characterized by substantial
frictions in developing countries (Fafchamps, 1993; Udry, 1997; LaFave & Thomas, 2016),
even where these markets are particularly active (Kaur, 2014; Breza et al., 2018). Economic
theory suggests land and labor market failures reduce agricultural productivity by gener-
ating ineﬃcient allocations of labor and land across farms (Fei & Ranis, 1961; Benjamin,
1992). More recent empirical work has found that these ineﬃciencies are quantitatively im-
portant (Udry, 1997; Adamopoulos & Restuccia, 2014; Adamopoulos et al., 2017; Foster &
Rosenzweig, 2017; Adamopoulos & Restuccia, 2018).
In this paper, we demonstrate that incomplete land and labor markets contribute to the
productivity gap by limiting technology adoption.1 We do so in the context of a poten-
tially transformative technology: irrigation. Irrigation increases agricultural productivity in
several ways: it adds additional agricultural seasons, enables cultivation of water-intensive
crops, and reduces production uncertainty. However, irrigation is also costly: it requires
large construction and maintenance costs, and is associated with increased usage of comple-
mentary inputs, such as labor, fertilizer, and improved seeds. Market failures, including in
factor markets, therefore have the potential to cause ineﬃcient levels of irrigation adoption
1
A related question is explored in papers which evaluate the eﬀects of land titling and other formalized
property rights on farm investment (Besley, 1995; Goldstein & Udry, 2008; Deininger & Feder, 2009; Besley
& Ghatak, 2010; Ali et al., 2014; Goldstein et al., 2018). In our context, farmers have been assigned formal
titles to our plots and so we identify the inﬂuence of factor market frictions on technology adoption in the
presence of formalized rights. Our emphasis on the role of labor market frictions is also distinct.
3
as they induce a wedge between shadow prices and market prices of these inputs.
We proceed in 3 steps. First, we establish that irrigation is a productive technology, but
adoption is partial. Second, we demonstrate that this partial adoption is ineﬃcient. Third,
we show that labor market failures generate constraints to adoption of irrigation.
We begin by estimating the returns to irrigation in Rwanda. We identify these returns
using a plot-level spatial discontinuity design in newly constructed hillside irrigation schemes.
We sample plots within 50 meters of gravity fed canals, which originate from a distant
water source and must maintain a consistent gradient along the hillside. We survey 969
cultivators on 1,753 plots for 4 years.2 We then compare plots just inside the command area,
which have access to water for irrigation, to plots just outside the command area, which do
not. Treatment on the treated estimates reveal that irrigation enables the transition to dry
season cultivation of horticulture. While we ﬁnd no eﬀects on rainy season yields, labor, or
inputs, dry season estimates correspond to 44% - 71% growth in annual cash proﬁts. To
our knowledge, this is the ﬁrst study to use a natural experiment to estimate the returns to
irrigation in sub-Saharan Africa; our estimate is almost identical to an estimate from Duﬂo
& Pande (2007) in India.3 Despite the large eﬀects we estimate, adoption is low: only 30%
of plots are irrigated 4 years after canals became operational. At this level of adoption, the
sustainability of hillside irrigation systems is in doubt: even the large gains in cash proﬁts
to adopters are unable to generate enough surplus to pay for routine maintenance costs.4
We investigate the eﬀect of irrigation on inputs to shed light on what might determine
farmers’ decisions to adopt irrigation. In this context, the dominant input associated with
2
These numbers are only for the sample of households whose sampled plot is within 50 meters of the
associated discontinuity; in full we survey 1,695 cultivators on 3,332 plots.
3
Existing work that estimates the returns to irrigation using natural experiments is predominantly from
groundwater irrigation in South Asia, leveraging variation in slope characteristics of river basins (Duﬂo
& Pande, 2007), aquifer characteristics (Sekhri, 2014; Loeser, 2020), or well-failures (Jacoby, 2017) for
identiﬁcation. Estimates of the return to irrigation in Africa include Dillon (2011), who estimates the returns
to irrigation using propensity score matching in Mali. More broadly, Dillon & Fishman (2019) review the
literature on the impacts of surface water irrigation infrastructure.
4
This is distinct from the collective action failures discussed in (Ostrom, 1990). Low adoption of irrigation
as a threat to sustainability has also been documented by Attwood (2005), who argues that cost recovery was
a challenge for canal irrigation systems in nineteenth and early twentieth century India until the introduction
of sugarcane.
4
irrigation is households’ own labor. The shadow wage that prices household labor is notori-
ously diﬃcult to value, but if this labor were valued at the market wage, estimated eﬀects on
household labor would be 6 times as large as estimated eﬀects on expenditures on hired labor
and other inputs, and estimated eﬀects on proﬁts would fall from 44% - 71% to -12% - 38%.
Valuing household labor at the market wage may not be appropriate: rural market wages
are likely to be ineﬃciently high in developing countries (Kaur, 2014; Breza et al., 2018),
and labor market failures in rural areas may generate heterogeneity in the shadow wage
(Singh et al., 1986; Benjamin, 1992; LaFave & Thomas, 2016). Heterogeneity in the shadow
wage would then cause ineﬃcient adoption of irrigation across households.5 Alternatively,
these results could also be consistent with unconstrained proﬁt maximization if farmers have
heterogeneous returns to or costs of adopting irrigation (Suri, 2011) and optimize at market
wages.
We derive a test for ineﬃcient adoption of irrigation caused by market failures. To
produce this test, we build on seminal agricultural household models (Singh et al., 1986;
Benjamin, 1992) and model households’ production decisions, incorporating uncertainty,
plot-level heterogeneity, and failures in insurance, credit, and labor markets. Consistent with
our reduced form results, we model access to irrigation as a labor- and input-complementing
increase in plot-level productivity. Our test is as follows. With complete markets, farmers
maximize proﬁts on each plot and access to irrigation on one plot does not aﬀect production
decisions on other plots. In contrast, when there are failures in land and other markets, access
to irrigation on one plot causes substitution of labor and inputs away from other plots.6 This
test is joint for the null of frictionless land markets: if land markets are frictionless, then
markets should reallocate land to farmers who can cultivate most proﬁtably.
We implement our test for ineﬃcient adoption caused by market failures, exploiting the
5
This heterogeneity could only exist if there were frictions in at least one other market in addition to
labor markets.
6
The mechanism is straightforward: access to irrigation on one plot increases input use on that plot.
That increase does not aﬀect input demand on the farmers’ other plots; however, if the farmer faces binding
constraints in input, risk, or labor markets, that increase in input use must be associated with a decrease in
input use on other plots.
5
plot-level discontinuity in access to irrigation. We test whether farmers who have a plot just
inside the command area reduce their input use on their other plots compared to farmers
who have a plot just outside the command area. We ﬁnd large substitution eﬀects, strongly
rejecting complete markets: for farmers with a plot in the command area, an additional
irrigated plot caused by access to irrigation is associated with a 68 percentage point decrease
in the probability of irrigating the second plot. We ﬁnd similarly large eﬀects for adoption
of horticulture, household labor, and inputs. These results conﬁrm a simple descriptive
analysis, which shows that few households are able to irrigate more than one command area
plot. Applying these results, a simple back-of-the-envelope calculation implies that, absent
this substitution, adoption of irrigation would be at least 21% higher. Moreover, the presence
of this substitution implies current adoption of irrigation is ineﬃcient: diﬀerent households
make diﬀerent adoption decisions on technologically identical plots because of their access
to irrigation on their other plots.7
The previous test shows that ineﬃcient adoption of irrigation is caused by failures of
land markets, and at least one other market; however, it does not establish which other
market fails. We produce two tests that suggest that labor market constraints, as opposed
to ﬁnancial constraints, bind in our context.
First, we extend the model and propose a test for whether labor market frictions con-
tribute to ineﬃciently low adoption in this context. To produce this test, we consider the
eﬀects of household size and wealth on input substitution across plots, in the presence of
insurance, credit, and labor market failures. We demonstrate that, while many patterns of
diﬀerential substitution are possible, only labor market failures can explain irrigation access
on one plot leading to greater input substitution across plots for richer households, and de-
creased input substitution across plots for larger households. We then estimate diﬀerential
7
With suﬃcient time, these sites could reach an equilibrium in which this misallocation would have
slowly been corrected by markets (Gollin & Udry, 2019). However, we note that our results are 4 years after
initial access to irrigation, and we do not observe dynamics after 2 years. This is suﬃcient for our results to
have meaningful implications for the long run sustainability of these schemes. Our results also complement
evidence from the United States which suggests that initial allocations can persist for many decades even
with seemingly well functioning land markets (Bleakley & Ferrie, 2014; Smith, 2019).
6
substitution with respect to household size and wealth to test for labor market failures. We
ﬁnd exactly this pattern: households with two additional members substitute 62% - 86% less
than average size households, while one standard deviation wealthier households substitute
40% - 80% more than average wealth households. As these patterns of diﬀerential substi-
tution can only be explained by labor market failures, and not credit or insurance market
failures, these results imply that labor market failures cause substitution and contribute to
ineﬃcient adoption of irrigation.
We then complement this result with experimental evidence. We conduct three random-
ized controlled trials with the farmers who have access to irrigation. Two of these trials
focus on characteristics peculiar to irrigation systems: usage fees and failures of operations
and maintenance; we ﬁnd neither plausibly aﬀects farmers’ adoption decisions in our con-
text. In the third experiment, we distribute minikits which contain all necessary inputs for
horticulture cultivation to randomly selected farmers. Previous work has shown providing
free minikits targets credit, risk, and information constraints: it reduces costs of growing
horticulture under irrigation, basis risk, and costs of experimentation, respectively (Emerick
et al., 2016; Jones et al., 2018). We ﬁnd no eﬀects of receiving minikits on adoption of
horticulture in our context, in contrast to existing work. A closer analysis indicates that the
farmers who take up the minikits are the same farmers who would have been likely to cul-
tivate horticulture absent the intervention. Combining this evidence with the model-based
test above, we conclude that ﬁnancial and informational constraints are unlikely to be a
primary explanation for low and ineﬃcient adoption of irrigation.
This paper demonstrates that frictions in land and labor markets cause ineﬃcient adop-
tion of hillside irrigation in Rwanda. This result integrates key ﬁndings from three large
literatures in development economics. First, our result provides some ground-level evidence
for the mechanisms underlying misallocation (Adamopoulos & Restuccia, 2014; Adamopou-
los et al., 2017; Foster & Rosenzweig, 2017; Adamopoulos & Restuccia, 2018). We document
that land misallocation hinders technology adoption, and that frictions in labor markets are
7
one reason why land market failures generate production ineﬃciencies. The intuition for our
test expands on a deep literature on separation failures which empirically demonstrates that
factor market failures aﬀect the allocation of land and labor across households (Singh et al.,
1986; Benjamin, 1992; LaFave & Thomas, 2016; Dillon & Barrett, 2017; Dillon et al., 2019).8
Our context allows us to innovate by demonstrating that separation failures induce diﬀeren-
tial adoption of irrigation on technologically identical plots. In doing so, we also contribute to
a literature leveraging production function estimates to document misallocation of labor and
inputs by inferring their marginal products from their allocations across plots or households
(Jacoby, 1993; Skouﬁas, 1994; Udry, 1996; Restuccia & Santaeulalia-Llopis, 2017).9 Our
test for ineﬃcient technology adoption caused by land and labor market failures therefore
complements this literature, by both imposing less structure and leveraging our plot-level
discontinuity in access to irrigation as an exogenous labor- and input-complementing pro-
ductivity shock.
This paper is organized as follows. Section 2 describes the context we study and our
sources of data. Section 3 presents our estimates of the impacts of irrigation in Rwanda.
Section 4 presents our model of adoption of irrigation in the presence of market failures. We
implement tests of constraints to adoption and labor market failures suggested by the model
in Section 5, and experimental tests in Section 6. Section 7 concludes.
8
The existing literature does so by testing whether households with diﬀerent characteristics use diﬀerent
levels of inputs; however, this type of test stops short of showing that these allocations are ineﬃcient (Udry,
1997). In particular, it can only conclude that one market has failed; because it can not conclude that at
least two markets have failed, by Walras’ Law it is insuﬃcient to demonstrate an ineﬃciency.
9
Although demonstrating heterogeneity in the marginal product of labor is suﬃcient to show that labor
market failures generate ineﬃciencies, the methods employed by this literature are typically not robust to
the presence of unobserved heterogeneity across plots or measurement error (Gollin & Udry, 2019).
8
2 Data and context
2.1 Irrigation in Rwanda
We study 3 hillside irrigation schemes, located in Karongi and Nyanza districts of Rwanda,
that were constructed by the government in 2014; a timeline of construction and our surveys
is presented in Figure 1. Rainfed irrigation in and around these sites is seasonal, with three
potential seasons per year. During the main rainy season (“Rainy 1”; September - January),
rainfall is suﬃcient for production in most years. In the second rainy season (“Rainy 2”;
February - May), rainfall is suﬃcient in an average year but insuﬃcient in dry years. In
the dry season (“Dry”; June - August), rainfall is insuﬃcient for agricultural production for
seasonal crops. Absent irrigation, agricultural production in these sites consists of a mix of
staples (primarily maize and beans) which are cultivated seasonally and primarily consumed
by the cultivator, as well as perennial bananas which are sold commercially;10 most farmers
adopt either a rotation of staples, fallowing land in the dry season, or cultivate bananas.
Irrigation in these schemes is expected to increase yields by reducing risk in the second
rainy season and enabling cultivation in the short dry season. As the dry season is rela-
tively short, cultivating the primary staple crops is not possible, even with irrigation, for
households that cultivate during the two rainy seasons. Instead, cultivating shorter cycle
horticulture during the dry season becomes a possibility with the availability of irrigation.
Horticulture production (most commonly eggplant, cabbage, carrots, tomatoes, and onions)
can be sold at local markets where it is both consumed locally and traded for consumption
in Kigali.11 As horticultural production is relatively uncommon during the dry season in
Rwanda due to limited availability of irrigation, ﬁnding buyers for these crops is relatively
easy during this time. Absent irrigation, horticulture is familiar but uncommon around these
areas; at baseline 3.2% of plots outside of the command area are planted with at least some
10
Staple rotations also include smaller amounts of sorghum and tubers, while there is also some cultivation
of the perennial cassava, along with other minor crops. In our data, maize, beans, or bananas are the main
crop for 85% of observations excluding horticulture.
11
Kigali is less than a 3 hour drive from these markets, facilitating trade.
9
horticulture, primarily during the rainy seasons.
In this context, the three schemes we study were constructed by the government from
2009 - 2014, with water beginning to ﬂow to some parts of the schemes in 2014 Dry and
becoming fully operational by 2015 Rainy 1 (August 2014 - January 2015). The schemes in
our study share some common features; a picture from one of the schemes is presented in
Figure 2. In each site, land was terraced in preparation for the irrigation works (as hillside
irrigation would be infeasible on non-terraced land). Construction and rehabilitation of
terraces in these sites began in 2009 - 2010. The schemes are all gravity fed, and use surface
water as the source.12 From these water sources, a main canal (visible in Figure 2) was
constructed along a contour of the hillside; engineering speciﬁcations required the canal to
be suﬃciently steep so as to allow water to ﬂow, but suﬃciently gradual to control the speed
of the ﬂow, preventing manipulation of the path of the canal. Underground pipes run down
the terraces from the canal every 200 meters. Farmers draw water from valves on these pipes
located on every third terrace, from which ﬂexible hoses and dug furrows enable irrigation
on all plots below the canal. The “command area” for these schemes, the land that receives
access to irrigation, is the plots which are below the canal and located within 100 meters of
one of these valves.
In all sites, suﬃcient water is available to enable irrigation year-round. To the extent
that there is heterogeneity in plot-level water pressure, the plots nearest to the canal face
the lowest pressure.13 The primary cost to farmers of irrigating a plot in this context is their
labor associated with the actual irrigation, including maintaining the dug furrows and using
the hoses to apply water from the valves to their plots. At the time of the study, there are
no fees associated with the use of irrigation water14
12
In two sites, a river provides the water source, while in the third site, a dammed lake is the source.
13
The lower pressure on these plots is attributable to the design of the pipes, which ﬁll up with water
before valves are opened; forces of gravity and the lower volume of water in the pipes above the highest
valves generates somewhat weaker pressure than at the lower valves (though pressure is still suﬃcient for
eﬀective irrigation). This diﬀerence in pressure could become more serious if lower valves were opened at
the same time as higher valves; in practice, schedules of water usage are agreed upon to prevent this from
happening.
14
The government does have an objective of developing the ﬁnancial self-suﬃciency of the schemes. To
10
We exploit a spatial discontinuity in irrigation coverage to estimate the impacts of irri-
gation. Because the main canals must conform to prescribed slopes relative to a distant and
originally inaccessible water source, the geologic accident of altitude relative to this source
determines which plots will and will not receive access to irrigation water. Hence, before
construction, plots just above the canal should be similar to plots just below the canal, and
importantly, should be managed by similar farmers. Following construction, however, the
plots just below the canal fall inside the command area and have access to irrigation, while
the terraces just above the canal fall outside the command area and do not have access to
irrigation.
2.2 Data
2.2.1 Spatial sampling
To take advantage of the spatial discontinuity in access generated by the command area
boundary, we randomly sampled plots in close proximity to this discontinuity. In practice,
we constructed this sample of plots by dropping a uniform grid of points across the site at
2-meter resolution, and then randomly sampling points within the grid within 50m of the
command area boundary.15 After each point was sampled, we excluded all points within
10m of that point (to avoid selecting multiple points too close together).
Enumerators were then given GPS devices with the locations of the points, and sent to
do so, land taxes are intended to be applied to the plots in the command area, which (as land taxes) should
not inﬂuence cultivation decisions. These taxes are intended to be small in magnitude compared to potential
farmer yields as they are meant to fund only ongoing operations and maintenance costs rather than full cost
recovery; the highest fees across the sites were 77,000 RwF/ha/year, while our dry season treatment on the
treated estimates presented in Section 3 are 300,000 - 450,000 RwF/ha. The ﬁrst attempts to collect these
taxes were made in 2017 Rainy 1. The survey team engaged in an experiment to test whether these taxes
were a barrier to use of the irrigation system by randomizing subsidies across farmers at up to 100%; we
do not ﬁnd any evidence that the taxes changed farming practices (results available from authors). This
is perhaps unsurprising as tax compliance was very low, with 4% of scheduled taxes collected from farmers
who did not receive full subsidies from the research team.
15
In all three irrigation sites, we additionally sampled some points further from the canal inside the
command area. We use these points primarily to examine experimental treatments described below in
Section 6. Additionally, only two of the three sites have a viable boundary of cultivable land both just
inside and just outside the command area; we use only these sites for our analysis of the impacts of access
to irrigation in Section 3 and Section 5.
11
each point with a key informant (often the village leader). For each point, they were asked
to identify if the point was on cultivable land (this was to discard forest, swamps, thick
bushes, bodies of water, or other terrain which would make cultivation impossible). When
a point fell on cultivable land, they recorded the name of the cultivator of the plot, their
contact information, as well as a suﬃciently detailed description of the plot. In the rest of
this paper, we refer to all plots thus identiﬁed as sample plots. Our main household sample
was built from this sampling procedure: the data from this listing was used to construct a
roster of all the unique names of cultivators, eliminating duplicate names. Finally, for each
household with points falling on multiple plots, one of these points was randomly selected
to be that household’s sample plot.
2.2.2 Survey
Our baseline survey was implemented in August - October 2015 and includes detailed agri-
cultural production data (season-by-season) for seasons 2014 Dry through 2015 Rainy 2, that
is, spanning the year from June 2014 - May 2015; the dates of this survey and follow up
surveys, along with the agricultural seasons they cover, are presented in Figure 1. Details
of the construction of key variables we use for the analysis are presented in Appendix A. As
mentioned above, this is not a “true” baseline as some farmers had already gained access to
irrigation in 2014 Dry. However, relatively small parts of the site had access to irrigation
at this point; in Section 3.2.1 we highlight that 2014 Dry adoption of irrigation is less than
25% of adoption in subsequent dry seasons, and in Section 3.1.1 we show balance across the
command area boundary in household and plot characteristics. Production and input data
are collected plot-by-plot; in the baseline we conducted this production data for up to four
plots, although subsequent surveys maintain a panel of two plots. Each of these plots was
also mapped using GPS devices during the baseline; we use this data to construct the area
of plots and their locations. The two plots on which panel data is collected represent the
primary data for analysis; they include the sample plot (described above) and the farmer’s
12
next most important plot (deﬁned at baseline; we refer to this as the “most important plot”).
We also collected data on household characteristics, labor force behavior, and a short con-
sumption and food security module. In analysis, we will focus on the sample plots to learn
about the eﬀects of the irrigation itself, and the most important plot to learn about how the
presence of irrigation on the sample plot impacts households’ productive decisions on their
other plots.
Three follow up household surveys were conducted in May - June 2017, November -
December 2017, and November 2018 - February 2019. In each survey, we asked for up to a
year of recall data on agricultural production; based on the timing of our surveys we therefore
have production for all agricultural seasons from June 2014 through August 2018, with the
exception of 2015 Dry (June - August 2015) and 2016 Rainy 1 (September 2015 - February
2016).
The sample for the follow up surveys consists of all the baseline respondents. To build
a panel of households and plots, we interviewed households from the baseline and recorded
information on all their baseline plots. Whenever a household’s sample plot or most impor-
tant plot was sold or rented out to another household, or a household stopped renting in
that plot if it was not the owner (“transacted”), we ran a “tracking survey”. Speciﬁcally, we
tracked and interviewed the new household responsible for cultivation decisions on that plot
to record information about cultivation and production, along with household characteristics
when the new household was not already in our baseline sample. Data from this tracking
survey is incorporated in all our plot level analysis, limiting plot attrition.
Attrition in our survey is low, and details on attrition are presented in Table A11. Only
6.0% (6.4%) of plot-by-season observations for sample plots outside the command area in
our primary analysis sample (deﬁned in Section 3.1) are missing during the dry season (rainy
season). There are three sources of attrition: household attrition, plots transacted to other
farmers that we were not successful in tracking, and plots rented out to commercial farmers
who were based in the capital or internationally (from whom we were unable to collect
13
agricultural production data). We do not ﬁnd evidence of diﬀerential attrition of sample
plots due to household attrition or plots transacted to other farmers that we did not track,
however we do ﬁnd access to irrigation causes an additional 6.4 - 10.2pp of plots to be rented
out to the commercial farmer. We interpret the lack of data on these plots as biasing our
primary estimates of the impacts of irrigation downwards, as these plots are cultivated with
productive export crops, and we discuss attrition further in Appendix G.
2.3 Stylized facts
To motivate our analysis of the impacts of hillside irrigation, we ﬁrst introduce some stylized
facts about irrigation in this context. Table 1 presents summary statistics for agricultural
production from our four years of data, pooled across seasons; Figure 3 presents a subset of
these statistics graphically.
