metadata: authors: 0: author: Jones,Maria Ruth
1: author: Kondylis,Florence
2: author: Loeser,John Ashton
3: author: Magruder,Jeremy
count: Rwanda
docna: 0: docna: Factor Market Failures and the Adoption of
            Irrigation in Rwanda
docty: Policy Research Working Paper
subtopic: Irrigation and Drainage,Agricultural Irrigation and Drainage,Labor Markets,Rural Labor Markets,Climate Change and Agriculture,Hydrology,Macroeconomic Management,Governance Diagnostic Capacity Building,Economic Forecasting
teratopic: Macroeconomics and Economic Growth,Governance,Agriculture,Social Protections and Labor,Rural Development,Water Resources
abstracts: cdata!: This paper examines constraints to
            adoption of new technologies in the context of hillside
            irrigation schemes in Rwanda. It leverages a plot-level
            spatial regression discontinuity design to produce 3 key
            results. First, irrigation enables dry season horticultural
            production, which boosts on-farm cash profits by 53–71
            percent. Second, adoption is constrained: access to
            irrigation causes farmers to substitute labor and inputs
            away from their other plots. Eliminating this substitution
            would increase adoption by at least 30 percent. Third, this
            substitution is largest for smaller households and wealthier
            households. This result can be explained by labor market
            failures in a standard agricultural household model.
geo_reg_key: 517196,517191
repnme: repnme: Factor Market Failures and the Adoption of
            Irrigation in Rwanda
display_title: Factor Market Failures and the
            Adoption of Irrigation in Rwanda
listing_relative_url: /research/2019/12/31651633/factor-market-failures-adoption-irrigation-rwanda
topicv3: Labor Markets m1326488 855,Water m1326522 137,Market Failures m1327149 1068,Irrigation and Drainage m1504475 3676,Horticulture m1582639 4730
publishtoextweb_dt: 2019-12-18T00:00:00Z
historic_topic: Macroeconomics and Economic Growth,Governance,Agriculture,Social Protections and Labor,Rural Development,Water Resources
origu: Development Impact Evaluation (DECIE)
no_of_pages: 101
author_keys: 0: author_key: 1053648
1: author_key: 797414
2: author_key: 1594783
3: author_key: 1096502
model_extractions: 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 A verified reproducibility package for this paper is available at http://reproducibility.worldbank.org, click **here** for direct access.
## Policy Research Working Paper 9092

# **Abstract**

This paper examines constraints to adoption of new technologies in the context of hillside irrigation schemes in Rwanda. It leverages a plot-level spatial regression discontinuity design to produce 3 key results. First, irrigation enables dry season horticultural production, which boosts on-farm cash profits by 53–71 percent. Second, adoption is constrained: access to irrigation causes farmers to substitute labor and inputs away from their other plots. Eliminating this substitution would increase adoption by at least 30 percent. Third, this substitution is largest for smaller households and wealthier households. This result can be explained by labor market failures in a standard agricultural household model.

This paper is a product of the Development Impact Evaluation Group, Development Economics. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The authors may be contacted at fkondylis@worldbank.org. A verified reproducibility package for this paper is available at http://reproducibility.worldbank.org, click **here** for direct access.

<!-- Start of picture text --> TRANSPARENT<br>ANALYSIS<br>G<br>R E<br>N<br>S<br>I P<br>Y E<br>K A<br>C A<br>R P<br>LI R<br>O E<br>O C<br>W R<br>H<br>S<br>P<br><!-- End of picture text --> _The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# Factor Market Failures and the Adoption of Irrigation in Rwanda<sup>∗</sup>

Maria Jones<sup>†</sup> Florence Kondylis<sup>†</sup> John Loeser<sup>†</sup> Jeremy Magruder<sup>‡</sup> _Updated_ January 2021 JEL Classification Codes: O1, O12, O13, Q12, Q15 Keywords: Technology adoption, Irrigation, Factor markets ∗ This draft benefited from comments from Abhijit Banerjee, 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, Georgia State University, Harvard University/MIT, Michigan State University, North Carolina State University, Northwestern University, University of California, Berkeley, University of Pittsburgh, University of Southern California, and the World Bank. 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 technical 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. This study was approved by UC Berkeley IRB (2016-06-8861), the Rwanda National Ethics Committee, and IPA IRB (10951), and is registered in the AEA RCT Registry (AEARCTR0001323). 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
# **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 may be underutilized due to inefficiencies in the markets faced by farmer households (Udry, 1997). A recent literature has provided robust evidence that these market failures distort 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 factor 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 generating inefficient allocations of labor and land across farms (Fei & Ranis, 1961; Benjamin, 1992). More recent empirical work has found that these inefficiencies are quantitatively important (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 distorting technology adoption.<sup>1</sup> We do so in the context of a potentially 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 complementary inputs, such as labor, fertilizer, and improved seeds. Market failures, including in factor markets, therefore have the potential to cause inefficient irrigation adoption 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

> 1A 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.

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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.<sup>2</sup> 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 53% - 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.<sup>3</sup> 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.<sup>4</sup> 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 irrigation is households’ own labor. The shadow wage that prices household labor is notoriously 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

> 2These 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.

> 3Existing 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), 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.

> 4This 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.

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on profits would fall from 53% - 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.<sup>5</sup> 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.<sup>6</sup> 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 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: an additional