Stylized Fact 1. Irrigation in Rwanda is primarily used to cultivate horticulture in the dry
season.
Farmers in our data rarely irrigate their plots in the rainy seasons, and almost never use
irrigation when cultivating staples or bananas (only 2% of plots cultivated with staples or
bananas use irrigation in our data). In contrast, 93% of plots cultivated with horticulture
in the dry season use irrigation. This stylized fact makes agronomic sense as the rainfall in
rainy seasons in this part of Rwanda is usually suﬃcient for either staple or horticultural
production (and in wet years may be harmfully excessive for horticulture). Additionally,
as staples do not have a suﬃciently short cycle to permit cultivation during the relatively
short dry season (while horticulture does), it is not agronomically feasible to use irrigation
to cultivate staples during the dry season.
Stylized Fact 2. Horticultural production is more input intensive than staple cultivation,
which in turn is (much) more input intensive than banana cultivation.
14
The mean horticultural plot uses about 420 days/ha of household labor, 60 days/ha of
hired labor, and 50,000 RwF/ha of inputs, regardless of the season in which it is planted.16
This contrasts to staple plots (260 days/ha of household labor, 40 days/ha of hired labor,
20,000 - 40,000 RwF/ha of inputs), and bananas (100 days/ha of household labor, 10 days/ha
of hired labor, 3,000 RwF/ha of inputs).
Stylized Fact 3. Horticultural production produces much higher cash proﬁts than other
forms of agriculture.
Horticultural production produces much higher cash proﬁts (deﬁned as yields net of
expenditures on inputs and hired labor) than other forms of agricultural production in and
around these sites. Plots planted to horticulture yield about 500,000 RwF/ha in cash proﬁts,
in both rainy and dry seasons. This contrasts with about 250,000 RwF/ha of cash proﬁts
producing either staples or bananas.
Stylized Fact 4. Household labor is the primary input to production of any crop, and the
economic proﬁtability of horticulture depends critically on the shadow wage.
A large existing literature examines separation failures in labor markets faced by agricul-
tural households (e.g., Singh et al. (1986); Benjamin (1992); LaFave & Thomas (2016)). If
households are constrained in the quantity of labor they are able to sell on the labor market,
they may work within the household at a marginal product of labor well below the mar-
ket wage. Here, we see that if we value household labor allocated to horticulture at market
wages, then cultivating horticulture appears less proﬁtable than cultivating bananas (though
both appear more proﬁtable than cultivating staples).17 As a result, ultimately the economic
proﬁtability of horticulture relative to bananas will depend critically on the constraints on
household labor supply decisions.
16
For reference, in the study period, the exchange rate was approximately 800 RwF = 1 USD
17
Both horticulture and bananas are also primarily commercial crops, unlike staples. Farmers may place
higher value on staples if consumer prices are higher than producer prices (Key et al., 2000), or if there is
price risk in production and consumption, both of which may contribute to cultivation decisions as well.
15
3 Impacts of irrigation
3.1 Empirical strategy
We start our analysis through a simple OLS framework, and we restrict this and subsequent
analysis to sample plots within 50 meters of the discontinuity. If these nearby plots are
suﬃciently similar so that irrigation access can be taken as random within this sample, we
can simply regress
y1ist = β0 + β1 CA1is + αst + 1ist (1)
Where ykist is outcome y for plot k of household i located in site s in season t, CAkis
is an indicator for that plot being in the command area, and αst are site-by-season ﬁxed
eﬀects meant to control for any diﬀerences or trend diﬀerences across sites (including market
access or prices). We use k = 1 to indicate the household’s sample plot, as opposed to the
household’s most important plot.
Next, we consider two primary potential sources of omitted variable bias. First, plots that
are positioned relatively higher on the hillside may have diﬀerent agronomic characteristics,
and accordingly farmers may diﬀerentially sort into these plots. As plots inside the command
area are lower on the hillside (below the canal) and plots outside the command area are higher
on the hillside (above the canal), the command area indicator will be correlated with position
on the hillside and β1 may be biased. Second, as the construction of the canal slices through
plots on the hillside, this may diﬀerentially change the area of plots that are positioned
higher or lower on the hillside. For example, roads are more often located higher on the
hillside, leaving less room for plots to extend above the canal relative to below the canal. As
we anticipate this will cause plots to be relatively larger just inside the command area, and
plots exhibit strong evidence of diminishing returns to scale in this context, this eﬀect will
likely bias β1 downwards.
We account for these two potential sources of omitted variable bias by including con-
trols. First, to account for position on the hillside, we control for distance of the plot from
16
the command area boundary, and distance of the plot from the command area boundary
interacted with the command area indicator.18 This is a standard regression discontinuity
speciﬁcation, and as such compares sample plots that are just inside the command area to
sample plots that are just outside the command area. Second, to account for diﬀerences in
area of plots, we control for the log area of sample plots. Speciﬁcally, we estimate
y1ist = β0 + β1 CA1is + β2 Dist1is + β3 Dist1is ∗ CA1is + αst + γX1is + 1ist (2)
where Dist1is is the distance of plot 1 from the command area boundary (positive for plots
within the command area, negative for plots outside the command area) and X1is is the log
plot area.
Next, we consider additional concerns related to selection into our sample caused by
access to irrigation. This may arise for two reasons. First, during the construction of the
hillside irrigation schemes, forest was deliberately preserved or planted just outside of the
command area in order to protect the new investment from erosion. As these forested plots
are not agricultural, they are not included in our sampling strategy.19 Second, marginal plots
which would have been too unproductive to cultivate absent irrigation, and would thus have
been left permanently fallow, may now be suﬃciently productive to be worth cultivating with
access to irrigation. While our sampling strategy selected both cultivated and uncultivated
plots, it did not select plots which had been left overgrown with thick bushes, as it would have
been diﬃcult to identify the household responsible for those plots. In practice, the latter
is likely uncommon, as typical household landholdings are small in the hillside irrigation
schemes we study (around 0.3 ha), and agricultural land is highly valued – median rental
prices in our data are 150,000 RwF/ha, approximately 25% of annual yields.
We account for this potential source of bias using spatial ﬁxed eﬀects (SFE; see Gold-
18
We calculate distance using the distance of the plot boundary to the command area boundary.
19
Typically, forests were planted or preserved in areas of low productivity, where the slope of the hillside
was relatively high and erosion was relatively common. Therefore, this amounts to selection out of our
sample of low productivity plots outside the command area, which would bias β1 downwards.
17
stein & Udry (2008); Conley & Udry (2010); Magruder (2012, 2013)), which use a spatial
demeaning procedure to eliminate spatially correlated unobservables, such as unobserved
heterogeneity in productivity caused by soil characteristics. This spatial demeaning ensures
that comparisons are made only over proximate plots. For example, if some areas of low
productivity are left forested outside of the command area, but not inside, then plots inside
the command area will be systematically (unobservably) less productive than plots outside
the command area. However, because SFE estimators only compare neighboring plots, the
low productivity plots inside the command area that are near forested low productivity ar-
eas will not have nearby comparison plots outside the command area, and therefore will not
contribute to the estimation of the eﬀect of the command area.20
In practice, we deﬁne a set Nkist to be the group of ﬁve closest plots to plot k ob-
served in season t, including the plot itself. Then, for any variable zkist , deﬁne z kist =
(1/|Nkist |) k ∈Nkist zk i st . The SFE speciﬁcation then estimates
y1ist − y 1ist = β1 (CA1is − CA1is ) + (V1is − V 1is ) γ + ( 1ist − 1ist ) (3)
where Vkis includes all controls from Equation 2, except the subsumed site-by-season ﬁxed
eﬀects.
Our sampling strategy yields the following plot proximity: restricting to the sample plots
in our main sample for regression discontinuity analysis, 49% of plots have 3 plots (self
inclusive) within 50 meters, and 87% have 3 plots within 100m; 60% of plots have all 5 plots
(self inclusive) within 100m, while 83% have all 5 plots within 150m. As reference, Conley &
Udry (2010) use 500m as the bandwidth for their estimator, while Goldstein & Udry (2008)
use 250m as the bandwidth; we therefore anticipate that underlying land characteristics are
likely to be quite similar between each plot and its comparison plots.
When estimating speciﬁcations (1) and (2), we cluster standard errors at the level of the
20
Formally, SFE estimators leverage the identiﬁcation assumption lim||k−k ||→0 E [ kist |Xkist ] =
E[ k i st |Xk i st ], where ||k − k || represents the distance between plot k and plot k .
18
nearest water user group, the group of plots that can source water from the same secondary
pipe. When estimating speciﬁcation (3), the spatial ﬁxed eﬀects generate correlation between
the errors of close observations. To allow for this, we calculate Conley (1999) standard
errors.21
3.1.1 Balance
We now use speciﬁcations (1), (2), and (3) to examine whether the plots in our sample and the
households who cultivate them are comparable at baseline. For each of these speciﬁcations,
we show balance both with key controls omitted (Columns 3, 5, and 6), and our preferred
speciﬁcations which we use in our analysis with key controls included (Columns 4, 7, and 8).
First, in speciﬁcations which control for distance to the boundary (Columns 5 through 8,
Table 2), our sample plots are balanced in terms of ownership and rentals. Additionally, the
vast majority of sample plot owners on both sides of the canal owned the land over 5 years,
or prior to the start of the irrigation construction. There is, however, some imbalance on plot
size; as discussed in Section 3.1, log area (measured in hectares) is larger inside the command
area than outside the command area. This imbalance is weaker in the SFE speciﬁcation than
in the RDD speciﬁcation, such that the omnibus test fails to reject the null of balance for
the SFE speciﬁcation (although we reject for the RDD speciﬁcation). However, we note that
this imbalance would bias us against ﬁnding the eﬀects we see in Section 3.2 on horticulture,
input use, labor use, and yields, as all of these variables are larger in smaller plots in both
the command area and outside the command area. Additionally, as suggested in Section
3.1, we ﬁnd some additional imbalance on duration of plot ownership when the important
control for distance to the boundary is omitted in Columns 3 and 4.22 We therefore present
21
Speciﬁcally, we allow plot managed by household j and plot managed by household j to have
correlated errors if there exists a plot k such that ∈ Nkist or k ∈ N jst , and ∈ Nkist or k ∈ N j st .
22
We note that this imbalance goes the opposite direction suggested by the concern that the construction
of the command area caused an increase in transactions before our baseline. This, combined with the
coeﬃcient dropping to 0 with the inclusion of controls, indicates that this imbalance is caused by relative
position on the hillside and not by the command area. In fact, as shown in Table A11, we do ﬁnd in follow
up surveys that the command area causes an increase in rentals out to other farmers. However, as discussed
in Appendix G, because we tracked plots across transactions, this did not lead to diﬀerential attrition and
19
results estimated using Equation (1), which does not control for distance to the boundary
or log area, and using Equations (2) and (3), which do control for distance to the boundary
and log area.
Following the ownership results, Table 3 examines the characteristics of households whose
sample plots are just inside or just outside the command area. First, note that Column 1,
which does not restrict to the discontinuity sample, performs poorly here; we ﬁnd signiﬁcant
imbalance on half of our variables, and the omnibus test rejects the null of balance. However,
we fail to reject balance for our preferred speciﬁcations (Columns 4, 7, and 8, Table 3) which
restrict to the discontinuity sample; households with sample plots just inside the command
area appear similar to households with sample plots just outside the command area. In
Column 5, there are signiﬁcant diﬀerences in whether the household head is female is the
age of the household head, and in Column 7, there is a signiﬁcant diﬀerence in whether the
household head has completed primary schooling or not. We note that 1 out of 10 variables
signiﬁcant at the 10% level is what one would expect due to chance.
Lastly, in Section 5.1.1, we consider the characteristics of households’ most important
plots; we show that these appear similarly balanced.
3.2 Estimating the eﬀects of irrigation
3.2.1 Adoption Dynamics
Figure 4 presents the share of plots irrigated by season for sample plots just inside the
command area and sample plots outside the command area. First, as the irrigation sites
were already partially online in our baseline, we already observe some increased adoption
of irrigation in the command area in 2014 Dry: sample plots in the command area are
approximately 5pp more likely to be irrigated than sample plots outside the command area.
We present results from 2014 Dry and 2015 Rainy 1 and 2 in Appendix F; consistent with
this low adoption, we do not ﬁnd signiﬁcant impacts of access to irrigation on inputs or
therefore does not bias our results.
20
output in these seasons. Second, starting with 2015, adoption of irrigation does not appear
to trend, but exhibits meaningful seasonality. Diﬀerences remain around 3pp - 6pp in the
rainy seasons, and 19pp - 26pp in the dry seasons.
Given the limited changes in adoption dynamics after 2014 and the stark diﬀerences in
adoption across dry and rainy seasons, for the remainder of our analysis we estimate (1),
(2), and (3) pooling across our three years of follow up surveys, splitting our results across
dry and rainy seasons.
3.2.2 Impacts of irrigation
We now present our results on the impact of access to irrigation on crop choices, on input
use, and on production. First, we present graphical evidence of the regression discontinuity
in Figure 5; for parsimony, we do so only for the dry seasons (2016 Dry, 2017 Dry, and 2018
Dry).23 In each of the regression discontinuity ﬁgures, distance to the canal in meters is
represented on the x-axis, with a positive sign indicating that the plot is on the command
area side of the boundary. Second, we present regression evidence in Tables 4, 5, and 6. In
the discussion below, we focus on results from the tables, but we note that these results are
consistent with visual intuition from Figure 5.
First, in line with results from Section 3.2.1, command area plots are 16pp - 20pp more
likely to be irrigated during the dry season than plots outside the command area, and almost
all of this increase is explained by the transition to cultivation of high value horticulture
during this dry season. In contrast, adoption of irrigation during the rainy season is much
lower, with increases of just 4pp - 6pp. This transition to dry season horticulture substitutes
for cultivation of perennial bananas, a less productive but less input intensive commercial
crop; we estimate a decrease of 13pp - 17pp in the command area, and as a consequence we
observe no impacts on overall cultivation in the dry season.24
23
Rainy season diﬀerences are always smaller and generally not visually noteworthy; we focus most of our
discussion on the dry season results.
24
As bananas are perennials, plots cultivated with bananas typically have harvests in each season. In
contrast, the rotations of staples and horticulture (or simply horticulture) that replace bananas may only
21
Second, we ﬁnd large increases in dry season input use, which are dominated by increases
in household labor. These results are consistent with the transition from perennial bananas,
which require little inputs and labor, into horticulture, which is highly input and labor in-
tensive. To interpret these results, we conduct a treatment on the treated analysis under
the assumption that the command area increases input use only through its eﬀect on irri-
gation. Doing so, we ﬁnd that adoption of irrigation increases household labor use, input
expenditures, and hired labor expenditures by 340 - 450 person-days/ha, 25,000 - 39,000
RwF/ha, and 19,000 - 28,000 RwF/ha, respectively; these numbers are similar to diﬀerences
in input intensity of dry season horticulture and bananas reported in Table 1. The impacts
on household labor are particularly large – valued at a typical wage of 800 RwF/person-day,
this labor would be priced at 280,000 - 360,000 RwF/ha, an order of magnitude larger than
the eﬀects on input expenditures or hired labor expenditures. Additionally, as reference,
applying this labor to 0.3 ha (median household landholdings) of command area land would
require roughly 4 person-months of labor during the 3 month dry season. In contrast to
these dry season results, we ﬁnd no eﬀects on input use during the rainy seasons.
Third, consistent with our estimates of impacts on input use, we ﬁnd large increases in
dry season agricultural production. Treatment on the treated analysis suggests adoption
of irrigation increases yields by 300,000 - 450,000 RwF/ha, 49 - 72% of annual agricultural
production. As horticulture is primarily commercial: each 1 RwF/ha increase in yields is
associated with a 0.76 - 0.89 RwF/ha increase in sales. Once again, these results on outputs
are consistent with diﬀerences between bananas and horticulture production reported in
Table 1. Additionally, these impacts on yields are much larger than our estimates of impacts
on input and hired labor expenditures; our results suggest irrigation increases yields net
of expenditures by 250,000 - 390,000 RwF/ha, a 44 - 71% increase in annual yields net of
expenditures. However, we should not interpret this as impacts on proﬁts, as it implicitly
places no value on the large increases in household labor. If we instead value household
involve two plantings and harvests, and we therefore see a modest decrease in cultivation during the rainy
seasons of 5pp - 9pp on a baseline of 84%.
22
labor at 800 RwF/person-day, the median wage we observe, these impacts vanish completely.
Therefore, the proﬁtability of the transition to dry season horticulture enabled by irrigation
depends crucially on the shadow wage at which household labor is valued.25
Taken together, these results suggest that irrigation leads to a large change in production
practices for a minority of farmers. Those farmers cultivate horticulture in the dry season
and a mix of horticulture, staples, and fallowing in the rainy seasons, they have substantially
higher earnings in the dry season but similar earnings in the other seasons, and they invest
more in inputs and much more in household labor in the dry seasons. Our estimates suggest
that irrigation has the potential to be transformative in Africa, in light of the 44 - 71% in-
creases in yields net of expenditures that we document from just three months of cultivation.
At the same time, these results also suggest that the shadow wage, and therefore labor mar-
ket frictions, are likely to be important for the decision to cultivate horticulture. Building
on this result, we next adapt the classical agricultural household model (Singh et al., 1986;
Benjamin, 1992) to develop tests for the role of market failures in adoption of irrigation.
3.2.3 Discussion of spillovers
There are three categories of spillovers we anticipate in our context – across household
spillovers, within plot (across season) spillovers, and within household (across plot) spillovers.
The across household spillovers we anticipate are general equilibrium eﬀects. First, as
access to irrigation increases demand for labor, we expect this to put upward pressure on
wages. Second, as access to irrigation increases sales of horticulture, we expect the prices
of horticultural crops to decrease.26 Although our discontinuity design does not allow us
25
In Appendix B, we estimate impacts of access to irrigation on household welfare. Although these
estimates are imprecise, all point estimates are positive and some are statistically signiﬁcant. These results
are consistent with positive impacts of access to irrigation on proﬁts, although smaller impacts than implied
by estimates that do not value household labor.
26
We do not anticipate general equilibrium eﬀects in other markets would meaningfully aﬀect our results.
First, agricultural inputs are signiﬁcantly more tradable than horticultural output, and we therefore do
not anticipate eﬀects on agricultural input prices. Second, although we do also ﬁnd an increase in land
transactions caused by access to irrigation in Appendix G, only a small share of plots that receive access to
irrigation are transacted. We therefore anticipate any general equilibrium eﬀects through land markets to
be small.
23
to estimate these general equilibrium eﬀects, in Appendix C we plot wages and prices of
agricultural output by season to see if we observe any increase in wages or decrease in the
price of horticulture. While we ﬁnd no evidence that wages or staple prices changed after
the hillside irrigation schemes became operational, we ﬁnd some suggestive evidence that
prices of horticultural crops decreased in one of the sites.27
To interpret the impact of these potential price eﬀects, ﬁrst note that, abstracting from
within household spillovers, our estimates are the partial equilibrium eﬀect of access to
irrigation conditional on observed wages and prices. Second, note that essentially all dry
season horticultural production in these sites is on irrigated plots. If horticulture prices
decline in these sites in response to irrigation, we therefore interpret that eﬀects of irrigation
access on revenues and proﬁts are smaller than they would be with frictionless trade.
The within plot (across season) spillovers we anticipate are driven by the shift out of
perennial bananas, which causes a change in patterns of cultivation during the rainy season,
while adoption of irrigation is primarily during the dry season. We estimate these spillovers
and discuss further in Section 3.2.2; we do not ﬁnd strong evidence of impacts on rainy
season labor, inputs, yields, or proﬁts.
The within household (across plot) spillovers we anticipate are driven by the increase
in demand for labor and inputs we observe on the sample plot, which may lead households
to substitute labor and inputs away from their other plots. If households face constraints,
this spillover may be ﬁrst order in our context and would generate ineﬃciency in technology
adoption. To address this, in Section 4 we model a household’s agricultural production
decisions and how they can generate substitution across plots, and in Section 5 we estimate
these spillovers and quantify their implications for our estimates and for eﬃciency.
27
In section 5 we will provide evidence that farmers are optimizing labor inputs with respect to shadow
wages rather than market wages. This may explain why market wages do not respond to the increased labor
demand from irrigation.
24
4 Testing for binding constraint
4.1 Model
Farmers have 2 plots, indexed by k : k = 1 indicates the sample plot, while k = 2 indicates
the most important plot. On each plot k , they have access to a simple production technology
σAk Fk (Mk , Lk ) where Ak is plot productivity, Mk is the inputs applied to plot k and Lk is the
household labor applied to plot k . The common production shock σ is a random variable such
that σ ∼ Ψ(σ ), E [σ ] = 1.28 While this speciﬁcation assumes a single production function
on each plot, we can think of Fk (Mk , Lk ) as the envelope of production functions from
cultivating diﬀerent fractions of bananas and horticulture on the dry season; thus we will
think of cultivating bananas as optimizing at a low input intensity. Utilizing subscripts to
indicate partial derivatives and subsuming arguments we assume FkM > 0, FkL > 0, FkM L >
0, FkM M < 0, FkLL < 0.29 Farmers have a budget of M which, if not utilized for inputs, can
be invested in a risk-free asset which appreciates at rate r. In this context, farmers maximize
expected utility over consumption and leisure l, considering their budget constraint and a
labor constraint L which is allocated to labor on each plot, leisure, and up to LO units of oﬀ
farm labor LO .30 Finally, we model irrigation access as an increase in A1 . As we consider
the role of each diﬀerent constraint, we develop the necessary assumptions to produce the
results from Section 3: that this increase in A1 generates an increase in demand for inputs
and labor on plot A1 .
28
While we refer to σ as a production shock, this incorporates general uncertainty in the value of produc-
tion which includes joint price and production risk.
29
Among these, FkM L > 0 is the most controversial. Existing evidence on FkM L in developing country
agriculture is mixed (see Heisey & Norton (2007) for discussion). In our context, we expect FkM L > 0 pri-
marily because Fk (·, ·) encompasses the transition from bananas to horticulture, which should be associated
with increased input demands according to Stylized Fact 2.
30
We follow Benjamin (1992) in modeling incomplete labor markets as driven by an oﬀ farm labor con-
straint. As in Benjamin (1992), we do so to match the observation that rural wages appear to be higher than
the productivity of on-farm labor. However, for the predictions that follow it is suﬃcient that households
face a downward sloping labor demand curve.
25
Farmers maximize expected utility
max E [u(c, l)]
M1 ,M2 ,L1 ,L2 ,l,LO
subject to the constraints enumerated above
σA1 F (M1 , L1 ) + σA2 F (M2 , L2 ) + wLO + r(M − M1 − M2 ) = c
M1 + M2 ≤ M
L1 + L2 + l + LO = L
LO ≤ LO
In this framework, there are three crucial constraints farmers may face that cause deviations
from expected proﬁt maximization: access to insurance may be limited, reducing input use
to avoid basis risk; credit or access constraints may limit input use; and farmers’ oﬀ farm
labor allocations may be constrained from above, resulting in overutilization of labor on the
household farm. In analyzing model predictions we discuss the cases in which each of these
constraints do or do not bind.31
After substituting in the constraints which bind with equality, we derive the following
ﬁrst order conditions32
cov(σ,uc )
(Mk ) 1+ E[uc ]
Ak FkM = (1 + λM )r (4)
cov(σ,uc )
(Lk ) 1+ E[uc ]
Ak FkL = (1 − λL )w (5)
E[u ]
( ) E[uc ]
= (1 − λL )w (6)
Intuitively, the ﬁrst order conditions for inputs and labor include three parts. First, each
31
These constraints correspond with those most commonly cited by farmers in focus groups as driving crop
choice. In particular, farmers frequently cite imbaraga, or strength, of the household head (corresponding to
labor market constraints), igishoro, or access to capital (corresponding to credit or input market constraints),
and isoko, or access to markets (corresponding to price risk, or insurance market constraints).
32
The derivation is in Appendix D.
26
contains the marginal product of the factor, Ak FkM and Ak FkL respectively, on the left hand
side, and the market price of the factor, r and w respectively, on the right hand side. The
second piece, 1 + cov( σ,uc )
E[uc ]
, is the ratio of the marginal utility from agricultural production to
the marginal utility from certain consumption. This ratio scales down the marginal product
of the factor. It is less than 1 because agricultural production is uncertain, and higher
in periods in which marginal utility is lower, so cov(σ, u1 ) < 0. With perfect insurance,
cov(σ, u1 ) = 0, and this piece disappears. Without it, however, farmers will underinvest
in both inputs and labor relative to the perfect insurance optimum.33 Third, there are the
Lagrange multipliers associated with the input constraint λM and with the labor constraint
λL , which scale the associated factor prices up and down, respectively.
When these constraints do not bind, and with perfect insurance, we have the familiar
result that marginal products equal marginal prices. However, if any of these constraints
bind, then separation fails: farmer characteristics which are related to λL , λM , or cov(σ, u1 )
will be correlated with ineﬃcient input allocation on all plots (ineﬃciently low in the case
of inputs and ineﬃciently high in the case of labor).
4.2 A test for separation failures
In this context, we consider a new test of separation: the eﬀect of a change in access to
irrigation on the sample plot on production decisions on the most important plot. Much of
the literature that tests for separation, building on Benjamin (1992), has focused on tests
built around the assumption that household characteristics should not aﬀect the household’s
optimal production decisions under perfect markets. We instead leverage the assumption
that access to irrigation on the sample plot (the “sample plot shock”) should not aﬀect the
optimal production decisions on the household’s most important plot.
Following our model, we show how these market failures in insurance, labor, or input
33
This result does not generically hold in models of agricultural households, as when consumption is
separately modeled, households that are net buyers of an agricultural good may overinvest in inputs and
labor relative to the perfect insurance optimum (Barrett, 1996). This is unlikely to be ﬁrst order in our
context, as we sampled cultivators and our results are driven by production of commercial crops.
27
markets generate a separation failure between production decisions on the sample plot and
production decisions on the most important plot. First, we derive the classic separation
result from Singh et al. (1986) in our framework when there are no market imperfections.
Proposition 1. If no constraint binds, separation holds and input and labor use on the most
important plot does not respond to the sample plot shock.
Showing this result is straightforward: with perfect markets for inputs, labor, and insur-
cov(σ,uc )
ance, E[uc ]
= 0, λL = 0, and λM = 0, respectively. The ﬁrst order conditions then simplify
to
(Mk ) Ak FkM = r
(Lk ) Ak FkL =w
E [u ]
( ) E[uc ]
=w
The household’s labor and input allocations on plot 2 depend only on plot 2 productivity
A2 , the price of inputs r, and the wage w, and not on access to irrigation on plot 1 (A1 ).
In contrast to the case with perfect markets, in the presence of market failures, the sample
plot shock can aﬀect the households allocations on its most important plot. Roughly speak-
ing, the sample plot shock increases the household’s agricultural production, and increases
its labor and input demands on the sample plot. When markets fail, this reduces the value
the household places on agricultural production, and increases its opportunity costs of labor
and inputs, and the household reduces its labor and input allocations on its most important
plot. The following propositions require additional assumptions on the shape of the utility
function or on the distribution of σ ; we highlight those in the text below each proposition.
Proposition 2. If input, labor, or insurance constraints bind, then input and labor use are
reduced on the most important plot in response to the sample plot shock.34
34
See proof in Appendix D.
28
The logic case-by-case is as follows. First, if input constraints bind, then the increase in
inputs on the sample plot caused by access to irrigation must be associated with a reduction
in inputs on the most important plot. As inputs and labor are complements, this causes labor
allocations on the most important plot to fall as well. Second, if labor constraints bind, then
the increase in labor on the sample plot caused by access to irrigation must be associated
with a reduction in the sum of leisure and labor on the most important plot. Under standard
restrictions on the household’s on farm labor supply, this must be associated with a reduction
in labor on the most important plot.35 As inputs and labor are complements, this causes
input allocations on the most important plot to fall as well. Third, absent insurance, then
the increase in agricultural production caused by access to irrigation reduces the marginal
utility from agricultural production relative to the marginal utility from consumption.36 In
turn, this causes labor and input allocations to the most important plot to fall.
An implicit assumption we make that generates this result is the absence of function-
ing land markets. With perfectly functioning land markets, shocks to the household’s land
endowment, such as the sample plot shock, should not aﬀect productive decisions on the
household’s most important plot. Instead, both the sample plot and most important plot
would ﬂow to the household with the highest willingness-to-pay for them. In practice, land
transactions do occur; as discussed in Section 2.2.2, our survey tracks plots across transac-
tions in land markets, so we are able to directly test the prediction that the sample plot
shock does not aﬀect the productive decisions on the most important plot itself.
Proposition 2 produces a test of separation. Rejecting separation with this test implies
that the levels of irrigation adoption are ineﬃcient and that land market failures contribute
to this ineﬃciency. At the same time, this test does not allow us to test for which other con-
straints interact with land market frictions to generate separation failures. This is because
35
Speciﬁcally, we assume that leisure demand is increasing in consumption; this assumption is not neces-
sary but is suﬃcient.
36
This does not generically hold; however, restrictions on the distribution of σ are suﬃcient to imply that
marginal utility from agricultural production relative to the marginal utility from consumption is falling in
agricultural production. Details are in Appendix D.
29
the presence of any set of constraints that generate separation failures yields the same predic-
tion: the sample plot shock should cause input and labor allocations on the most important
plot to fall. In particular, the intuition that observing changes in input allocations, labor
allocations, or cropping decisions on the most important plot might suggest the presence
of input constraints, labor constraints, or insurance constraints, respectively, fails, because
inputs, labor, and horticulture are all complements in the production function.
4.3 Separating constraints
To shed light on which other constraints generate separation failures, we leverage the fact
that our model oﬀers predictions about how households with diﬀerent characteristics should
diﬀerentially respond to the sample plot shock. Roughly speaking, depending on which
constraint binds, changes in diﬀerent household characteristics may slacken or tighten the
binding constraint. We focus on two important household characteristics in our model: we
use household size to shift L, the household’s total available labor, and wealth to shift M , the
household’s exogenous income available for input expenditures. We present these predictions
below.
Proposition 3. If input constraints or insurance constraints bind, then the input and labor
allocations on the most important plot of larger households (wealthier households) should be
less (less) responsive to the sample plot shock.37
Under insurance constraints, both wealth and household size enter the model symmetri-
cally by increasing consumption; therefore, in all cases, wealthier and larger households will
respond similarly to the sample plot shock. If we additionally assume that risk aversion is
decreasing suﬃciently quickly in consumption, then the allocations of wealthier and larger
households will be closer to those maximizing expected proﬁts, and therefore allocations on
the most important plot will be less responsive to the sample plot shock.
37
See proof in Appendix D.
30
Under input constraints, wealthier households are less likely to see the constraint bind.
As the allocations on the most important plot of unconstrained households do not respond
to the sample plot shock, wealthier households should be less responsive. Now, note that
in this model, farmers cannot use labor income to purchase additional inputs. In a more
general model with borrowing, they may be able to; in that case, both wealthier households
and larger households are less likely to see the constraint bind, and therefore will both be
less responsive to the sample plot shock on their most important plots.38
Proposition 4. If labor constraints bind, then the relative responsiveness of input and labor
allocations on the most important plot of larger households (wealthier households) to the sam-
ple plot shock cannot be signed without further assumptions. If larger households and poorer
households have more elastic on farm labor supply schedules, and if on farm labor supply
exhibits suﬃcient curvature, then the input and labor allocations on the most important plot
of larger households (wealthier households) should be less (more) responsive to the sample
plot shock.39
When labor constraints bind, the household responds to the sample plot shock by allo-
cating additional labor to the sample plot, but they may withdraw that labor from either
the most important plot or from leisure. Whether wealthier or larger households withdraw
relatively more labor from the most important plot depends on the higher order derivatives
of the utility and production functions; in general, these diﬀerential responses can not be
signed.40 Additionally, one key diﬀerence from the insurance case and input case is that
household size and wealth no longer enter the model symmetrically. In one sense, household
size and wealth instead enter the model as opposing forces: wealthier households allocate
less labor to their plots, as they value leisure relatively more than consumption, while larger
38
If all households are input constrained, then the eﬀect of the sample plot shock on input allocations
on the most important plot depends on characteristics of the production function. Note that in this case,
larger households will still exhibit a response in the same direction as wealthier households as both eﬀects
enter only through the wealth channel.
39
See proof in Appendix D.
40
Of course, the potential for ambiguous responses is heightened further if other forms of labor constraints,
for example on hiring labor, are also considered.
31
households allocate more labor to their plots.
We focus on one particular case that builds on this intuition, presented in Figure 6.
When on farm labor supply exhibits suﬃcient curvature, then changes in responsiveness to
the sample plot shock of allocations on the most important plot are dominated by changes
in the elasticity of on farm labor supply; suppose this to be the case, and further suppose
that the elasticity of on farm labor supply is decreasing in the shadow wage. As we can
think of household size as shifting out on farm labor supply (by increasing L), and wealth
as shifting in on farm labor supply (by increasing the marginal utility of leisure relative to
the marginal utility of consumption), then larger households are located on a more elastic
portion of their on farm labor supply schedule, while wealthier households are located on a
less elastic portion of their on farm labor supply schedule.41 As a result, larger households
will be less responsive to the sample plot shock, as they will primarily draw labor on the
sample plot from leisure, while wealthier households will be more responsive to the sample
plot shock, as they will primarily draw labor on the sample plot from the most important
plot.
These predictions of the model, summarized in Table 7, generate a test that allows us to
reject the absence of labor constraints. In particular, note that while insurance constraints
or input constraints can rationalize the allocations of wealthier households to their most
important plot as less responsive to the sample plot shock, only the presence of labor con-
straints can rationalize them as more responsive to the sample plot shock. Additionally,
note that the model would struggle to rationalize larger households as more responsive to
the sample plot shock, although it is possible to do so in the presence of labor constraints. In
sum, we would interpret observing larger households as (weakly) less responsive and richer
households as less responsive to the sample plot shock as most consistent with the presence
of either input or insurance constraints, observing larger households as less responsive and
richer households as more responsive as evidence for the presence of labor constraints, and
41
This relationship between household size, wealth, and on farm labor supply elasticity has been posited
as far back as Lewis (1954), and is discussed in depth in Sen (1966).
32
observing larger households as more responsive as inconsistent with our model.
5 Separation failures and adoption of irrigation
5.1 Empirical strategy
Our ﬁrst speciﬁcation to test for separation failures mirrors Equation (1), which we use to
estimate the impacts of irrigation. We still make use of the discontinuity across the command
area boundary, but outcomes are now on the household’s most important plot (plot 2) instead
of the sample plot (plot 1).
y2ist = β0 + β1 CA1is + αst + 2ist (7)
We report β1 , the eﬀect of the sample plot shock on outcomes on the most important plot.
In other speciﬁcations, we also consider heterogeneity with respect to the location of the
most important plot, and include CA1is ∗ CA2is to test for this. In these speciﬁcations, we
also report this diﬀerence in diﬀerences coeﬃcient. For both this coeﬃcient and β1 , in line
with the model predictions in Table 7, we interpret negative coeﬃcients on labor, inputs,
irrigation use, and horticulture, as evidence of separation failures.
As in Section 3, we include speciﬁcations with progressively more controls. Speciﬁcally,
we also estimate
y2ist = β0 + β1 CA1is + β2 Dist1is + β3 CA1is ∗ Dist1is + β4 CA2is + γ1 X1is + γ2 X2is + αst + 2ist (8)
y2ist − y 2ist = β1 (CA1is − CA1is ) + (V1is − V 1is ) γ1 + (V2is − V 2is ) γ2 + ( 2ist − 2ist ) (9)
Equation 8 includes controls CA2is , an indicator for whether the most important plot is in
the command area, and X1is and X2is , the log area of the sample plot and the most important
33
plot, respectively. Equation 9 uses spatial ﬁxed eﬀects, as described in Section 3.1.42
Our benchmark speciﬁcation to test for which constraints drive the separation failures is
similar, but also includes the interaction of households characteristics with the sample plot
shock. For parsimony, we only present the speciﬁcation of this interaction for a speciﬁcation
similar to Equation 8; all tables present results with interactions included in Equation 7 and
Equation 9 similarly.
y2ist = β0 + β1 CA1is + Wi β2 + CA1is ∗ Wi β3 + β4 Dist1is + β5 CA1is ∗ Dist1is
+β6 CA2is + X1is γ1 + X2is γ2 + αst + 2ist (10)
where Wi is a vector of household characteristics, which includes household size and an asset
index in our primary speciﬁcations. We focus on β3 : the heterogeneity, with respect to
household characteristics, of the impacts of the sample plot shock on outcomes on the most
important plot. The signs on β3 give our main test of which market failures cause separation
failures; Table 7 presents which signs map to which market failures.
5.1.1 Balance
We now use speciﬁcations (7), (8), and (9) to examine whether the most important plots in
our sample are comparable for households whose sample plot is just inside or just outside
the command area. As in Section 3.1.1, for each of these speciﬁcations, we show balance
both with key controls omitted (Columns 3, 5, and 6), and our preferred speciﬁcations which
we use in our analysis with key controls included (Columns 4, 7, and 8). Balance tests for
most important plots are reported in Table 8. First, note that speciﬁcations that do not
restrict to the discontinuity sample perform particularly poorly here. Most notably, most
important plots are more likely to be located in the command area when sample plots are
42
Note that all diﬀerencing in this speciﬁcation is done using the location of sample plots; in other words,
most important plots whose associated sample plots are near each other are compared, as opposed to most
important plots which are near each other.
34
also located in the command area, as households’ plots tend to be located near each other.
In contrast, our preferred speciﬁcations (Columns 4, 7, and 8, Table 8) which restrict to the
discontinuity sample correct for this imbalance. Otherwise, we have a p-value of less than 0.1
for one variable in Column 4 (an indicator for owning the plot); for all three speciﬁcations,
the omnibus test fails to reject the null of balance.
As an additional check, in Appendix F, we estimate for 2014 Dry speciﬁcations (7), (8),
and (9), and speciﬁcations with heterogeneity following Equation (10). As the command
area, as of the baseline, had not yet caused a large increase in demand for labor or inputs,
or caused large increases in agricultural production, we would not anticipate any eﬀects on
MIPs. In line with this prediction, we fail to ﬁnd any consistent signiﬁcant eﬀects on MIPs,
either in our main speciﬁcations or for heterogeneity.
5.2 Results
5.2.1 A test for separation failures
We now present results on separation failures, demonstrating that the sample plot shock
causes farmers to substitute away from their most important plot.43 First, we present graph-
ical evidence of this substitution in Figure 7. As in earlier ﬁgures, distance of the sample
plot to the canal in meters is represented on the x-axis, with a positive sign indicating that
the plot is on the command area side of the boundary. However, we now plot outcomes on
both the sample plot and the most important plot. In this ﬁgure, substitution will manifest
as decreases in input and labor use on the most important plot when the sample plot is
in the command area, while input and labor use increase on the sample plot. Second, we
present regression evidence in Tables 9, 10, and 11. In the discussion below, we focus on
results from the tables, but we note that these results are consistent with visual intuition
43
We present results only for the dry seasons (2016 Dry, 2017 Dry, and 2018 Dry), because these are the
primary seasons for irrigation use, during which we anticipate substitution eﬀects. Additionally, we present
results only on cultivation decisions and input use, because we expect these substitution eﬀects to be smaller
than the direct eﬀects and therefore we do not anticipate being able to detect eﬀects on output. These
additional results are available upon request.
35
from Figure 7.
First, consistent with the presence of separation failures, in Columns 3 through 5 we ﬁnd
households substitute labor and inputs away from their most important plot. Households
decrease allocations of household labor (11 - 33 person-days/ha) and inputs (2,100 - 6,700
RwF/ha) on their most important plot in response to the sample plot shock. Additionally,
they substitute away from labor and input intensive technologies, consistent with our in-
terpretation of the production function as the envelope of production functions across crop
choices. Households decrease use of irrigation (1.9 - 4.4pp) and cultivation of horticulture
(1.6 - 3.8pp), while increasing cultivation of bananas (6.5 - 9.2pp).44
Next, we expect the results above to be driven primarily by most important plots located
in the command area for most outcomes. This is because there is limited irrigation, and
therefore input use or horticulture during the dry season, on plots that cannot be irrigated.
Consistent with this, in Columns 6 through 8, we ﬁnd our results on irrigation, horticulture,
and inputs are all driven by plots located in the command area. When the most important
plot is located in the command area, the 16 - 20pp increase in irrigation use on sample plots in
the command area coincides with a 8 - 10pp decrease in irrigation use on the most important
plot; these relative magnitudes suggest that separation failures cause few households to be
able to use irrigation on more than one plot in the command area.
As discussed in Section 3, the direct eﬀects of the command area appear driven by
enabling the transition to dry season horticultural cultivation and substitution away from
lower value banana cultivation. However, the model in Section 4 is agnostic about whether
decreases in labor and input allocations on the most important plot are driven by extensive
margin responses (i.e., decreases in horticulture) or intensive margin responses (i.e., decreases
in labor and input allocations conditional on crop choice). To test this, in Tables 12 and 13,
44
While these results are not consistently statistically signiﬁcant, the speciﬁcations used lose power by
including most important plots outside the command area, which are almost never irrigated and have small
allocations of labor and inputs during the dry season. As discussed in the next paragraph, speciﬁcations which
include the interaction of the sample plot command area indicator with a most important plot command
area indicator are more precise for irrigation use, horticulture cultivation, and labor and input use.
36
we present results of the sample plot shock on labor and input use on sample plots and most
important plots, controlling for cultivation and crop choice.45 Table 12 conﬁrms that the
eﬀects we document in Section 3 are driven by the shift to dry season horticulture, as eﬀects
on sample plots all but disappear controlling for crop choice. However, Table 13 suggests
that much of the eﬀect of the sample plot shock on labor and input use on most important
plots is driven by intensive margin responses, as coeﬃcients on household labor and inputs
fall by only 18% - 36%. Combined with our results on irrigation use and horticulture,
this suggests that households respond to the sample plot shock on both the intensive and
extensive margins on their most important plot.
These results on separation failures imply the existence of a within household negative
spillover, as they show that having one additional plot in the command area causes a house-
hold to substitute away from their other plots, reducing their use of irrigation, labor, and
inputs on those plots. In principle, this means that our estimates of the impacts of irriga-
tion are the impacts of irrigating one of a farmers’ plots, gross of any input reallocations
made by the farmers across plots in response to that irrigation. We would be particularly
concerned about the bias generated by these reallocations if inputs were being shifted out
of production on non-irrigated plots: in that case, our estimated impacts of access to irri-
gation would include reduced farming intensity on non-irrigated plots. However, we don’t
observe large reallocations of inputs away from non-CA plots: when the MIP is out of the
command area, the estimated eﬀect of an additional command area plot on inputs applied
to the MIP is usually about 1/4 the magnitude of the eﬀect on inputs in a command area
MIP46 and generally not statistically diﬀerent from zero. We therefore conclude that the
dominant within-household spillover is a reduced intensity of cultivation on irrigated plots,
45
As crop ﬁxed eﬀects are a “bad control” (Angrist & Pischke, 2008), which introduces selection bias, we
interpret these results as suggestive. However, we anticipate that selection conditional on crop choice should
bias us towards ﬁnding no intensive margin eﬀect on most important plots, as the particularly constrained
households switching out of horticulture in response to the sample plot shock are likely to be the households
who used less labor and inputs.
46
The coeﬃcient on sample plot in CA is usually about 1/3 the magnitude of the coeﬃcient on sample
plot in CA * MIP in CA in tables 9, 10, and 11 and MIPs in the CA experience the sum of both eﬀects
37
suggesting that any bias in our ToT estimates above may be small and render those estimates
conservative47 .
5.2.2 Impacts of separation failures on adoption of irrigation
We now quantify the impact of separation failures on adoption of irrigation. We ask what
would happen to adoption of irrigation if all households with two or more plots in the
command area only had one plot in the command area. This counterfactual follows naturally
from our estimates of the eﬀect of the sample plot shock on adoption of irrigation on the
most important plot, which we can interpret as the eﬀect of a household’s second plot (the
sample plot) being moved to the command area on adoption of irrigation on its ﬁrst plot in
the command area (the most important plot).
Speciﬁcally, we calculate
(# of HH with 2 CA plots) ∗ 2 ∗ (β1 + β3,CA )
(# of HH with 2 CA plots) ∗ 2 + (# of HH with 1 CA plot)
First, (β1 + β3,CA ) is the total eﬀect of the sample plot shock on adoption of irrigation on
most important plots in the command area. Second, in the denominator, we count the
total number of command area plots among households’ sample plots and most important
plots.48 Third, in the numerator, we apply the estimated substitution caused by the sample
plot shock to both the sample plot and the most important plot, as households are also
substituting away from their sample plot when the most important plot is in the command
area.
We ﬁnd adoption of irrigation would be 21% - 24% higher under this counterfactual.
This counterfactual relates to land market frictions – absent these frictions, we would expect
that the increased adoption of irrigation caused by this reallocation would be achieved by
47
This view is further supported by table 12, which indicates that conditional on crop choice sample plots
in the CA are cultivated with very similar intensity to sample plots outside of the CA
48
We implicitly ignores households’ other plots; we do so because our research design has little to say
about the impacts of additional command area plots, or on households’ behavior on these plots, so we
interpret this exercise as estimating a lower bound on the impact of reallocation on adoption of irrigation.
38
land markets. Intuitively, under perfect land markets, characteristics of the household that
manages a particular command area plot at baseline, including the number of other command
area plots that household managed at baseline, should not aﬀect equilibrium adoption of
irrigation on that plot. Relatedly, as shown in the model, this would also be true if all
markets (except potentially land markets) were frictionless.
5.2.3 Separating constraints
We now provide evidence on the source of the separation failure by estimating heterogeneous
impacts, with respect to household size and wealth, of the sample plot shock on outcomes on
the most important plot. Recall that for this analysis, the key predictions of the model were
1) if only insurance or input constraints bind, wealthier households and larger households
should be less responsive, and 2) if only labor constraints bind, diﬀerential responsiveness of
wealthier and larger households is ambiguous, but under reasonable assumptions wealthier
households should be more responsive and larger households should be less responsive. Note
that this test does not allow us to reject a null that a particular constraint exists; any pattern
of diﬀerential responses is consistent with all constraints binding. However, if we observe
that wealthier households are more responsive, we can reject the null of no labor constraints.
Additionally, we would interpret observing wealthier households to be more responsive and
larger households to be less responsive as the strongest evidence of the presence of labor
constraints from this test.
We present the results of this test in Tables 14 and 15. First, larger households are less
responsive to the sample plot shock across every outcome. A household with 2 additional
members, approximately one standard deviation of household size, is less responsive to the
sample plot shock on its most important plot by 50% - 94% for irrigation use, 73% - 102%
for horticulture, 63% - 75% for household labor, and 20% - 21% for inputs, with all but
the input coeﬃcient statistically signiﬁcant and robust across speciﬁcations.49 In contrast,
49
These percentages, and the remainder of percentages in this paragraph, are expressed relative to the esti-
mated impact of the sample plot shock on the most important plot, and are calculated only for Speciﬁcations
39
wealthier households are more responsive to the sample shock across these same outcomes.
A household with a one standard deviation higher asset index is more responsive to the
sample plot shock on its most important plot by 41% - 97% for irrigation use, 39% - 81%
for horticulture, 39% - 72% for household labor, and 42% - 58% for input use; however,
these results are less precise. In eﬀect, these results suggest that our estimates of separation
failures are driven by the behavior of small, rich households, while large, poor households
do not change their allocations on their most important plot in response to the sample plot
shock. As discussed in Section 4.3, these results are very diﬃcult to reconcile with a model
that does not feature labor market failures.
In sum, these results provide strong evidence for the existence of labor market failures
that generate separation failures, which in turn cause ineﬃcient adoption of irrigation.
6 Experimental evidence
Our results leveraging the discontinuity suggest that land and labor market frictions combine
to constrain the adoption of hillside irrigation in Rwanda. We design and run three experi-
ments to test for the presence of other constraints to adoption of irrigation – speciﬁcally, we
focus on operations and maintenance of irrigation schemes, and ﬁnancial and informational
constraints. These experimental results corroborate that labor market failures are a primary
constraint to adoption of irrigation in this context. Additional details on the motivation,
treatment assignment protocols, and logistics of implementation of each of these experiments
are presented in Appendix E.
First, we test whether failures of operations and maintenance impose a constraint that
limits farmers’ adoption of irrigation. The government implementing agency designed a
centralized O&M system to establish and enforce water usage schedules to ensure farmers’
access to water. If farmers faced limited access to water due to problems in the operations
and maintenance system, this could constrain adoption of irrigation. We sought to alleviate
(8) and (9).
40
this potential constraint by randomizing empowerment of local monitors to assist system
operators and report maintenance needs. We ﬁnd no evidence this experiment changed
cultivation practices. This result is likely because very few farmers report any challenges
related to operations and maintenance over the four years of survey data collection. Second,
the government planned to charge farmers in the command area land taxes, which were
unconditional on cultivation decisions, to fund operations and maintenance in the schemes.
To test whether these fees would limit farmers adoption of irrigation, we randomized subsidies
of farmers’ fees. We ﬁnd no evidence this experiment changed cultivation practices. This
result is likely because compliance with the fees was extremely low (4%), so collected fees were
too low to plausibly constrain farmers. We discuss these experiments further in Appendix
E.2, and conclude here that these issues were not relevant in this context.
Third, we test whether ﬁnancial and informational constraints limit adoption of irriga-
tion. To do so, we assigned horticultural minikits to randomly selected farmers from water
user group member lists. Each minikit included horticultural seeds, chemical fertilizer, and
insecticide, in suﬃcient quantities to cultivate 0.02 ha. In principle, these minikits should
resolve constraints related to input access, including credit constraints. In addition, they
should reduce basis risk which may resolve insurance constraints. Lastly, they should facili-
tate experimentation and increase adoption if information is a constraint. In other contexts,
minikits of similar size relative to median landholdings have been shown to increase adop-
tion of new crop varieties or varieties with low levels of adoption (Emerick et al., 2016; Jones
et al., 2018). To test for spillovers, water user groups were randomly assigned to 20%, 60%,
or 100% minikit saturation, with rerandomization for balance on Zone and O&M treatment
status. Minikits were oﬀered to assigned individuals prior to 2017 Rainy 1 and 2017 Dry.50
50
Each of these three interventions exist only in the command area. As such, the eﬀects of irrigation
estimated throughout this paper are averages across the experimental treatments. Overall, this concern
is mitigated by the fact that all three experimental treatments had very limited impacts on cultivation
practices. In addition, the ﬁrst two of these treatments (fee subsidies and monitoring systems) vary char-
acteristics which would be heterogeneous across diﬀerent irrigation systems; we are therefore comfortable
with the interpretation that estimates above exist for the average of these treatments. Readers may be most
concerned about interpretations of treatment eﬀects in the presence of the minikit treatment; in addition to
the modest eﬀects on cultivation described below, we have also conducted analysis excluding minikit winners
41
6.1 Empirical strategy and results
We estimate the impact of minikits using the speciﬁcation
y1ist = β0 + β1 Assigned minikiti + β2 Minikit saturationi + X1is γ + 1ist (11)
Assigned minikiti is a dummy for whether household i was randomly assigned to receive a
minikit, Minikit saturationi is the probability of receiving a minikit for households in the
water user group of household i’s sample plot, and X1is includes the stratiﬁcation variables
(Zone ﬁxed eﬀects and O&M treatment status), as well as indicator variables reﬂecting the
probability that a household would receive a minikit51 and in some speciﬁcations 2016 Dry
horticulture adoption. As minikit saturation is assigned at the water user groups level,
robust standard errors are clustered at the water user group level.
For our primary outcomes y , we focus on whether households used a minikit (in 2017
Rainy 1 or in 2017 Dry) and adoption of horticulture. Impacts on minikit use are our ﬁrst
stage and impacts on adoption of horticulture are our measure of learning from the minikits.
For precision, we restrict to command area plots, and for plot level outcomes we focus on
2017 Dry and 2018 Dry; these are the plots and seasons in which we expect households to
adopt horticulture in response to being assigned a minikit.
We present the results of this analysis in Table 16. First, we ﬁnd a strong ﬁrst stage;
households assigned to receive a minikit are 40pp more likely to use a minikit than households
not assigned to receive a minikit. Almost all non-compliance is driven by households who
were assigned to receieve a minikit but did not pick it up – 4.8% of households not assigned to
received a minikit used one, while 43.8% of households assigned to receive a minikit used one.
Second, we ﬁnd no eﬀects of minikits on horticulture use, and we have suﬃcient precision to
and conclusions are qualitatively unaﬀected.
51
After matching names from the lists of water user group members to our baseline survey, we found that
32% of households either had multiple household members on the lists of water user group members or had
a single household member listed multiple times; these households are more likely to be assigned to receive
a minikit and may diﬀer from other households
42
reject estimates from other contexts of the eﬀect of minikits on technology adoption (Emerick
et al., 2016; Jones et al., 2018). Third, consistent with this null eﬀect on horticulture use,
we ﬁnd no eﬀects of minikit saturation, although these estimates are less precise than those
of the impacts of assignment to receive a minikit; we note that we also fail to reject that the
sum of the coeﬃcients on assigned minikit and minikit saturation (the eﬀect on adoption in
a fully treated compared to an untreated waater user group) is zero. Fourth, we ﬁnd strong
positive selection into using a minikit: farmers who grew horticulture in 2016 Dry, who are
30.6pp more likely to grow horticulture in 2017 and 2018 Dry, are 13.1pp more likely to use
a minikit in response to assignment to receieve a minikit receipt.
We interpret these results as corroborating evidence that information and ﬁnancial con-
straints are not dominant constraints to adoption of irrigation. Most farmers assigned to
receive a minikit do not pick it up and use it, and the farmers who do pick it up typically
would have grown horticulture even if not assigned to receive a minikit. We similarly ﬁnd
no evidence that saturation of minikits lead to increased adoption, as we might expect if
learning was important.52 Our experimental evidence therefore supports the conclusion that,
in this context, ﬁnancial and informational frictions are not the primary explanations for the
low and ineﬃcient irrigation use we observe.
7 Conclusions
This paper provides evidence that irrigation has the potential to be a transformative technol-
ogy in sub-Saharan Africa. Using data from very proximate plots which receive diﬀerential
access to irrigation, we document that the construction of an irrigation system leads to a
44% - 71% increase in cash proﬁts. These proﬁts are generated by a switch in cropping
patterns from perennial bananas towards a rotation of dry-season horticulture and rainy-
season staples, which itself is associated with an increase in input intensity. In our context,
52
That information is not a binding constraint is also consistent with the stability in levels of irrigation
adoption that we observe over time, in contrast to an S-curve of adoption which would be consistent with
learning.
43
the primary increase in input demands is for household labor, which is used intensively on
horticulture and minimally on banana cultivation.
These results suggest that irrigation may have similar potential in Africa to the transfor-
mative role it played in South Asia, where other studies have documented similar impacts of
irrigation on farmer revenues and yields. In some ways, this is surprising: other evidence on
the use of inputs in Africa and the returns to those inputs often ﬁnds lower usage and tech-
nological returns in the African context. These two facts together suggest that expanding
irrigation access in Africa may be a necessary contributor to shrinking the yield gap.
At the same time, even with access to a new, highly productive technology provided
freely by the government we observe a minority of farmers adopting this technology four
years after introduction. Given the returns identiﬁed above, we take this as evidence that
the existence of a productive technology is not itself suﬃcient to generate majority adoption
in all agricultural contexts. We further document that frictions in land and labor markets
contribute to low utilization of irrigation systems by examining farmers’ input utilization
on other plots in response to irrigation investments. This result provides novel evidence
that separation failures in agricultural household production lead to land misallocation and
ineﬃcient adoption of a new technology in Rwanda.
These results highlight the need for more evidence on both the role of factor markets
in technology adoption, and the identiﬁcation of particular institutions which contribute
to or which can smooth those market failures. In some cases, these market failures may
pose a competing constraint which coexists with other, more conventional constraints to
production: if frictions in factor markets similarly constrain adoption of new technologies in
other environments, then incomplete factor markets may generate limits to the eﬀectiveness
of ﬁnancial and information interventions in improving agricultural productivity.
44
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Figure 1: Timeline
Notes: A timeline of events on the 3 hillside irrigation schemes we study is presented in this ﬁgure. Black
lines are used to indicate when (or the period during which) events took place, while pink lines are used to
indicate survey recall periods.
50
Figure 2: Hillside irrigation scheme
Notes: A photograph of Karongi 12, one of the hillside irrigation schemes in this study, is presented in this
ﬁgure.
51
Figure 3: Irrigation used for dry season labor intensive horticulture, proﬁtability depends
on household’s shadow wage
Notes: Sample averages of outcomes by crop per agricultural season are presented in this ﬁgure. In the
top panel, the height of bars is yield. Columns A show proﬁts calculated valuing household labor at 0
RwF/person-day, while Columns B show proﬁts calculated valuing household labor at 800 RwF/person-day
(the median wage in our data). In the middle and bottom panel, bars represent, in our data, the share
of observations of each set of crops that are irrigated compared to rainfed and are during the dry season
compared to the rainy season, respectively.
52
Figure 4: Adoption dynamics
Notes: Average adoption of irrigation by season on sample plots in the main discontinuity sample, inside
and outside the command area, is presented in this ﬁgure. Averages outside the command area are in black,
while averages inside the command area and 95% conﬁdence intervals for the diﬀerence are in pink. Robust
standard errors are clustered at the nearest water user group level.
53
Figure 5: Regression discontinuity estimates of impacts of irrigation
Notes: Visual regression discontinuity analysis on sample plots in the main discontinuity sample during the
dry season is presented in this ﬁgure. Distance to the boundary is reported in meters, with positive distance
corresponding to sample plots inside the command area. Points are binned average outcomes. Predicted
outcomes from regressions of outcomes on distance to the command area boundary, a command area dummy,
and their interaction are presented with 95% conﬁdence intervals on the prediction. Robust standard errors
are clustered at the nearest water user group level.
54
Figure 6: Diﬀerential responses to sample plot shock under labor constraints
Shadow wage
SM
L2 L1 + L2 L1 + L2 L − LO − l
BIG
L − LO − l
dL2 /dA1 dL2 /dA1 On-farm labor
Notes: Households’ labor allocations under a binding oﬀ farm labor constraint are presented in this ﬁgure.
Lk and l are the household’s labor allocation on plot k and choice of leisure, respectively, as a function of
the shadow wage, with the argument suppressed. L1 + L2 is total household on farm labor demand; if the
household’s sample plot (k = 1) is in the command area (“sample plot shock”), on farm labor demand shifts
SM
out to L1 + L2 . L − LO − l is household on farm labor supply; for large households, on farm labor supply
BIG
is shifted out to L − LO − l. The shadow wage is determined by the intersection of on farm labor demand
and on farm labor supply, and labor allocations on the most important plot are L2 evaluated at this shadow
wage. In this ﬁgure, larger households are on a more elastic portion of their on farm labor supply schedule; as
a result, the sample plot shock causes a smaller increase in the shadow wage, and in turn a smaller decrease
in labor allocations on the most important plot (smaller in magnitude dL2 /dA1 ).
55
Figure 7: Regression discontinuity estimates of most important plot responses to sample plot
shock
Notes: Visual regression discontinuity analysis on sample plots and associated most important plots during
the dry season, for sample plots in the main discontinuity sample, is presented in this ﬁgure. Distance to the
boundary is reported in meters, with positive distance corresponding to sample plots inside the command
area. Points are binned average outcomes. Predicted outcomes from regressions of outcomes on distance
to the command area boundary, a command area dummy, and their interaction are presented with 95%
conﬁdence intervals on the prediction. Robust standard errors are clustered at the nearest water user group
level.
56
Table 1: Summary statistics on agricultural production
Staples Horticulture
Staples Maize Beans Bananas All Rainy Dry
(1) (2) (3) (4) (5) (6) (7)
Yield 302 318 285 273 575 588 566
Hired labor (days) 37 37 37 9 61 66 57
HH labor (days) 266 248 260 101 417 414 420
Inputs 19 35 16 3 50 50 50
Proﬁts
Shadow wage = 0 RwF/day 256 255 241 263 481 489 475
Shadow wage = 800 RwF/day 43 56 34 182 147 158 139
Sales share 0.19 0.30 0.14 0.46 0.62 0.60 0.63
Irrigated 0.02 0.02 0.02 0.02 0.65 0.25 0.93
Rainy 0.99 1.00 1.00 0.50 0.42 1.00 0.00
log area -2.44 -2.26 -2.47 -2.10 -2.71 -2.83 -2.62
Share of obs. 0.65 0.13 0.42 0.19 0.12 0.05 0.07
Notes: Sample averages of outcomes by crop per agricultural season are presented in this table. Yield, inputs,
and proﬁts are reported in units of ’000 RwF/ha, labor variables are reported in units of person-days/ha,
and log area is in units of log hectares. All other variables are shares or indicators. For reference, the median
wage in our data is 800 RwF/person-day.
57
Table 2: Balance: Sample plot characteristics
Full sample RD sample
Coef. (SE) [p] Dep. var. Coef. (SE) [p]
(1) (2) (3) (4) (5) (6) (7) (8)
log area 0.045 -2.515 0.219 0.285 0.425 0.200
(0.077) (1.179) (0.087) (0.087) (0.121) (0.128)
[0.554] 969 [0.012] [0.001] [0.000] [0.118]
Own plot -0.012 0.894 0.003 -0.001 0.004 -0.004 -0.001 -0.006
(0.020) (0.309) (0.023) (0.024) (0.032) (0.038) (0.032) (0.038)
[0.535] 969 [0.897] [0.966] [0.907] [0.921] [0.972] [0.877]
Owned plot >5 years 0.045 0.880 0.070 0.072 0.019 0.012 0.007 0.010
(0.019) (0.326) (0.026) (0.025) (0.037) (0.035) (0.036) (0.034)
[0.020] 686 [0.006] [0.004] [0.613] [0.723] [0.834] [0.767]
Rented out, farmer 0.027 0.032 0.018 0.019 -0.003 0.009 -0.009 0.007
(0.012) (0.177) (0.014) (0.014) (0.023) (0.027) (0.023) (0.027)
[0.022] 969 [0.197] [0.182] [0.884] [0.726] [0.699] [0.796]
Omnibus F-stat [p] 2.6 3.4 4.9 3.2 0.6 0.1 0.1
[0.038] [0.010] [0.001] [0.013] [0.639] [0.979] [0.984]
Site FE X X X
Distance to boundary X X X X
log area X X
Spatial FE X X
Notes: Balance for sample plot characteristics is presented in this table. Column 2 presents, for sample plots
in the main discontinuity sample that are outside the command area, the mean of the dependent variable, the
standard deviation of the dependent variable in parentheses, and the total number of observations. Columns
1 and 3 through 8 present regression coeﬃcients on a command area indicator, with standard errors in
parentheses, and p-values in brackets. Robust standard errors are clustered at the nearest water user group
level in speciﬁcations without Spatial FE, and Conley (1999) standard errors are used in speciﬁcations with
Spatial FE. Controls are listed below. The ﬁnal row of each column presents the Omnibus F-stat for the
null of balance on all outcomes, with the p-value for the associated test in brackets. Column 1 uses the full
sample, while Columns 2 through 8 use the discontinuity sample. Column 4 uses the speciﬁcation in Equation
(1), Column 7 uses the speciﬁcation in Equation (2), and Column 8 uses the speciﬁcation in Equation (3).
58
Table 3: Balance: Household characteristics
Full sample RD sample
Coef. (SE) [p] Dep. var. Coef. (SE) [p]
(1) (2) (3) (4) (5) (6) (7) (8)
HHH female 0.041 0.221 0.057 0.055 0.045 0.044 0.043 0.041
(0.025) (0.416) (0.029) (0.029) (0.046) (0.050) (0.046) (0.050)
[0.094] 969 [0.054] [0.063] [0.326] [0.378] [0.345] [0.412]
HHH age 0.5 47.5 1.5 1.5 2.1 0.7 1.4 0.3
(0.8) (14.5) (0.9) (0.9) (1.4) (1.8) (1.4) (1.9)
[0.497] 967 [0.096] [0.087] [0.127] [0.694] [0.298] [0.863]
HHH completed primary 0.069 0.287 0.044 0.052 0.128 0.102 0.119 0.099
(0.025) (0.453) (0.031) (0.032) (0.047) (0.062) (0.047) (0.062)
[0.005] 966 [0.159] [0.106] [0.006] [0.097] [0.012] [0.111]
HHH worked oﬀ farm 0.023 0.410 -0.023 -0.033 -0.039 -0.019 -0.024 -0.011
(0.027) (0.493) (0.035) (0.035) (0.051) (0.064) (0.050) (0.064)
[0.392] 969 [0.516] [0.350] [0.441] [0.763] [0.631] [0.868]
# of plots 0.61 5.19 0.37 0.16 0.20 0.35 0.36 0.40
(0.18) (3.38) (0.22) (0.21) (0.36) (0.46) (0.36) (0.46)
[0.001] 969 [0.099] [0.442] [0.582] [0.448] [0.319] [0.382]
# of HH members 0.17 4.89 0.04 0.02 -0.00 -0.03 -0.01 -0.03
(0.11) (2.16) (0.15) (0.15) (0.21) (0.25) (0.22) (0.25)
[0.104] 969 [0.799] [0.916] [0.985] [0.917] [0.971] [0.908]
# who worked oﬀ farm 0.10 0.77 0.04 0.02 0.01 0.03 0.01 0.04
(0.05) (0.85) (0.06) (0.06) (0.08) (0.10) (0.08) (0.10)
[0.039] 969 [0.523] [0.771] [0.909] [0.799] [0.906] [0.722]
Housing expenditures -2.3 49.2 3.5 3.3 -5.6 -16.7 -6.5 -18.6
(6.9) (127.4) (9.0) (9.0) (14.9) (19.0) (14.7) (19.1)
[0.739] 962 [0.700] [0.717] [0.707] [0.380] [0.658] [0.328]
Asset index 0.11 -0.12 0.06 0.07 0.15 0.06 0.13 0.04
(0.05) (0.99) (0.07) (0.07) (0.12) (0.13) (0.12) (0.13)
[0.034] 967 [0.372] [0.303] [0.215] [0.647] [0.291] [0.738]
Omnibus F-stat [p] 3.6 1.6 1.6 1.8 0.8 1.5 0.9
[0.000] [0.122] [0.118] [0.080] [0.571] [0.158] [0.507]
Site FE X X X
Distance to boundary X X X X
log area X X
Spatial FE X X
Notes: Balance for household characteristics is presented in this table. Column 2 presents, for sample plots
in the main discontinuity sample that are outside the command area, the mean of the dependent variable, the
standard deviation of the dependent variable in parentheses, and the total number of observations. Columns
1 and 3 through 8 present regression coeﬃcients on a command area indicator, with standard errors in
parentheses, and p-values in brackets. Robust standard errors are clustered at the nearest water user group
level in speciﬁcations without Spatial FE, and Conley (1999) standard errors are used in speciﬁcations with
Spatial FE. Controls are listed below. The ﬁnal row of each column presents the Omnibus F-stat for the
null of balance on all outcomes, with the p-value for the associated test in brackets. Column 1 uses the full
sample, while Columns 2 through 8 use the discontinuity sample. Column 4 uses the speciﬁcation in Equation
(1), Column 7 uses the speciﬁcation in Equation (2), and Column 8 uses the speciﬁcation in Equation (3).
59
Table 4: Access to irrigation enables transition to dry season horticulture from perennial
bananas
Dry season Rainy seasons
Dep. var. Coef. (SE) [p] Dep. var. Coef. (SE) [p]
(1) (2) (3) (4) (5) (6) (7) (8)
Cultivated 0.391 0.033 0.005 0.022 0.838 -0.054 -0.092 -0.053
(0.488) (0.031) (0.041) (0.044) (0.369) (0.020) (0.025) (0.027)
2,537 [0.289] [0.909] [0.610] 4,236 [0.006] [0.000] [0.051]
Irrigated 0.058 0.202 0.162 0.171 0.016 0.044 0.035 0.059
(0.233) (0.019) (0.024) (0.030) (0.127) (0.007) (0.009) (0.012)
2,537 [0.000] [0.000] [0.000] 4,236 [0.000] [0.000] [0.000]
Horticulture 0.065 0.180 0.137 0.156 0.073 0.044 0.016 0.048
(0.246) (0.020) (0.024) (0.029) (0.260) (0.011) (0.018) (0.025)
2,536 [0.000] [0.000] [0.000] 4,235 [0.000] [0.371] [0.056]
Banana 0.245 -0.134 -0.133 -0.142 0.274 -0.149 -0.158 -0.168
(0.430) (0.024) (0.037) (0.035) (0.446) (0.024) (0.038) (0.034)
2,536 [0.000] [0.000] [0.000] 4,235 [0.000] [0.000] [0.000]
Site-by-season FE X X X X
Distance to boundary X X X X
log area X X X X
Spatial FE X X
Notes: Regression analysis is presented in this table. Columns 1 through 4 restrict to observations during
the dry season, while columns 5 through 8 restrict to observations during the rainy season. Columns 1
and 5 present, for sample plots in the main discontinuity sample that are outside the command area, the
mean of the dependent variable, the standard deviation of the dependent variable in parentheses, and the
total number of observations. Columns 2 through 4 and 6 through 8 present regression coeﬃcients on a
command area indicator, with standard errors in parentheses, and p-values in brackets. Robust standard
errors are clustered at the nearest water user group level in speciﬁcations without Spatial FE, and Conley
(1999) standard errors are used in speciﬁcations with Spatial FE. Columns 2 and 6 use the speciﬁcation in
Equation (1). Columns 3 and 7 use the regression discontinuity speciﬁcation in Equation (2). Columns 4
and 8 use the spatial ﬁxed eﬀects speciﬁcation in Equation (3).
60
Table 5: Access to irrigation causes large increases in dry season labor and input use
Dry season Rainy seasons
Dep. var. Coef. (SE) [p] Dep. var. Coef. (SE) [p]
(1) (2) (3) (4) (5) (6) (7) (8)
HH labor/ha 59.5 69.6 70.8 76.9 226.7 -7.7 8.5 9.9
(201.4) (14.7) (17.5) (20.7) (316.7) (18.3) (23.1) (24.7)
2,523 [0.000] [0.000] [0.000] 4,215 [0.671] [0.714] [0.689]
Input exp./ha 2.5 7.4 6.3 4.3 16.1 2.5 1.1 2.1
(17.4) (1.3) (1.5) (1.8) (40.9) (2.0) (2.9) (3.1)
2,527 [0.000] [0.000] [0.019] 4,223 [0.205] [0.710] [0.511]
Hired labor exp./ha 3.7 5.6 3.7 3.2 15.9 7.1 3.7 3.1
(25.6) (1.9) (2.1) (2.6) (47.1) (2.4) (3.4) (4.5)
2,527 [0.003] [0.082] [0.221] 4,223 [0.003] [0.276] [0.490]
Site-by-season FE X X X X
Distance to boundary X X X X
log area X X X X
Spatial FE X X
Notes: Regression analysis is presented in this table. Columns 1 through 4 restrict to observations during
the dry season, while columns 5 through 8 restrict to observations during the rainy season. Columns 1
and 5 present, for sample plots in the main discontinuity sample that are outside the command area, the
mean of the dependent variable, the standard deviation of the dependent variable in parentheses, and the
total number of observations. Columns 2 through 4 and 6 through 8 present regression coeﬃcients on a
command area indicator, with standard errors in parentheses, and p-values in brackets. Robust standard
errors are clustered at the nearest water user group level in speciﬁcations without Spatial FE, and Conley
(1999) standard errors are used in speciﬁcations with Spatial FE. Columns 2 and 6 use the speciﬁcation in
Equation (1). Columns 3 and 7 use the regression discontinuity speciﬁcation in Equation (2). Columns 4
and 8 use the spatial ﬁxed eﬀects speciﬁcation in Equation (3).
61
Table 6: Access to irrigation causes large increases in dry season yields and sales, proﬁtability
depends on household’s shadow wage
Dry season Rainy seasons
Dep. var. Coef. (SE) [p] Dep. var. Coef. (SE) [p]
(1) (2) (3) (4) (5) (6) (7) (8)
Yield 82.3 61.2 73.1 55.0 271.5 -45.1 -22.6 -15.4
(278.7) (20.7) (23.2) (28.5) (457.0) (22.0) (30.8) (30.8)
2,402 [0.003] [0.002] [0.054] 4,085 [0.041] [0.462] [0.617]
Sales/ha 49.7 52.3 55.5 49.3 85.1 -4.8 -13.3 5.6
(180.8) (13.3) (14.5) (19.2) (229.1) (10.8) (18.5) (21.6)
2,527 [0.000] [0.000] [0.010] 4,223 [0.660] [0.472] [0.793]
Proﬁts/ha
Shadow wage = 0 76.1 49.6 63.9 49.1 239.8 -53.4 -26.4 -19.4
(265.9) (18.6) (21.0) (25.7) (432.5) (20.5) (28.5) (27.5)
2,402 [0.008] [0.002] [0.057] 4,085 [0.009] [0.354] [0.480]
Shadow wage = 800 32.8 -0.3 9.3 -3.0 59.5 -47.2 -31.8 -27.3
(224.1) (12.0) (16.5) (20.8) (364.5) (16.5) (26.4) (31.9)
2,400 [0.978] [0.573] [0.886] 4,078 [0.004] [0.228] [0.393]
Site-by-season FE X X X X
Distance to boundary X X X X
log area X X X X
Spatial FE X X
Notes: Regression analysis is presented in this table. Columns 1 through 4 restrict to observations during
the dry season, while columns 5 through 8 restrict to observations during the rainy season. Columns 1
and 5 present, for sample plots in the main discontinuity sample that are outside the command area, the
mean of the dependent variable, the standard deviation of the dependent variable in parentheses, and the
total number of observations. Columns 2 through 4 and 6 through 8 present regression coeﬃcients on a
command area indicator, with standard errors in parentheses, and p-values in brackets. Robust standard
errors are clustered at the nearest water user group level in speciﬁcations without Spatial FE, and Conley
(1999) standard errors are used in speciﬁcations with Spatial FE. Columns 2 and 6 use the speciﬁcation in
Equation (1). Columns 3 and 7 use the regression discontinuity speciﬁcation in Equation (2). Columns 4
and 8 use the spatial ﬁxed eﬀects speciﬁcation in Equation (3).
62
Table 7: Model predictions
dL2 d dL2 d dL2
dA1 dL dA1 dM dA1
No constraints 0 0 0
Constraints
Insurance − + +
Inputs − 0/+ +
Labor − +∗ −∗
Notes: Predicted signs from the model for key comparative statics of interest are presented in this table. Pre-
dL2
dictions in the no constraints case correspond to Proposition 1. Predictions on dA 1
correspond to Proposition
d dL2 d dL2
2. Predictions on dL dA1 and dM dA1 when insurance or input constraints bind correspond to Proposition
3, and when labor constraints bind correspond to Proposition 4. * is used to indicate predictions that hold
when additional assumptions are made.
63
Table 8: Balance: Most important plot characteristics
Full sample RD sample
Coef. (SE) [p] Dep. var. Coef. (SE) [p]
(1) (2) (3) (4) (5) (6) (7) (8)
log area -0.108 -2.381 0.043 0.089 0.094 0.074
(0.068) (1.041) (0.083) (0.082) (0.128) (0.136)
[0.114] 784 [0.603] [0.275] [0.460] [0.588]
Own plot 0.025 0.875 0.048 0.043 0.040 0.033 0.039 0.029
(0.019) (0.331) (0.023) (0.023) (0.033) (0.039) (0.032) (0.037)
[0.174] 784 [0.037] [0.064] [0.226] [0.392] [0.232] [0.436]
Owned plot >5 years 0.005 0.960 -0.004 -0.003 0.012 0.033 0.011 0.030
(0.014) (0.197) (0.016) (0.016) (0.024) (0.024) (0.023) (0.025)
[0.728] 585 [0.811] [0.853] [0.617] [0.175] [0.617] [0.233]
Rented out, farmer 0.013 0.033 -0.006 -0.006 -0.026 -0.040 -0.029 -0.041
(0.010) (0.179) (0.013) (0.013) (0.022) (0.025) (0.023) (0.026)
[0.224] 784 [0.664] [0.645] [0.249] [0.114] [0.222] [0.116]
Command area 0.187 0.399 0.074 0.045 -0.053 -0.079
(0.032) (0.491) (0.039) (0.037) (0.058) (0.059)
[0.000] 784 [0.059] [0.219] [0.360] [0.183]
Terraced 0.017 0.626 -0.030 -0.043 -0.099 -0.091 -0.076 -0.058
(0.028) (0.485) (0.035) (0.035) (0.053) (0.055) (0.051) (0.052)
[0.539] 784 [0.403] [0.225] [0.063] [0.099] [0.134] [0.260]
Rented out, comm. farmer 0.035 0.081 0.017 0.008 -0.042 -0.016 -0.036 -0.004
(0.018) (0.273) (0.025) (0.023) (0.040) (0.034) (0.036) (0.031)
[0.054] 784 [0.486] [0.735] [0.292] [0.638] [0.324] [0.895]
Omnibus F-stat [p] 5.6 1.8 1.6 1.3 1.5 1.4 1.2
[0.000] [0.093] [0.132] [0.278] [0.153] [0.209] [0.292]
Site FE X X X
Distance to boundary X X X X
log area X X
MIP log area X X
MIP CA X X
Spatial FE X X
Notes: Balance for most important plot characteristics is presented in this table. Column 2 presents,
for sample plots in the main discontinuity sample that are outside the command area, the mean of the
dependent variable, the standard deviation of the dependent variable in parentheses, and the total number
of observations. Columns 1 and 3 through 8 present regression coeﬃcients on a command area indicator,
with standard errors in parentheses, and p-values in brackets. Robust standard errors are clustered at the
nearest water user group level in speciﬁcations without Spatial FE, and Conley (1999) standard errors are
used in speciﬁcations with Spatial FE. Controls are listed below. The ﬁnal row of each column presents the
Omnibus F-stat for the null of balance on all outcomes, with the p-value for the associated test in brackets.
Column 1 uses the full sample, while Columns 2 through 8 use the discontinuity sample. Column 4 uses
the speciﬁcation in Equation (7), Column 7 uses the speciﬁcation in Equation (8), and Column 8 uses the
speciﬁcation in Equation (9).
64
Table 9: Sample plot shock causes households to substitute labor and input intensive irri-
gated horticulture away from most important plot
Sample plot MIP
Coef. (SE) [p] Dep. var. Coef. (SE) [p]
(1) (2) (3) (4) (5) (6) (7) (8)
Cultivated
CA 0.033 0.368 0.049 0.038 0.004 0.085 0.076 0.059
(0.031) (0.483) (0.023) (0.040) (0.049) (0.030) (0.043) (0.048)
[0.289] 2,179 [0.035] [0.344] [0.930] [0.005] [0.079] [0.215]
CA * MIP CA -0.094 -0.089 -0.121
(0.053) (0.052) (0.056)
[0.078] [0.089] [0.030]
Joint F-stat [p] 3.9 2.1 2.7
[0.021] [0.122] [0.070]
Irrigated
CA 0.202 0.114 -0.019 -0.044 -0.036 0.013 -0.004 0.010
(0.019) (0.319) (0.017) (0.026) (0.033) (0.008) (0.020) (0.026)
[0.000] 2,179 [0.251] [0.087] [0.270] [0.123] [0.836] [0.686]
CA * MIP CA -0.097 -0.094 -0.103
(0.035) (0.035) (0.045)
[0.006] [0.007] [0.021]
Joint F-stat [p] 4.1 3.6 2.7
[0.019] [0.028] [0.069]
Site-by-season FE X X X X X
Distance to boundary X X X X
log area X X X X
Spatial FE X X
MIP log area X X X X
MIP CA X X X X X
Notes: Regression analysis is presented in this table. Column 1 uses outcomes on the sample plot (and
replicates analysis in Table 4), while Columns 3 through 8 use outcomes on the associated most important
plot. All columns restrict to observations during the dry season. Column 2 presents, for the most important
plot associated with sample plots in the main discontinuity sample that are outside the command area, the
mean of the dependent variable, the standard deviation of the dependent variable in parentheses, and the
total number of observations. For Columns 1 and 3 through 8, Rows “CA” present coeﬃcients on a command
area indicator for the sample plot, while Rows “CA * MIP in CA” present coeﬃcients on the interaction of
a command area indicator for the sample plot with a command area indicator for the most important plot;
standard errors are in parentheses, and p-values are in brackets. Robust standard errors are clustered at
the nearest water user group level in speciﬁcations without Spatial FE, and Conley (1999) standard errors
are used in speciﬁcations with Spatial FE. Column 3 uses the speciﬁcation in Equation (7), Column 4 uses
the speciﬁcation in Equation (8), and Column 5 uses the speciﬁcation in Equation (9). Columns 6 though 8
uses analogous speciﬁcations building on Equation (10).
65
Table 10: Sample plot shock causes households to substitute labor and input intensive
irrigated horticulture away from most important plot
Sample plot MIP
Coef. (SE) [p] Dep. var. Coef. (SE) [p]
(1) (2) (3) (4) (5) (6) (7) (8)
Horticulture
CA 0.180 0.109 -0.016 -0.038 -0.037 0.010 -0.004 -0.007
(0.020) (0.312) (0.016) (0.024) (0.029) (0.009) (0.018) (0.023)
[0.000] 2,179 [0.323] [0.110] [0.206] [0.244] [0.813] [0.771]
CA * MIP CA -0.082 -0.080 -0.066
(0.035) (0.035) (0.044)
[0.020] [0.021] [0.133]
Joint F-stat [p] 2.9 2.7 1.3
[0.060] [0.070] [0.286]
Banana
CA -0.134 0.199 0.066 0.092 0.065 0.077 0.096 0.087
(0.024) (0.399) (0.023) (0.032) (0.036) (0.033) (0.041) (0.044)
[0.000] 2,179 [0.004] [0.004] [0.072] [0.021] [0.019] [0.047]
CA * MIP CA -0.013 -0.009 -0.048
(0.043) (0.042) (0.044)
[0.766] [0.824] [0.275]
Joint F-stat [p] 5.9 4.5 2.0
[0.003] [0.013] [0.139]
Site-by-season FE X X X X X
Distance to boundary X X X X
log area X X X X
Spatial FE X X
MIP log area X X X X
MIP CA X X X X X
Notes: Regression analysis is presented in this table. Column 1 uses outcomes on the sample plot (and
replicates analysis in Table 4), while Columns 3 through 8 use outcomes on the associated most important
plot. All columns restrict to observations during the dry season. Column 2 presents, for the most important
plot associated with sample plots in the main discontinuity sample that are outside the command area, the
mean of the dependent variable, the standard deviation of the dependent variable in parentheses, and the
total number of observations. For Columns 1 and 3 through 8, Rows “CA” present coeﬃcients on a command
area indicator for the sample plot, while Rows “CA * MIP in CA” present coeﬃcients on the interaction of
a command area indicator for the sample plot with a command area indicator for the most important plot;
standard errors are in parentheses, and p-values are in brackets. Robust standard errors are clustered at
the nearest water user group level in speciﬁcations without Spatial FE, and Conley (1999) standard errors
are used in speciﬁcations with Spatial FE. Column 3 uses the speciﬁcation in Equation (7), Column 4 uses
the speciﬁcation in Equation (8), and Column 5 uses the speciﬁcation in Equation (9). Columns 6 though 8
uses analogous speciﬁcations building on Equation (10).
66
Table 11: Sample plot shock causes households to substitute labor and input intensive
irrigated horticulture away from most important plot
Sample plot MIP
Coef. (SE) [p] Dep. var. Coef. (SE) [p]
(1) (2) (3) (4) (5) (6) (7) (8)
HH labor/ha
CA 69.6 66.8 -11.2 -32.2 -33.2 3.2 -13.6 -15.4
(14.7) (210.5) (11.9) (20.0) (23.8) (6.2) (14.1) (19.2)
[0.000] 2,166 [0.351] [0.107] [0.162] [0.609] [0.338] [0.422]
CA * MIP CA -41.7 -44.1 -39.7
(26.8) (23.5) (31.2)
[0.120] [0.060] [0.204]
Joint F-stat [p] 1.2 1.8 1.1
[0.290] [0.164] [0.324]
Input exp./ha
CA 7.4 5.6 -2.1 -6.0 -6.7 0.2 -3.3 -3.8
(1.3) (28.2) (1.5) (2.7) (2.8) (0.7) (1.8) (2.1)
[0.000] 2,169 [0.158] [0.028] [0.017] [0.805] [0.070] [0.076]
CA * MIP CA -6.3 -6.3 -6.5
(3.4) (3.2) (3.7)
[0.067] [0.044] [0.079]
Joint F-stat [p] 1.7 2.6 3.0
[0.190] [0.078] [0.050]
Hired labor exp./ha
CA 5.6 3.9 -0.9 -1.8 -0.5 0.8 0.2 1.5
(1.9) (24.6) (1.3) (2.1) (2.3) (1.2) (2.1) (2.6)
[0.003] 2,169 [0.506] [0.404] [0.825] [0.477] [0.922] [0.546]
CA * MIP CA -4.4 -4.7 -4.5
(2.7) (2.5) (3.1)
[0.099] [0.066] [0.146]
Joint F-stat [p] 1.4 1.8 1.1
[0.255] [0.175] [0.345]
Site-by-season FE X X X X X
Distance to boundary X X X X
log area X X X X
Spatial FE X X
MIP log area X X X X
MIP CA X X X X X
Notes: Regression analysis is presented in this table. Column 1 uses outcomes on the sample plot (and
replicates analysis in Table 5), while Columns 3 through 8 use outcomes on the associated most important
plot. All columns restrict to observations during the dry season. Column 2 presents, for the most important
plot associated with sample plots in the main discontinuity sample that are outside the command area, the
mean of the dependent variable, the standard deviation of the dependent variable in parentheses, and the
total number of observations. For Columns 1 and 3 through 8, Rows “CA” present coeﬃcients on a command
area indicator for the sample plot, while Rows “CA * MIP in CA” present coeﬃcients on the interaction of
a command area indicator for the sample plot with a command area indicator for the most important plot;
standard errors are in parentheses, and p-values are in brackets. Robust standard errors are clustered at
the nearest water user group level in speciﬁcations without Spatial FE, and Conley (1999) standard errors
are used in speciﬁcations with Spatial FE. Column 3 uses the speciﬁcation in Equation (7), Column 4 uses
the speciﬁcation in Equation (8), and Column 5 uses the speciﬁcation in Equation (9). Columns 6 though 8
uses analogous speciﬁcations building on Equation (10).
67
Table 12: Impacts of access to irrigation are explained by transition to horticulture from
bananas
Sample plot
Dep. var. Coef. (SE) [p]
(1) (2) (3) (4) (5) (6) (7)
HH labor/ha 59.5 69.6 70.8 76.9 12.0 30.0 29.0
(201.4) (14.7) (17.5) (20.7) (10.2) (13.2) (14.8)
2,523 [0.000] [0.000] [0.000] [0.239] [0.023] [0.051]
Input exp./ha 2.5 7.4 6.3 4.3 0.6 1.2 -1.5
(17.4) (1.3) (1.5) (1.8) (0.9) (1.2) (1.4)
2,527 [0.000] [0.000] [0.019] [0.509] [0.330] [0.302]
Hired labor exp./ha 3.7 5.6 3.7 3.2 1.7 0.8 0.3
(25.6) (1.9) (2.1) (2.6) (1.5) (2.0) (2.5)
2,527 [0.003] [0.082] [0.221] [0.275] [0.681] [0.894]
Site-by-season FE X X X X
Distance to boundary X X X X
log area X X X X
Spatial FE X X
Crop X X X
Notes: Regression analysis is presented in this table. All columns restrict to observations during the dry
season. Column 1 presents, for sample plots in the main discontinuity sample that are outside the command
area, the mean of the dependent variable, the standard deviation of the dependent variable in parentheses,
and the total number of observations. Columns 2 through 7 present regression coeﬃcients on a command area
indicator, with standard errors in parentheses, and p-values in brackets. Robust standard errors are clustered
at the nearest water user group level in speciﬁcations without Spatial FE, and Conley (1999) standard errors
are used in speciﬁcations with Spatial FE. Columns 2 and 5 use the speciﬁcation in Equation (1). Columns
3 and 6 use the regression discontinuity speciﬁcation in Equation (2). Columns 4 and 7 use the spatial ﬁxed
eﬀects speciﬁcation in Equation (3). Columns 5, 6, and 7 also include controls for cultivation, horticulture,
and bananas.
68
Table 13: Impacts of sample plot shock on most important plot are on both extensive and
intensive margins
MIP
Dep. var. Coef. (SE) [p]
(1) (2) (3) (4) (5) (6) (7)
HH labor/ha 66.8 -11.2 -32.2 -33.2 -9.2 -25.0 -21.4
(210.5) (11.9) (20.0) (23.8) (9.1) (14.1) (16.8)
2,166 [0.351] [0.107] [0.162] [0.312] [0.077] [0.203]
Input exp./ha 5.6 -2.1 -6.0 -6.7 -1.5 -4.6 -4.9
(28.2) (1.5) (2.7) (2.8) (1.2) (2.1) (2.2)
2,169 [0.158] [0.028] [0.017] [0.227] [0.032] [0.023]
Hired labor exp./ha 3.9 -0.9 -1.8 -0.5 -0.8 -1.4 0.2
(24.6) (1.3) (2.1) (2.3) (1.2) (1.9) (2.1)
2,169 [0.506] [0.404] [0.825] [0.483] [0.482] [0.915]
Site-by-season FE X X X X
Distance to boundary X X X X
log area X X X X
MIP log area X X X X
MIP CA X X X X
Spatial FE X X
Crop X X X
Notes: Regression analysis is presented in this table. All columns restrict to observations during the dry
season. Column 1 presents, for the most important plot associated with sample plots in the main discontinuity
sample that are outside the command area, the mean of the dependent variable, the standard deviation of
the dependent variable in parentheses, and the total number of observations. Columns 2 through 7 present
regression coeﬃcients on a command area indicator for the sample plot, with standard errors in parentheses,
and p-values in brackets. Robust standard errors are clustered at the nearest water user group level in
speciﬁcations without Spatial FE, and Conley (1999) standard errors are used in speciﬁcations with Spatial
FE. Columns 2 and 5 use the speciﬁcation in Equation (7). Columns 3 and 6 use the regression discontinuity
speciﬁcation in Equation (8). Columns 4 and 7 use the spatial ﬁxed eﬀects speciﬁcation in Equation (9).
Columns 5, 6, and 7 also include controls for cultivation, horticulture, and bananas.
69
Table 14: Larger and poorer households do not substitute away from most important plot
in response to sample plot shock
MIP MIP
Coef. (SE) [p] Coef. (SE) [p]
(1) (2) (3) (1) (2) (3)
Cultivated Horticulture
CA -0.046 -0.069 -0.188 CA -0.082 -0.107 -0.129
(0.073) (0.086) (0.098) (0.041) (0.046) (0.047)
[0.526] [0.424] [0.056] [0.045] [0.020] [0.006]
CA * # of HH members 0.019 0.021 0.039 CA * # of HH members 0.013 0.014 0.019
(0.013) (0.013) (0.014) (0.008) (0.007) (0.007)
[0.158] [0.112] [0.007] [0.109] [0.061] [0.012]
CA * Asset index -0.007 -0.013 -0.043 CA * Asset index -0.019 -0.015 -0.030
(0.028) (0.027) (0.032) (0.020) (0.017) (0.021)
[0.814] [0.620] [0.181] [0.353] [0.384] [0.156]
Joint F-stat [p] 2.4 1.5 3.5 Joint F-stat [p] 1.5 1.8 2.6
[0.072] [0.213] [0.015] [0.225] [0.147] [0.050]
Irrigated Banana
CA -0.071 -0.097 -0.121 CA 0.036 0.052 -0.052
(0.043) (0.048) (0.051) (0.064) (0.065) (0.083)
[0.098] [0.046] [0.017] [0.573] [0.418] [0.532]
CA * # of HH members 0.010 0.011 0.017 CA * # of HH members 0.006 0.008 0.023
(0.009) (0.007) (0.008) (0.011) (0.011) (0.015)
[0.227] [0.155] [0.030] [0.596] [0.485] [0.110]
CA * Asset index -0.022 -0.018 -0.035 CA * Asset index 0.009 -0.003 -0.012
(0.020) (0.016) (0.020) (0.024) (0.023) (0.026)
[0.256] [0.277] [0.077] [0.696] [0.900] [0.661]
Joint F-stat [p] 1.3 1.5 2.3 Joint F-stat [p] 3.0 3.1 2.1
[0.284] [0.214] [0.079] [0.031] [0.026] [0.094]
# of HH members X X X # of HH members X X X
Asset index X X X Asset index X X X
Site-by-season FE X X Site-by-season FE X X
Distance to boundary X X Distance to boundary X X
log area X X log area X X
MIP log area X X MIP log area X X
MIP CA X X MIP CA X X
Spatial FE X Spatial FE X
Notes: Regression analysis is presented in this table. All columns use outcomes on most important plots
and restrict to observations during the dry season.. Rows “CA” present coeﬃcients on a command area
indicator for the sample plot, while Rows “CA * W” present coeﬃcients on the interaction of a command
area indicator for the sample plot with a household characteristic W; standard errors are in parentheses,
and p-values are in brackets. Robust standard errors are clustered at the nearest water user group level in
speciﬁcations without Spatial FE, and Conley (1999) standard errors are used in speciﬁcations with Spatial
FE. The Row “Joint F-stat [p]” presents F-statistics for the null that all 3 coeﬃcients are 0, with the p-value
for the associated test in brackets. Columns 1, 2, and 3 use regression speciﬁcations building on Equation
(10) following Equations (7), (8), and (9), respectively.
70
Table 15: Larger and poorer households do not substitute away from most important plot
in response to sample plot shock
MIP MIP
Coef. (SE) [p] Coef. (SE) [p]
(1) (2) (3) (1) (2) (3)
HH labor/ha Hired labor exp./ha
CA -78.5 -82.7 -94.6 CA -4.1 -4.5 -2.1
(32.0) (34.8) (38.9) (2.9) (3.6) (3.5)
[0.014] [0.018] [0.015] [0.155] [0.216] [0.551]
CA * # of HH members 13.4 10.1 12.5 CA * # of HH members 0.6 0.5 0.3
(5.5) (4.5) (4.5) (0.5) (0.5) (0.5)
[0.015] [0.025] [0.006] [0.201] [0.273] [0.539]
CA * Asset index -22.7 -12.4 -24.0 CA * Asset index -0.1 0.3 -0.3
(12.7) (10.2) (12.7) (1.4) (1.4) (1.4)
[0.074] [0.226] [0.060] [0.968] [0.856] [0.813]
Joint F-stat [p] 2.1 2.0 2.9 Joint F-stat [p] 0.8 0.6 0.1
[0.099] [0.122] [0.033] [0.488] [0.592] [0.937]
Input exp./ha # of HH members X X X
Asset index X X X
CA -6.2 -9.1 -10.3 Site-by-season FE X X
(3.5) (4.2) (4.1) Distance to boundary X X
[0.075] [0.031] [0.013] log area X X
MIP log area X X
CA * # of HH members 0.8 0.6 0.7
MIP CA X X
(0.6) (0.5) (0.5)
Spatial FE X
[0.161] [0.237] [0.185]
CA * Asset index -3.2 -2.5 -3.9
(1.8) (1.6) (1.7)
[0.076] [0.117] [0.025]
Joint F-stat [p] 1.4 1.9 2.6
[0.239] [0.128] [0.051]
# of HH members X X X
Asset index X X X
Site-by-season FE X X
Distance to boundary X X
log area X X
MIP log area X X
MIP CA X X
Spatial FE X
Notes: Regression analysis is presented in this table. All columns use outcomes on most important plots
and restrict to observations during the dry season.. Rows “CA” present coeﬃcients on a command area
indicator for the sample plot, while Rows “CA * W” present coeﬃcients on the interaction of a command
area indicator for the sample plot with a household characteristic W; standard errors are in parentheses,
and p-values are in brackets. Robust standard errors are clustered at the nearest water user group level in
speciﬁcations without Spatial FE, and Conley (1999) standard errors are used in speciﬁcations with Spatial
FE. The Row “Joint F-stat [p]” presents F-statistics for the null that all 3 coeﬃcients are 0, with the p-value
for the associated test in brackets. Columns 1, 2, and 3 use regression speciﬁcations building on Equation
(10) following Equations (7), (8), and (9), respectively.
71
Table 16: Minikits do not cause increased adoption of horticulture, strong positive selection
into minikit takeup
Minikit takeup Horticulture
(1) (2) (3) (4)
Assigned minikit 0.398 0.395 0.035 0.052
(0.038) (0.044) (0.041) (0.042)
[0.000] [0.000] [0.396] [0.221]
Minikit saturation -0.047 -0.064 -0.078 -0.067
(0.056) (0.057) (0.054) (0.054)
[0.394] [0.260] [0.149] [0.218]
Horticulture (2016 Dry) 0.046 0.306
(0.049) (0.053)
[0.345] [0.000]
Assigned minikit * Horticulture (2016 Dry) 0.131 -0.019
(0.068) (0.070)
[0.052] [0.788]
# of lotteries entered X X X X
O&M treatment X X X X
Zone FE X X X X
# of observations 910 762 838 727
# of clusters 187 170 182 167
Notes: Regression analysis is presented in this table. All columns use outcomes on sample plots. Each row
presents coeﬃcients, with robust standard errors clustered at the water user group level in parentheses, and
p-values in brackets. “Assigned minikit” is an indicator for whether the household was assigned to receive
a minikit, “Minikit saturation” is the probability of minikit assignment that was assigned to the water user
group of the household’s sample plot, and “Horticulture (2016 Dry)” is an indicator that the household
planted horticulture on their sample plot in 2016 Dry.
72
A Main variable appendix
Household variables: All household variables are constructed from the baseline.
• HHH female : Indicator that the household head is female.
• HHH age : Age of the household head.
• HHH completed primary : Indicator that the household head completed primary.
• HHH worked oﬀ farm : Indicator that the household head worked oﬀ farm.
• # of plots : Number of plots reported as managed by the household. Includes plots
rented in, plots owned and cultivated in the past year, and plots rented out.
• # of HH members : Number of members of the household.
• # of HH members who worked oﬀ farm : Number of members of the household who
worked oﬀ farm.
• Housing expenditures : Expenditures over the past year on housing and furnishing.
Winsorized at the 99th percentile.
• Asset index : First principal component of log number of assets-by-category owned and
an indicator for positive number of assets-by-category owned, where the categories are
cows, goats, pigs, chickens, radios, mobile phones, pieces of furniture, bicycles, and
shovels. Standardized to be mean 0 and standard deviation 1, with positive values
indicating more assets.
• Food security index : First principal component of log days in the past week of con-
sumption of food item-by-category and an indicator for any consumption of food item-
by-category. In baseline, categories are ﬂour, bread, rice, meat and ﬁsh, poultry and
eggs, dairy products, cooking oil, fruits, beans, vegetables, plantains and cassava and
potatoes, juice and soda, sugar and honey, salt and spices, meals prepared outside
73
home, and groundnut and other oilseed ﬂour. In follow up surveys, categories are
ﬂour, bread, cakes and chapati and mandazi, rice, small ﬁsh, meats and other ﬁsh,
poultry and eggs, dairy products, peanut oil, palm oil and other cooking oil, avocados,
other fruits, beans, tomato, onion, other vegetables, plantains, Irish potatoes, sweet
potatoes, sugar, salt, local banana beer at home, groundnut ﬂour. Standardized to be
mean 0 and standard deviation 1, with positive values indicating more consumption.
• Overall index : Index constructed following Anderson (2008) using housing expendi-
tures, asset index, and food security index.
Plot variables: All plot variables are constructed from the baseline.
• Command area : Indicator that plot located in command area, equal 1 if any share of
the plot is inside of the command area. Calculated from plot map.
• Distance to boundary : Distance from plot boundary to command area boundary, 0 for
plots whose plot map intersects the boundary. Positive for plots that are inside the
command area, negative for plots that are outside the command area. Calculated from
plot map.
• Area : Area in hectares. Calculated from plot map.
• Water user group : Water user groups that the plot is located in, calculated from plot
map. If the plot intersects multiple water user group boundaries, the water user group
in which the largest share of the plot’s area is contained. Missing for plots that are
outside the command area.
• Nearest water user group : For plots inside the command area, the water user group. For
plots outside the command area, the water user group whose boundary the boundary
of the plot is the shortest distance from. Calculated from plot map.
• Terraced : Indicator that the plot was terraced.
74
Plot-season variables: All plot-season variables are constructed from the baseline when
used in balance tables. Variables related to attrition are observed at plot-season level when
used as outcomes in regressions testing for diﬀerential attrition.
• Own plot : Indicator that the surveyed cultivator owns the plot. 0 when the surveyed
cultivator rents in the plot.
• Owned plot >5 years : Indicator that the surveyed cultivator had owned the plot for
at least 5 years.
• Rented out to farmer : Indicator that the surveyed cultivator rented out the plot to
another farmer.
• Rented out to commercial farmer : Indicator that the plot was rented out to a com-
mercial farmer.
• HH attrition : Plot-season indicator that the household associated with the plot was
not reached for the survey.
• Transaction (not tracked) : Plot-season indicator that the plot was sold, rented out, or
no longer rented in, and the new household responsible for the plot was not successfully
followed up with.
• Tracked : Plot-season indicator that the plot was sold, rented out, or no longer rented
in, and the new household responsible for the plot was successfully followed up with
and asked questions on agricultural production on the plot.
• Missing : Plot-season indicator that agricultural production data is missing for that
plot. Sum of variables HH attrition, Rented out to commercial farmer, and Transaction
(not tracked).
Agricultural variables
75
• Cultivated : Plot-season indicator for any cultivation. All other agricultural variables
are set to 0 when no cultivation takes place.
• Irrigated : Plot-season indicator for any irrigation use.
• Horticulture : Plot-season indicator for any horticulture cultivated. As horticultural
crops are annuals, this will include activities associated with planting, growing, and
harvesting.53
• Banana : Plot-season indicator for any bananas cultivated. As bananas are perennials,
this refers to any activities associated with planting, growing, or harvesting, and need
not include all three.
• HH labor/ha : Plot-season sum of household labor use, divided by plot area. Winsorized
at the 99th percentile.
• Input expenditures/ha : Plot-season sum of expenditures on non-labor inputs, divided
by plot area. Winsorized at the 99th percentile.
• Hired labor expenditures/ha : Plot-season sum of expenditures on hired labor, divided
by plot area. Winsorized at the 99th percentile.
• Hired labor (days)/ha : Plot-season sum of hired labor use, divided by plot area. Win-
sorized at the 99th percentile.
• Price : Prices are calculated at the District-crop-season level, as the median of plot-
crop-season reported sales divided by reported kilograms sold. Prices are set to missing
when there are less than 10 observations that District-crop-season and either more
than two District-crop-seasons with at least 10 observations that District-crop-survey
or at least 30 observations that District-crop-survey; these cut-oﬀ points were chosen
53
In Figure 3 and Table 1, an alternative deﬁnition of crop choice is used, where a crop indicator indicates
that crop is the primary crop cultivated that plot-season.
76
to maximize inclusion of prices judged subjectively to be reasonable, and maximize
exclusion of prices judged subjectively to be not reasonable.
• Yield : Plot-season sum of prices times harvested quantities. Yields are missing when
all crops cultivated that plot-season have missing prices or missing harvested quanti-
ties. When multiple crops are grown on a plot-season and some have observed prices
and harvested quantities, those with missing prices or quantities are treated as 0 pro-
duction. After this procedure 3.6% of rainy season observations and 5.3% of dry season
observations in our discontinuity sample have missing yields. Winsorized at the 99th
percentile.
• Sales/ha : Plot-season total reported sales, divided by area. Winsorized at the 99th
percentile.
• Sales share : Sales/ha divided by yield, equal to 1 when reported sales/ha is greater
than yield.
• Proﬁts/ha (Shadow wage = 0 RwF/day) : Yield minus hired labor expenditures/ha
minus input expenditures/ha.
• Proﬁts/ha (Shadow wage = 800 RwF/day) : Yield minus hired labor expenditures/ha
minus input expenditures/ha minus 800 times HH labor/ha.
Experimental variables: Additional details on these variables are in Appendix E.
• Assigned minikit : Indicator that household was assigned to receive a minikit.
• Minikit saturation : Saturation of minikits assigned for the Water User Group of the
plot.
• Minikit takeup : Indicator that the household reported using a minikit.
• Zone : The Zone in which the plot’s Water User Group is located in. The plots in our
survey are located in 239 Water User Groups grouped into 33 Zones.
77
• O&M treatment : O&M treatment status of the Water User Group of the plot.
• # of lotteries entered, minikits : Number of lotteries for minikits the household was
entered into.
B Household results
We present results of the impacts of access to irrigation on household welfare outcomes in
Table A1. We estimate speciﬁcations similar to Equations (1), (2), and (3), but now use
annual outcomes at the household level (instead of outcomes on sample plots).
We ﬁnd suggestive evidence of positive impacts on household welfare. All point esti-
mates are positive, and impacts on housing expenditures and an Anderson (2008) index of
household welfare are each signiﬁcantly diﬀerent from zero in two speciﬁcations. The im-
plied treatment on the treated estimates are large. However, as impacts on household are
imprecisely estimated, we interpret these results with caution.
C Prices and wages
We present ﬁgures showing the evolution of wages (Figure A1) and sale prices (Figure A2)
across the 3 hillside irrigation schemes. In Figure A1, average wages do not appear to change
after the hillside irrigation schemes became fully operational.54 In Figure A2, median sale
prices appear to display more meaningful trends. In Karongi, there do not appear to be any
trends in sale prices of horticultural crops. However, in Nyanza, sale prices of both tomatoes
and eggplants appear lower after the hillside irrigation schemes became fully operational
than before. We discuss the interpretation of these changes, if one believes they are causal,
in Section 3.2.3.
54
Median wages (not presented here) remain constant within both of the sites used for the regression
discontinuity analysis, and are slightly higher in the third site after the hillside irrigation schemes became
fully operational.
78
D Model appendix
Derivation of ﬁrst order conditions. Substitute for LO using the household labor con-
straint, L1 + L2 + + LO = L, and substitute for c in the household’s maximization problem.
This leaves two constraints, M1 + M2 ≤ M , and L − L1 − L2 − ≤ LO ; call the multipliers
on these constraints λM and λL , respectively. Taking ﬁrst order conditions yields
(Mk ) E[uc σ ]Ak FkM − E[uc ]r = λM
(Lk ) E[uc σ ]Ak FkL − E[uc ]w = −λL
( ) E[u ] − E[uc ]w = −λL
To ease interpretation, normalize λM ≡ λM /rE[uc ] and λL ≡ λL /wE[uc ], and substitute
cov(σ, uc ) = E[uc σ ] − E[uc ]E[σ ] = E[uc σ ] − E[uc ]. This yields
cov(σ,uc )
(Mk ) 1+ E[uc ]
Ak FkM = (1 + λM )r
cov(σ,uc )
(Lk ) 1+ E[uc ]
Ak FkL = (1 − λL )w
E[u ]
( ) E[uc ]
= (1 − λL )w
No constraints. When no constraints bind, as discussed the ﬁrst order conditions simplify
to
(Mk ) Ak FkM = r
(Lk ) Ak FkL =w
u
( ) uc
=w
Note that the ﬁrst order conditions for M2 and L2 are functions only of (M2 , L2 ), and ex-
dM2 dL2
ogenous (A2 , r, w). Therefore, dA1
= dA1
= 0.
79
Insurance market failure. Consider the case when insurance markets fail. To abstract
fully from labor supply, we temporarily remove leisure from the model. To further sim-
plify, we drop other inputs from the production function; when the production function is
homogeneous in labor and other inputs, this is without loss of generality. Households solve
max E[u(c)]
L1 ,L2
σ (A1 F1 (L1 ) + A2 F2 (L2 )) − w(L1 + L2 ) + wL + rM = c
To simplify the analysis, this can be rewritten as the two step optimization problem
max E[u(c)]
L
σG(L; A1 ) − wL + wL + rM = c
max aF1 (L − L2 ) + A2 F2 (L2 ) = G(L; a)
L2
E[uc (σg +c)]
Next, let γ (g, c) = E[σuc (σg +c)]
; γ ≥ 1 is the ratio of the marginal utility from consumption
to the marginal utility from agricultural production. As above, to represent derivatives of G
and γ we use subscripts to indicate partial derivatives and subsume arguments. This yields
the ﬁrst order condition
(L) GL − γ (G(L; A1 ), w(L − L) + rM )w = 0
The central intuition for this case can be captured from just the ﬁrst order condition: L
and M enter symmetrically into the model, so larger households should respond similarly to
richer households. If absolute risk aversion decreases suﬃciently quickly (e.g., with CRRA
preferences), then for suﬃciently high levels of consumption E[σuc ] = E[σ ]E[uc ] = E[uc ] ⇒
γ = 1. Therefore, suﬃciently wealthy or suﬃciently large households should not respond
to the sample plot shock. Below, we will maintain the assumption that preferences exhibit
decreasing absolute risk aversion, and that limc→∞ γ (g, c) = 1.
80
Let FOCL be the left hand side of the ﬁrst order condition for the utility maximization
problem. Then, an application of the implicit function theorem yields dL
dA1
= − ddFOC L /dA1
FOCL /dL
.
Evaluating these derivatives yields
dFOCL
= GLL + γc w2 − γg GL w
dL
dFOCL
= GLa − γG Ga
dA1
dL GLa − γg Ga
=−
dA1 GLL + γc w2 − γg GL w
Next, we use the ﬁrst order condition for constrained production maximization. Some
applications of the envelope theorem and taking derivatives yields
GL = A1 F1L
Ga = F1
GLa = F1L (1 − dL2 /dL)
GLL = A1 F1LL (1 − dL2 /dL)
dL2 dL2 dL dL2
Lastly, note that dA1
= dL dA1
+ da
, as the increase in A1 shifts both arguments to G.
Let FOCL2 denote the left hand side of the ﬁrst order condition for constrained production
dL2 dFOC
L2 /dL
maximization. Then, applications of the implicit function theorem yield dL
= − dFOCL /dL2
2
81
dL2 dFOC /da
and da
= − dFOCLL2/dL2 . Additional math yields
2
FOCL2 = −aF1L + A2 F2L
dFOCL2
= F1L
da
dFOCL2
= −aF1LL
dL
dFOCL2
= aF1LL + A2 F2LL
dL2
dL2 aF1LL
=
dL aF1LL + A2 F2LL
dL2 F1L
=−
da aF1LL + A2 F2LL
dL2
substituting these into our expression for dA1
, and in turn our expressions for derivatives of
G (in the numerator), yields
dL2 −A1 F1LL (GLa − γg Ga ) + F1L (GLL + γc w2 − γg GL w)
=
dA1 (A1 F1LL + A2 F2LL )(GLL + γc w2 − γg GL w)
(F1L w2 )γc − (F1L w − F1LL F1 )A1 γg
=
(A1 F1LL + A2 F2LL )(GLL + γc w2 − γg GL w)
To sign this expression, note that the denominator is the product of two second order
conditions, for utility maximization and for maximization of production subject to L1 =
L − L2 ; each of these is negative, so the product is positive. Therefore sign(dL2 /dA1 ) =
sign((F1L w2 )γc −(F1L w−F1LL F1 )A1 γg ). Next, note that F1L w2 > 0 and −(F1L w−F1LL F1 )A1 <
0; therefore one suﬃcient condition for this derivative to be negative is that γc < 0 and
γg > 0; in other words, increasing consumption reduces the marginal utility from consump-
tion relative to the marginal utility from agricultural production, and increasing agricultural
production increases the marginal utility from consumption relative to the marginal utility
from agricultural production. The former generically holds under decreasing absolute risk
dL2
aversion, while the latter holds under some restrictions; under these restrictions, dA1
< 0.
For one suﬃcient restriction, we follow Karlan et al. (2014) and make restrictions on the
82
1
distribution of σ . We assume that, for some k > 1, σ = k with probability k
(“the good
k −1
state”) and σ = 0 with probability k
(“the bad state”); i.e., there is a crop failure with
k −1 E[uc ucc ]
probability k
. Under this assumption. Next, deﬁne R = − uc
E[uc ]
to be the household’s
average risk aversion, and Rk = −E[ ucc
uc
|σ = k ] to be the household’s risk aversion in the
good state. Note that by decreasing absolute risk aversion, Rk < R. From this, it follows
that
E[ucc ] E[σucc ]E[uc ]
γc = − = γ (Rk − R) < 0
E[σuc ] E[σuc ]2
E[σucc ] E[σ 2 ucc ]E[uc ] E[uc |σ = 0]
γg = − = (k − 1) Rk = (kγ − 1)Rk > 0
E[σuc ] E[σuc ]2 E[uc |σ = k ]
Finally, consider the limit as household wealth increases, and assume that agricultural
production will not grow inﬁnitely with household wealth; this holds when the marginal prod-
uct of labor on each plot falls suﬃciently quickly and is true of typical decreasing returns
to scale production functions. Then, limM →∞ γ = 1 and limM →∞ γc = limM →∞ γg = 0, and
dL2 d2 L2
therefore limM →∞ dA1
= 0. We therefore expect that, heuristically on average, dA1 dM
> 0,
dL2 dL2
as dA1
< 0 and dA1
approaches 0 for large M . As L and M enter symmetrically, the same
results hold for L.
Input constraint. When only the input constraint binds, the ﬁrst order conditions simplify
to
(Mk ) Ak FkM = (1 + λM )r
(Lk ) Ak FkL =w
E[u ]
( ) E[uc ]
=w
Note that the choice of leisure does not enter into the ﬁrst order conditions for Mk or Lk .
83
Substituting M2 = M − M1 yields the following system of equations
A1 F1M (M1 , L1 ) − (1 + λM )r = 0
A1 F1L (M1 , L1 ) − w = 0
A2 F2M (M − M1 , L2 ) − (1 + λM )r = 0
A2 F2L (M − M1 , L2 ) − w = 0
Stack the left hand sides into the vector FOCM . Deﬁne the Jacobian JM ≡ D(M1 ,L1 ,λM ,L2 ) FOCM .
−1
Applying the implicit function theorem yields D(A1 ) (M1 , L1 , λM , L2 ) = −JM D(A1 ) FOCM .
Some algebra yields
A1 F1M M A1 F1M L −r 0
A1 F1M L A1 F1LL 0 0
JM =
−A F 0 −r A2 F2M L
2 2M M
−A2 F2M L 0 0 A2 F2LL
D(A1 ) FOCM = (F1M , F1L , 0, 0)
dM2
= kM A2 F2LL A1 (F1L F1M L − F1M F1LL )
dA1
dL2
= −kM A2 F2M L A1 (F1L F1M L − F1M F1LL )
dA1
dM2
where kM is positive.55 As F2LL < 0, sign dA1
= −sign (F1L F1M L − F1M F1LL ). This is
negative whenever productivity growth on plot 1 would cause optimal input allocations,
dL2
holding ﬁxed the shadow price of inputs, to increase on plot 1. Similarly, sign dA1
=
dM2
sign(F2LM )sign dA1
. The labor response and input response on the second plot have the
same sign whenever labor and inputs are complements on the second plot.
55 1
kM = − (A1 F1LL )A2 (F2M M F2LL −F 2 )+( A2 F2LL )A2 2 . We make standard assumptions re-
2 2M L 1 (F1M M F1LL −F1M L )
quired for unconstrained optimization; second order conditions for unconstrained optimization imply kM is
positive.
84
Labor constraint. When only the labor constraint binds, the ﬁrst order conditions simplify
to
(Mk ) Ak FkM = r
(Lk ) Ak FkL = (1 − λL )w
u
( ) uc
= (1 − λL )w
Substituting = L − LO − L1 − L2 and LO = LO , and some rearranging yields
A1 F1M (M1 , L1 ) − r = 0
A1 F1L (M1 , L1 ) − (1 + λL )w = 0
A2 F2M (M2 , L2 ) − r = 0
A2 F2L (M2 , L2 ) − (1 + λL )w = 0
u Ak Fk (Mk , Lk ) + r(M − M1 − M2 ) + wLO , L − LO − L1 − L2 −
k∈{1,2}
(1 + λL )wuc Ak Fk (Mk , Lk ) + r(M − M1 − M2 ) + wLO , L − LO − L1 − L2 = 0
k∈{1,2}
Stack the left hand sides into the vector FOCL .
Additionally, it will be convenient to deﬁne the following derivatives of on farm labor
demand on plot k , LDk , with respect to the shadow wage w∗ and productivity Ak , on farm
input demand on plot k , MDk , with respect to productivity Ak , and on farm labor supply,
85
LS, with respect to the shadow wage w∗ and consumption (through shifts to wealth) c. Let
Ak FkM M
LDkw∗ = 2 2
Ak (FkM M FkLL −FkM L)
Ak FkM FkM L − Ak FkL FkM M
LDkAk =
A2 2
k (FkM M FkLL − FkM L )
Ak FkL FkM L − Ak FkM FkLL
MDkAk =
A2 2
k (FkM M FkLL − FkM L )
uc
LSw∗ = −
u − (1 + λL )wuc
uc − (1 + λL )wucc
LSc = −
u − (1 + λL )wuc
We make standard assumptions required for unconstrained optimization; these imply LDkw∗
is negative (labor demand decreasing in shadow wage), and LSw∗ is positive (labor supply in-
creasing in shadow wage). We further assume LDkAk and MDkAk are positive (labor demand
and input demand are increasing in productivity); an additional suﬃcient assumption for
this is that F is homogeneous. We further assume LSc is negative (labor supply is decreasing
in wealth); an additional suﬃcient assumption for this is that u is additively separable in c
and .
86
Next, deﬁne the Jacobian JL ≡ D(M1 ,L1 ,M2 ,L2 ,λL ) FOCL . Some algebra yields
AF A1 F1M L 0 0 0
1 1M M
A1 F1M L A1 F1LL
0 0 −w
JL =
0 0 A2 F2M M A2 F2M L 0
0 0 A2 F2M L A2 F2LL −w
dFOCL, dFOCL, dFOCL, dFOCL,
dM1 dL1 dM2 dL2
−wuc
dFOCL,
= A1 F1M (uc − (1 + λL )wucc )
dM1
dFOCL,
= A1 F1L (uc − (1 + λL )wucc ) − (u − (1 + λL )wuc )
dL1
dFOCL,
= A2 F2M (uc − (1 + λL )wucc )
dM2
dFOCL,
= A2 F2L (uc − (1 + λL )wucc ) − (u − (1 + λL )wuc )
dL2
−1
Applying the implicit function theorem yields D(A1 ) (M1 , L1 , M2 , L2 , λL ) = −JL D(A1 ) FOCL .
Some further algebra, and substitution, yields
D(A1 ) FOCL = (F1M , F1L , 0, 0, (uc − (1 + λL )wucc )F1 )
dL2 LD1A1 − LSc (F1M MD1A1 + F1L LD1A1 + F1 )
= LD2w∗
dA1 LSw∗ − (LD1w∗ + LD2w∗ ) − LSc (LD1A1 + LD2A2 )
dL2 1
= LD2w∗
dL LSw∗ − (LD1w∗ + LD2w∗ ) − LSc (LD1A1 + LD2A2 )
dL2 rLSc
= LD2w∗
dM LSw∗ − (LD1w∗ + LD2w∗ ) − LSc (LD1A1 + LD2A2 )
dL2
dA1
< 0; for interpretation, note that this expression is the derivative of labor demand on
plot 2 with respect to the shadow wage, times the eﬀect of the shock to A1 on the shadow
wage. The numerator of the latter is the eﬀect the shock on negative residual labor supply
through direct eﬀects (LD1A1 ) and wealth eﬀects, including through adjustments of labor
and inputs (−LSc (F1M MD1A1 + F1L LD1A1 + F1 )). The denominator of the latter is the
derivative of residual labor supply with respect to the shadow wage, adjusted for wealth
87
eﬀects (LSw∗ − (LD1w∗ + LD2w∗ ) − LSc (LD1A1 + LD2A2 )).
d2 L2 d2 L2
The signs of dLdA1
and dM dA1
are ambiguous. However, unlike the cases of input market
failures or insurance market failures, here these second derivatives may have opposite signs.
To see one example of this, consider a case where on farm labor and input demands are
approximately linear in the shadow wage and productivity, and on farm labor supply is
approximately linear in consumption, but exhibits meaningful curvature with respect to the
d L2 2 d 2
d L2 d
shadow wage. In this case, sign( dLdA ) = sign dL
LSw∗ and sign( dLdA ) = sign dM
LSw∗ .
1 1
d L2 2
To focus on one case, larger households are less responsive to the A1 shock ( dLdA > 0) if
1
d
and only if they are on a more elastic portion of their labor supply curve ( dL LSw∗ > 0).
That larger households, with more labor available for agriculture, or poorer households, who
likely have fewer productive opportunities outside agriculture, would be on a more elastic
portion of their labor supply curve is consistent with proposed models of household labor
supply dating back to Lewis (1954). This motivates the prediction we focus on: that larger
households should be less responsive to the A1 shock, and richer households should be more
responsive to the A1 shock.
E Experimental Appendix
E.1 Experimental design
We conducted three randomized controlled trials in these hillside irrigation schemes. First,
we manipulated operations and maintenance (O&M) in the hillside irrigation schemes, by
randomly assigning water user groups to diﬀerent approaches to monitoring. Qualitative
work raised concerns that the water user groups as established would not be suﬃcient to
enforce water usage schedules and that routine maintenance tasks would not be performed
adequately, as has been documented by Ostrom (1990). Second, we subsidized water usage
fees the government had planned to collect from farmers, which were as high as 77,000
RwF/ha/year. For reference, this is roughly 20% of our dry season treatment on the treated
88
estimates, and roughly 50% of median land rental prices. If farmers believed that they were
more likely to be required to pay the fees if they used the irrigation infrastructure, then
these fees had the potential to inﬂuence farmers production decisions, (even though they are
small relative to potential yield gains from irrigation use). Third, we provided agricultural
minikits, which included 0.02 ha of seeds, chemical fertilizer, and insecticide, which could
be used for horticulture cultivation. In other contexts, minikits of similar size relative to
median landholdings have been shown to increase adoption of new crop varieties or varieties
with low levels of adoption (Emerick et al., 2016; Jones et al., 2018). Although horticulture
is not unfamiliar in these areas, at baseline 3.2% of plots outside the command area were
planted with at least some horticulture, and primarily during the rainy seasons.
Assignment to experimental arms for O&M, minikits, and subsidies were as follows.
First, for the O&M intervention, 251 water user groups across three irrigation sites were
randomized, stratiﬁed across the 33 Zones these irrigation sites are divided into, into three
arms.56 Second, for the minikit intervention, water user groups were randomly assigned to
20%, 60% or 100% saturation, with rerandomization for balance on Zone and O&M treatment
status. Following this assignment, individuals on the lists of water user group members
provided to us by the sites were randomly assigned to receive minikits with probabilities
equal to that water user group’s saturation. Minikits were oﬀered to assigned individuals
prior to 2017 Rainy 1 and 2017 Dry. Third, for the subsidy intervention, our implementing
partner was concerned with the perception of an assignment rule that might be perceived as
hidden, so public lotteries for subsidies were conducted at the Zone level.57
56
40% were assigned to a status quo arm where the irrigator/operators employed by the site were respon-
sible for enforcing water usage schedules and reporting O&M problems to the local Water User Association.
30% were assigned to an arm where the water user group elected a monitor who was tasked with these
responsibilities, trained in implementing them, and given worksheets to ﬁll and return to the Water User
Association reporting challenges with enforcement of the water usage schedule and any O&M concerns. In
an additional 30%, the elected monitor was required to have a plot near the top of the water user group,
where the ﬂow of water is most negatively impacted when too many farmers try to irrigate at once. Monitors
were trained just before the 2016 Dry season, with refresher trainings during 2016 Dry and 2017 Rainy 1.
57
At these public lotteries, 40% of farmers received no subsidy, 20% received a 50% subsidy for one season,
20% received a 100% subsidy for one season, and 20% received a 100% subsidy for two seasons. The lotteries
took place at the start of the 2017 Rainy 1, and subsidies were for 2017 Rainy 1 and 2017 Rainy 2; at the
time the Water User Associations did not plan to collect fees during the Dry season.
89
E.2 O&M and Fee Subsidies
We ﬁnd no eﬀects of empowering monitors and fee subsidies on agricultural decisions in
our context; we oﬀer some qualitative evidence and simple descriptives from our data that
explain these null eﬀects.58
First, we ﬁnd no impact of empowering monitors. This is because O&M was highly
eﬀective in these irrigation schemes, and empowering monitors therefore had limited scope
for changing O&M practices. Farmers reported 14% as many days without enough water
during the dry seasons as they reported days using irrigation. Any event where conﬂict
among water user group members caused insuﬃcient water at some point during the dry
season was reported for 3% of irrigated plots.59 This success was far from guaranteed in
the early years of the schemes; site engineers have suggested that the combination of lower
adoption of irrigation than the schemes are designed for and high compliance with water
usage schedules among farmers have been the cause of this. Moreover, during the 2018 Dry
season we found evidence that control water user groups adopted the intervention, as some
members of control water user groups adopted the roles that were assigned to monitors.
Second, we ﬁnd no impact of fee subsidies. The reason for this is clear – although we have
a strong and large ﬁrst stage on fees owed by farmers in administrative data, the impacts
of subsidies on feed paid by farmers were 10% of the size of the impacts on fees owed, both
in administrative data and self reports. Moreover, the fees were implemented as land taxes
and not charged based on irrigation use so as not to discourage adoption. In sum, at the low
levels of enforcement observed during the 2017 Rainy seasons, they should not have aﬀected
farmers’ production decisions, consistent with the results we ﬁnd.
58
Results are available upon request.
59
This magnitude is small; as reference, Sekhri (2014) ﬁnds the share of farmers reporting disputes over
ground water in India increases by 29pp when water tables become suﬃciently low.
90
F Baseline results
We present results from 2014 Dry, when the hillside irrigation systems were online in only a
small part of the sites, and from 2015 Rainy 1 and Rainy 2, when hillside irrigation was just
beginning to come online. These surveys were just a few years after terracing occurred, and
shortly after the construction of the hillside irrigation schemes was completed.
To begin, we estimate speciﬁcations (1), (2), and (3) in Tables A2, A3, A4, and A5.
First, in Table A2, we consider two additional impacts of command area construction.
First, terracing occurred jointly with hillside irrigation. Although there was also meaning-
ful terracing outside the command area to protect against erosion, there was much more
terracing inside the command area, as it is impossible to have hillside irrigation without
terracing (as water would run oﬀ the sloped hillsides). We therefore note that our eﬀects
are the combined eﬀect of terracing and access to irrigation. However, we also note that
irrigation is used almost exclusively for dry season horticulture, and our results in Section 3
are fully explained by crop ﬁxed eﬀects, providing suggestive evidence that the transition to
dry season horticulture enabled by access to irrigation, as opposed to any direct productivity
eﬀects conditional on crop choice caused by terracing, drives our results. Second, rentals out
to commercial farmers occurred inside the command area, as these commercial farmers were
keen to take advantage of access to irrigation. These commercial farmers were private busi-
nesses exporting vegetables and they had negotiated land lease rates with the government,
and as such they were not willing to share detailed data on their proﬁtability. We discuss
the implications of this diﬀerential attrition for our results in Section G.
In addition, while our primarily agricultural outcomes for analysis are from recall over
the past three agricultural seasons, our measure of food security comes from the past week of
food consumption. Our baseline survey was conducted from August - October 2015, so most
irrigating households would have just recently harvested and sold any 2015 Dry horticultural
production. Consistent with this, in Table A2 we ﬁnd signiﬁcant impacts of the command
area on food security at baseline.
91
Second, in Table A3, we estimate impacts on cultivation, irrigation, and crop choice
decisions; consistent with irrigation not having come fully online, we observe limited adoption
of irrigation. In contrast to our main results from follow up surveys, at baseline cultivation
is lower in the dry season inside the command area. This is driven by a combination of
low adoption of irrigation and horticulture (only 2 - 5pp higher in the command area than
outside the command area), and lower cultivation of bananas (8 - 10pp lower). These banana
eﬀects are partially explained by terracing, during which bananas were torn up to construct
the terraces. These banana eﬀects are smaller than in follow up surveys, and the share
of plots cultivated with bananas is also lower outside the command area than in follow
up surveys. Together, we interpret these results as farmers beginning to replant bananas
following terracing, but less replanting occurring inside the command area than outside. As
irrigation had come online by 2015 Rainy 1 and 2, rainy season results look similar to rainy
season results in subsequent seasons – modestly lower cultivation, and signiﬁcant but modest
increases in adoption of irrigation and horticulture, and reduced banana cultivation.
Third, we estimate impacts on inputs in Table A4, and output in Table A5. Consistent
with the small increases in horticulture and modestly larger decreases in low input intensive
bananas, we do not ﬁnd consistent signiﬁcant eﬀects on input use, yields, sales, or measures
of proﬁts in the dry season or rainy season.
Lastly, as the command area, as of the baseline, had not yet caused a large increase
in demand for labor or inputs, or caused large increases in agricultural production, we
do not anticipate any MIP eﬀects. As a placebo check, we present MIP results, estimating
speciﬁcations (7), (8), and (9), and speciﬁcations with heterogeneity following Equation (10).
We present these results in Tables A6, A7, A8, A9, and A10. In line with our prediction, we
fail to ﬁnd any consistent signiﬁcant eﬀects on MIPs, either in our main speciﬁcations or for
heterogeneity.
92
G Attrition
We present results on attrition for our sample plot regressions for speciﬁcations (1), (2), and
(3) in Table A11; we do not ﬁnd signiﬁcant diﬀerential attrition on the MIP. Additionally,
we break attrition down into three causes: household attrition (typically caused by the
household having moved), transactions to other local farmers where we failed to track the
plot across the transaction, and rentals out to commercial farmers.
We ﬁnd signiﬁcant diﬀerential attrition, but this diﬀerential attrition is driven almost
entirely by rentals out to commercial farmers in one of the two sites. These were private
businesses exporting vegetables and they had negotiated land lease rates with the govern-
ment, and as such they were not willing to share detailed data on their proﬁtability. Because
they were producing chillies and stevia for export, land rented out to commercial farmers is
likely to have much higher production and to be farmed more intensively, and therefore not
having it in our data biases our main estimates downwards. Additionally, the commercial
farmers preferred to rent land in the most productive areas of the sites, and therefore our
estimates are if anything biased downward relative to the eﬀect of access to irrigation on
production for local farmers.
Some discussion of the two other sources of attrition is potentially warranted. First,
excluding rentals out to commercial farmers, attrition is low, at 4.8% outside the command
area, and is a non statistically signiﬁcant 0.9 - 3.5pp higher inside the command area. How-
ever, in one speciﬁcation we do ﬁnd 3.2pp higher household attrition statistically signiﬁcant
at the 10% level. Lastly, tracking plots was important to correct for diﬀerential attrition –
although command area plots were not diﬀerentially likely to be transacted to other farmers
and not tracked, they were signiﬁcantly more likely to be transacted to other farmers and
tracked during the dry season (1.8 - 3.5pp).
93
Figure A1: Wages
Notes: Average wages by season across the three hillside irrigation schemes are presented in this ﬁgure.
Average wages are calculated across household-by-plot-by-season observations within site-by-season and are
weighted by person days of hired labor.
94
Figure A2: Prices
(a) Karongi (b) Nyanza
Notes: Median sale prices by season are presented in this ﬁgure. Prices are calculated separately for Karongi
district (Karongi 12 and Karongi 13) and for Nyanza district (Nyanza 23). For each district, prices are
calculated for the most commonly sold banana crop, the two most commonly sold staple crops, and the two
most commonly sold horticultural crops.
95
Table A1: Household welfare
RD sample
Dep. var. Coef. (SE) [p]
(1) (2) (3) (4)
Housing expenditures 28.03 6.35 12.10 13.91
(86.45) (5.00) (6.73) (8.25)
2,771 [0.204] [0.072] [0.092]
Asset index -0.14 0.11 0.13 0.05
(0.95) (0.07) (0.11) (0.12)
2,776 [0.104] [0.224] [0.668]
Food security index -0.12 0.08 0.07 0.07
(0.98) (0.06) (0.08) (0.10)
2,772 [0.167] [0.372] [0.509]
Overall index -0.08 0.08 0.12 0.11
(0.68) (0.05) (0.07) (0.08)
2,764 [0.071] [0.077] [0.191]
Site-by-survey FE X X
Distance to boundary X X
log area X X
Spatial FE X
Notes: Regression analysis is presented in this table. Column 1 presents, for sample plots in the main
discontinuity sample that are outside the command area, the mean of the dependent variable, the standard
deviation of the dependent variable in parentheses, and the total number of observations. Columns 2 through
4 present regression coeﬃcients on a command area indicator, with standard errors in parentheses, and p-
values in brackets. Robust standard errors are clustered at the nearest water user group level in speciﬁcations
without Spatial FE, and Conley (1999) standard errors are used in speciﬁcations with Spatial FE. Column 2
uses the speciﬁcation in Equation (1). Column 3 uses the regression discontinuity speciﬁcation in Equation
(2). Column 4 uses the spatial ﬁxed eﬀects speciﬁcation in Equation (3).
96
Table A2: Terracing, baseline rentals to commercial farmer, and baseline food security in
command area
RD sample
Dep. var. Coef. (SE) [p]
(1) (2) (3) (4)
Terraced 0.484 0.428 0.407 0.450
(0.500) (0.034) (0.055) (0.053)
969 [0.000] [0.000] [0.000]
Rented out, comm. farmer 0.018 0.183 0.173 0.168
(0.132) (0.029) (0.031) (0.044)
969 [0.000] [0.000] [0.000]
Omnibus F-stat [p] 84.6 37.7 37.3
[0.000] [0.000] [0.000]
Site FE X X
Distance to boundary X X
log area X X
Spatial FE X
RD sample
Dep. var. Coef. (SE) [p]
(1) (2) (3) (4)
Food security index -0.13 0.16 0.19 0.15
(0.98) (0.06) (0.10) (0.10)
968 [0.008] [0.053] [0.122]
Site-by-survey FE X X
Distance to boundary X X
log area X X
Spatial FE X
Notes: Regression analysis is presented in this table. Column 1 presents, for sample plots in the main
discontinuity sample that are outside the command area, the mean of the dependent variable, the standard
deviation of the dependent variable in parentheses, and the total number of observations. Columns 2 through
4 present regression coeﬃcients on a command area indicator, with standard errors in parentheses, and p-
values in brackets. Robust standard errors are clustered at the nearest water user group level in speciﬁcations
without Spatial FE, and Conley (1999) standard errors are used in speciﬁcations with Spatial FE. Column 2
uses the speciﬁcation in Equation (1). Column 3 uses the regression discontinuity speciﬁcation in Equation
(2). Column 4 uses the spatial ﬁxed eﬀects speciﬁcation in Equation (3).
97
Table A3: Sample plots (baseline)
Dry season Rainy seasons
Dep. var. Coef. (SE) [p] Dep. var. Coef. (SE) [p]
(1) (2) (3) (4) (5) (6) (7) (8)
Cultivated 0.211 -0.099 -0.128 -0.120 0.756 -0.049 -0.067 -0.048
(0.409) (0.030) (0.046) (0.051) (0.430) (0.027) (0.038) (0.042)
894 [0.001] [0.005] [0.020] 1,632 [0.074] [0.076] [0.261]
Irrigated 0.009 0.045 0.029 0.029 0.011 0.044 0.043 0.041
(0.095) (0.012) (0.016) (0.016) (0.103) (0.009) (0.011) (0.015)
894 [0.000] [0.068] [0.067] 1,632 [0.000] [0.000] [0.006]
Horticulture 0.012 0.044 0.019 0.014 0.042 0.080 0.057 0.064
(0.109) (0.014) (0.019) (0.018) (0.200) (0.015) (0.022) (0.029)
894 [0.001] [0.304] [0.454] 1,632 [0.000] [0.008] [0.029]
Banana 0.145 -0.097 -0.103 -0.077 0.162 -0.101 -0.104 -0.093
(0.352) (0.022) (0.036) (0.041) (0.369) (0.022) (0.037) (0.038)
894 [0.000] [0.005] [0.060] 1,632 [0.000] [0.005] [0.015]
Site-by-season FE X X X X
Distance to boundary X X X X
log area X X X X
Spatial FE X X
Notes: Regression analysis is presented in this table. Columns 1 through 4 restrict to observations during
the dry season, while columns 5 through 8 restrict to observations during the rainy season. Columns 1
and 5 present, for sample plots in the main discontinuity sample that are outside the command area, the
mean of the dependent variable, the standard deviation of the dependent variable in parentheses, and the
total number of observations. Columns 2 through 4 and 6 through 8 present regression coeﬃcients on a
command area indicator, with standard errors in parentheses, and p-values in brackets. Robust standard
errors are clustered at the nearest water user group level in speciﬁcations without Spatial FE, and Conley
(1999) standard errors are used in speciﬁcations with Spatial FE. Columns 2 and 6 use the speciﬁcation in
Equation (1). Columns 3 and 7 use the regression discontinuity speciﬁcation in Equation (2). Columns 4
and 8 use the spatial ﬁxed eﬀects speciﬁcation in Equation (3).
98
Table A4: Sample plots (baseline)
Dry season Rainy seasons
Dep. var. Coef. (SE) [p] Dep. var. Coef. (SE) [p]
(1) (2) (3) (4) (5) (6) (7) (8)
HH labor/ha 41.3 -7.7 -26.9 -39.5 225.4 -13.6 -5.5 -7.3
(180.0) (14.6) (23.6) (28.2) (321.7) (20.6) (23.5) (34.4)
890 [0.598] [0.255] [0.162] 1,621 [0.508] [0.815] [0.831]
Input exp./ha 1.9 2.2 1.6 1.5 12.5 1.3 2.3 4.4
(18.3) (1.5) (2.1) (2.0) (34.8) (2.2) (3.4) (3.9)
894 [0.133] [0.437] [0.458] 1,632 [0.560] [0.492] [0.265]
Hired labor exp./ha 0.8 2.2 0.7 -0.1 12.8 6.5 3.0 3.9
(5.7) (1.2) (1.4) (1.6) (42.8) (2.9) (4.2) (6.0)
894 [0.060] [0.623] [0.930] 1,632 [0.025] [0.480] [0.518]
Site-by-season FE X X X X
Distance to boundary X X X X
log area X X X X
Spatial FE X X
Notes: Regression analysis is presented in this table. Columns 1 through 4 restrict to observations during
the dry season, while columns 5 through 8 restrict to observations during the rainy season. Columns 1
and 5 present, for sample plots in the main discontinuity sample that are outside the command area, the
mean of the dependent variable, the standard deviation of the dependent variable in parentheses, and the
total number of observations. Columns 2 through 4 and 6 through 8 present regression coeﬃcients on a
command area indicator, with standard errors in parentheses, and p-values in brackets. Robust standard
errors are clustered at the nearest water user group level in speciﬁcations without Spatial FE, and Conley
(1999) standard errors are used in speciﬁcations with Spatial FE. Columns 2 and 6 use the speciﬁcation in
Equation (1). Columns 3 and 7 use the regression discontinuity speciﬁcation in Equation (2). Columns 4
and 8 use the spatial ﬁxed eﬀects speciﬁcation in Equation (3).
99
Table A5: Sample plots (baseline)
Dry season Rainy seasons
Dep. var. Coef. (SE) [p] Dep. var. Coef. (SE) [p]
(1) (2) (3) (4) (5) (6) (7) (8)
Yield 46.5 -20.0 -30.4 -31.4 171.2 11.4 5.7 -1.6
(216.3) (17.3) (23.5) (30.4) (307.4) (19.0) (22.8) (29.0)
868 [0.249] [0.197] [0.302] 1,585 [0.548] [0.804] [0.957]
Sales/ha 27.1 -2.4 -26.2 -37.2 45.0 26.1 9.5 24.5
(148.7) (11.3) (21.7) (28.7) (144.7) (9.7) (13.8) (17.9)
894 [0.829] [0.227] [0.194] 1,632 [0.007] [0.491] [0.170]
Proﬁts/ha
Shadow wage = 0 45.0 -22.8 -31.7 -32.6 146.2 5.8 0.5 -9.6
(208.5) (16.6) (22.1) (29.2) (302.9) (18.7) (23.2) (28.9)
868 [0.169] [0.153] [0.264] 1,585 [0.757] [0.984] [0.739]
Shadow wage = 800 13.4 -11.5 -16.4 -7.9 -30.0 13.9 2.8 -6.5
(108.7) (7.2) (13.9) (19.2) (266.1) (15.4) (24.0) (35.0)
864 [0.113] [0.240] [0.682] 1,575 [0.369] [0.906] [0.853]
Site-by-season FE X X X X
Distance to boundary X X X X
log area X X X X
Spatial FE X X
Notes: Regression analysis is presented in this table. Columns 1 through 4 restrict to observations during
the dry season, while columns 5 through 8 restrict to observations during the rainy season. Columns 1
and 5 present, for sample plots in the main discontinuity sample that are outside the command area, the
mean of the dependent variable, the standard deviation of the dependent variable in parentheses, and the
total number of observations. Columns 2 through 4 and 6 through 8 present regression coeﬃcients on a
command area indicator, with standard errors in parentheses, and p-values in brackets. Robust standard
errors are clustered at the nearest water user group level in speciﬁcations without Spatial FE, and Conley
(1999) standard errors are used in speciﬁcations with Spatial FE. Columns 2 and 6 use the speciﬁcation in
Equation (1). Columns 3 and 7 use the regression discontinuity speciﬁcation in Equation (2). Columns 4
and 8 use the spatial ﬁxed eﬀects speciﬁcation in Equation (3).
100
Table A6: Most important plot (baseline)
Sample plot MIP
Coef. (SE) [p] Dep. var. Coef. (SE) [p]
(1) (2) (3) (4) (5) (6) (7) (8)
Cultivated
CA -0.099 0.186 0.041 0.034 0.018 0.025 0.015 0.039
(0.030) (0.390) (0.029) (0.048) (0.058) (0.040) (0.058) (0.068)
[0.001] 751 [0.160] [0.476] [0.750] [0.528] [0.800] [0.566]
CA * MIP CA 0.043 0.046 -0.046
(0.062) (0.062) (0.069)
[0.492] [0.461] [0.512]
Joint F-stat [p] 1.4 0.6 0.2
[0.240] [0.541] [0.779]
Irrigated
CA 0.045 0.030 -0.000 0.018 0.004 -0.001 0.020 0.009
(0.012) (0.172) (0.014) (0.018) (0.019) (0.011) (0.016) (0.017)
[0.000] 751 [0.973] [0.308] [0.853] [0.920] [0.196] [0.624]
CA * MIP CA -0.002 -0.005 -0.011
(0.031) (0.030) (0.029)
[0.936] [0.869] [0.700]
Joint F-stat [p] 0.0 0.8 0.2
[0.988] [0.430] [0.854]
Site-by-season FE X X X X X
Distance to boundary X X X X
log area X X X X
Spatial FE X X
MIP log area X X X X
MIP CA X X X X X
Notes: Regression analysis is presented in this table. Column 1 uses outcomes on the sample plot (and
replicates analysis in Table A3), while Columns 3 through 8 use outcomes on the associated most important
plot. All columns restrict to observations during the dry season. Column 2 presents, for the most important
plot associated with sample plots in the main discontinuity sample that are outside the command area, the
mean of the dependent variable, the standard deviation of the dependent variable in parentheses, and the
total number of observations. For Columns 1 and 3 through 8, Rows “CA” present coeﬃcients on a command
area indicator for the sample plot, while Rows “CA * MIP in CA” present coeﬃcients on the interaction of
a command area indicator for the sample plot with a command area indicator for the most important plot;
standard errors are in parentheses, and p-values are in brackets. Robust standard errors are clustered at
the nearest water user group level in speciﬁcations without Spatial FE, and Conley (1999) standard errors
are used in speciﬁcations with Spatial FE. Column 3 uses the speciﬁcation in Equation (7), Column 4 uses
the speciﬁcation in Equation (8), and Column 5 uses the speciﬁcation in Equation (9). Columns 6 though 8
uses analogous speciﬁcations building on Equation (10).
101
Table A7: Most important plot (baseline)
Sample plot MIP
Coef. (SE) [p] Dep. var. Coef. (SE) [p]
(1) (2) (3) (4) (5) (6) (7) (8)
Horticulture
CA 0.044 0.027 0.004 0.017 0.014 0.005 0.021 0.022
(0.014) (0.161) (0.013) (0.017) (0.016) (0.009) (0.016) (0.015)
[0.001] 751 [0.738] [0.309] [0.367] [0.583] [0.195] [0.140]
CA * MIP CA -0.006 -0.009 -0.018
(0.030) (0.030) (0.031)
[0.852] [0.773] [0.549]
Joint F-stat [p] 0.2 0.9 1.1
[0.858] [0.429] [0.337]
Banana
CA -0.097 0.129 0.054 0.037 0.048 0.040 0.016 0.056
(0.022) (0.336) (0.025) (0.038) (0.046) (0.038) (0.050) (0.057)
[0.000] 751 [0.031] [0.327] [0.293] [0.291] [0.752] [0.325]
CA * MIP CA 0.043 0.051 -0.018
(0.050) (0.050) (0.058)
[0.388] [0.311] [0.759]
Joint F-stat [p] 4.6 1.6 0.6
[0.011] [0.214] [0.572]
Site-by-season FE X X X X X
Distance to boundary X X X X
log area X X X X
Spatial FE X X
MIP log area X X X X
MIP CA X X X X X
Notes: Regression analysis is presented in this table. Column 1 uses outcomes on the sample plot (and
replicates analysis in Table A3), while Columns 3 through 8 use outcomes on the associated most important
plot. All columns restrict to observations during the dry season. Column 2 presents, for the most important
plot associated with sample plots in the main discontinuity sample that are outside the command area, the
mean of the dependent variable, the standard deviation of the dependent variable in parentheses, and the
total number of observations. For Columns 1 and 3 through 8, Rows “CA” present coeﬃcients on a command
area indicator for the sample plot, while Rows “CA * MIP in CA” present coeﬃcients on the interaction of
a command area indicator for the sample plot with a command area indicator for the most important plot;
standard errors are in parentheses, and p-values are in brackets. Robust standard errors are clustered at
the nearest water user group level in speciﬁcations without Spatial FE, and Conley (1999) standard errors
are used in speciﬁcations with Spatial FE. Column 3 uses the speciﬁcation in Equation (7), Column 4 uses
the speciﬁcation in Equation (8), and Column 5 uses the speciﬁcation in Equation (9). Columns 6 though 8
uses analogous speciﬁcations building on Equation (10).
102
Table A8: Most important plot (baseline)
Sample plot MIP
Coef. (SE) [p] Dep. var. Coef. (SE) [p]
(1) (2) (3) (4) (5) (6) (7) (8)
HH labor/ha
CA -7.7 40.6 -15.0 -9.5 -37.5 -9.6 -2.4 -23.5
(14.6) (184.3) (12.2) (20.5) (27.0) (11.9) (26.2) (31.2)
[0.598] 747 [0.222] [0.642] [0.165] [0.420] [0.927] [0.452]
CA * MIP CA -14.8 -16.9 -31.0
(27.0) (27.4) (28.8)
[0.586] [0.538] [0.281]
Joint F-stat [p] 0.8 0.4 1.7
[0.449] [0.663] [0.177]
Input exp./ha
CA 2.2 1.4 1.7 3.6 0.1 1.9 3.8 1.2
(1.5) (14.7) (1.5) (1.5) (1.3) (1.2) (1.9) (1.2)
[0.133] 751 [0.262] [0.017] [0.965] [0.121] [0.039] [0.292]
CA * MIP CA -0.6 -0.6 -2.6
(3.1) (3.2) (3.7)
[0.846] [0.859] [0.478]
Joint F-stat [p] 1.2 3.0 0.6
[0.298] [0.053] [0.573]
Hired labor exp./ha
CA 2.2 5.1 -4.0 -7.5 -11.6 -2.9 -6.3 -10.0
(1.2) (32.8) (2.2) (4.2) (5.7) (2.4) (5.4) (6.8)
[0.060] 751 [0.061] [0.078] [0.041] [0.227] [0.240] [0.142]
CA * MIP CA -2.9 -2.8 -3.6
(4.5) (4.7) (5.6)
[0.522] [0.554] [0.524]
Joint F-stat [p] 1.8 2.6 2.8
[0.168] [0.079] [0.059]
Site-by-season FE X X X X X
Distance to boundary X X X X
log area X X X X
Spatial FE X X
MIP log area X X X X
MIP CA X X X X X
Notes: Regression analysis is presented in this table. Column 1 uses outcomes on the sample plot (and
replicates analysis in Table A4), while Columns 3 through 8 use outcomes on the associated most important
plot. All columns restrict to observations during the dry season. Column 2 presents, for the most important
plot associated with sample plots in the main discontinuity sample that are outside the command area, the
mean of the dependent variable, the standard deviation of the dependent variable in parentheses, and the
total number of observations. For Columns 1 and 3 through 8, Rows “CA” present coeﬃcients on a command
area indicator for the sample plot, while Rows “CA * MIP in CA” present coeﬃcients on the interaction of
a command area indicator for the sample plot with a command area indicator for the most important plot;
standard errors are in parentheses, and p-values are in brackets. Robust standard errors are clustered at
the nearest water user group level in speciﬁcations without Spatial FE, and Conley (1999) standard errors
are used in speciﬁcations with Spatial FE. Column 3 uses the speciﬁcation in Equation (7), Column 4 uses
the speciﬁcation in Equation (8), and Column 5 uses the speciﬁcation in Equation (9). Columns 6 though 8
uses analogous speciﬁcations building on Equation (10).
103
Table A9: Heterogeneity with respect to household size and wealth (baseline)
MIP MIP
Coef. (SE) [p] Coef. (SE) [p]
(1) (2) (3) (1) (2) (3)
Cultivated Horticulture
CA 0.150 0.135 0.079 CA 0.002 0.013 -0.002
(0.086) (0.085) (0.104) (0.039) (0.040) (0.037)
[0.080] [0.113] [0.446] [0.952] [0.741] [0.957]
CA * # of HH members -0.023 -0.021 -0.013 CA * # of HH members 0.000 0.001 0.003
(0.016) (0.016) (0.019) (0.007) (0.007) (0.008)
[0.160] [0.185] [0.507] [0.968] [0.940] [0.687]
CA * Asset index 0.005 -0.003 0.033 CA * Asset index -0.003 -0.003 0.000
(0.037) (0.037) (0.047) (0.017) (0.016) (0.018)
[0.891] [0.940] [0.482] [0.860] [0.857] [0.992]
Joint F-stat [p] 1.5 1.2 0.2 Joint F-stat [p] 0.0 0.3 0.3
[0.217] [0.306] [0.867] [0.986] [0.810] [0.852]
Irrigated Banana
CA 0.027 0.045 0.013 CA 0.093 0.067 0.051
(0.042) (0.046) (0.045) (0.071) (0.065) (0.082)
[0.518] [0.333] [0.776] [0.191] [0.300] [0.531]
CA * # of HH members -0.006 -0.005 -0.002 CA * # of HH members -0.008 -0.007 -0.000
(0.008) (0.008) (0.008) (0.013) (0.013) (0.015)
[0.475] [0.498] [0.811] [0.535] [0.611] [0.988]
CA * Asset index 0.008 0.008 0.010 CA * Asset index 0.011 0.002 0.043
(0.017) (0.017) (0.018) (0.031) (0.030) (0.041)
[0.652] [0.656] [0.587] [0.725] [0.959] [0.284]
Joint F-stat [p] 0.2 0.4 0.1 Joint F-stat [p] 1.7 0.5 0.7
[0.915] [0.736] [0.933] [0.175] [0.658] [0.527]
# of HH members X X X # of HH members X X X
Asset index X X X Asset index X X X
Site-by-season FE X X Site-by-season FE X X
Distance to boundary X X Distance to boundary X X
log area X X log area X X
MIP log area X X MIP log area X X
MIP CA X X MIP CA X X
Spatial FE X Spatial FE X
Notes: Regression analysis is presented in this table. All columns use outcomes on most important plots
and restrict to observations during the dry season.. Rows “CA” present coeﬃcients on a command area
indicator for the sample plot, while Rows “CA * W” present coeﬃcients on the interaction of a command
area indicator for the sample plot with a household characteristic W; standard errors are in parentheses,
and p-values are in brackets. Robust standard errors are clustered at the nearest water user group level in
speciﬁcations without Spatial FE, and Conley (1999) standard errors are used in speciﬁcations with Spatial
FE. The Row “Joint F-stat [p]” presents F-statistics for the null that all 3 coeﬃcients are 0, with the p-value
for the associated test in brackets. Columns 1, 2, and 3 use regression speciﬁcations building on Equation
(10) following Equations (7), (8), and (9), respectively.
104
Table A10: Heterogeneity with respect to household size and wealth (baseline)
MIP MIP
Coef. (SE) [p] Coef. (SE) [p]
(1) (2) (3) (1) (2) (3)
HH labor/ha Hired labor exp./ha
CA 8.3 19.3 -20.7 CA -6.6 -9.8 -12.4
(32.3) (29.8) (31.6) (5.8) (6.0) (6.1)
[0.797] [0.518] [0.512] [0.256] [0.099] [0.044]
CA * # of HH members -5.0 -6.3 -3.8 CA * # of HH members 0.4 0.3 0.0
(5.6) (5.5) (6.1) (0.9) (0.9) (0.9)
[0.378] [0.255] [0.532] [0.674] [0.750] [0.977]
CA * Asset index -13.6 -10.8 -11.9 CA * Asset index -6.4 -6.4 -6.8
(17.3) (16.4) (15.9) (3.9) (3.8) (3.3)
[0.430] [0.507] [0.454] [0.097] [0.093] [0.039]
Joint F-stat [p] 1.1 1.2 0.7 Joint F-stat [p] 1.3 1.5 1.9
[0.331] [0.311] [0.541] [0.274] [0.224] [0.133]
Input exp./ha # of HH members X X X
Asset index X X X
CA -1.7 0.3 -3.0 Site-by-season FE X X
(4.7) (3.8) (3.5) Distance to boundary X X
[0.715] [0.935] [0.386] log area X X
MIP log area X X
CA * # of HH members 0.7 0.6 0.6
MIP CA X X
(0.8) (0.8) (0.6)
Spatial FE X
[0.432] [0.426] [0.325]
CA * Asset index -2.8 -2.7 -1.9
(2.3) (2.2) (2.0)
[0.236] [0.222] [0.343]
Joint F-stat [p] 2.0 2.5 0.7
[0.121] [0.057] [0.575]
# of HH members X X X
Asset index X X X
Site-by-season FE X X
Distance to boundary X X
log area X X
MIP log area X X
MIP CA X X
Spatial FE X
Notes: Regression analysis is presented in this table. All columns use outcomes on most important plots
and restrict to observations during the dry season.. Rows “CA” present coeﬃcients on a command area
indicator for the sample plot, while Rows “CA * W” present coeﬃcients on the interaction of a command
area indicator for the sample plot with a household characteristic W; standard errors are in parentheses,
and p-values are in brackets. Robust standard errors are clustered at the nearest water user group level in
speciﬁcations without Spatial FE, and Conley (1999) standard errors are used in speciﬁcations with Spatial
FE. The Row “Joint F-stat [p]” presents F-statistics for the null that all 3 coeﬃcients are 0, with the p-value
for the associated test in brackets. Columns 1, 2, and 3 use regression speciﬁcations building on Equation
(10) following Equations (7), (8), and (9), respectively.
105
Table A11: Sample plots
Dry season Rainy seasons
Dep. var. Coef. (SE) [p] Dep. var. Coef. (SE) [p]
(1) (2) (3) (4) (5) (6) (7) (8)
Tracked 0.032 0.018 0.023 0.035 0.047 0.011 0.019 0.036
(0.177) (0.010) (0.014) (0.019) (0.211) (0.011) (0.016) (0.023)
2,907 [0.056] [0.083] [0.069] 4,845 [0.306] [0.224] [0.114]
Missing 0.060 0.111 0.127 0.103 0.064 0.102 0.121 0.094
(0.238) (0.020) (0.025) (0.028) (0.244) (0.020) (0.026) (0.028)
2,907 [0.000] [0.000] [0.000] 4,845 [0.000] [0.000] [0.001]
Reason data is missing
HH attrition 0.038 0.007 0.032 0.034 0.039 0.007 0.032 0.035
(0.192) (0.014) (0.019) (0.022) (0.194) (0.014) (0.019) (0.022)
2,907 [0.590] [0.096] [0.129] 4,845 [0.601] [0.096] [0.121]
Rented out comm. farmer 0.012 0.102 0.092 0.069 0.011 0.099 0.089 0.064
(0.108) (0.017) (0.019) (0.015) (0.105) (0.016) (0.019) (0.015)
2,907 [0.000] [0.000] [0.000] 4,845 [0.000] [0.000] [0.000]
Transaction (not tracked) 0.010 0.002 0.003 0.001 0.014 -0.004 0.000 -0.005
(0.099) (0.005) (0.005) (0.007) (0.116) (0.005) (0.006) (0.008)
2,907 [0.681] [0.539] [0.921] 4,845 [0.465] [0.945] [0.542]
Site-by-season FE X X X X
Distance to boundary X X X X
log area X X X X
Spatial FE X X
Notes: Regression analysis is presented in this table. Columns 1 through 4 restrict to observations during
the dry season, while columns 5 through 8 restrict to observations during the rainy season. Columns 1
and 5 present, for sample plots in the main discontinuity sample that are outside the command area, the
mean of the dependent variable, the standard deviation of the dependent variable in parentheses, and the
total number of observations. Columns 2 through 4 and 6 through 8 present regression coeﬃcients on a
command area indicator, with standard errors in parentheses, and p-values in brackets. Robust standard
errors are clustered at the nearest water user group level in speciﬁcations without Spatial FE, and Conley
(1999) standard errors are used in speciﬁcations with Spatial FE. Columns 2 and 6 use the speciﬁcation in
Equation (1). Columns 3 and 7 use the regression discontinuity speciﬁcation in Equation (2). Columns 4
and 8 use the spatial ﬁxed eﬀects speciﬁcation in Equation (3).
106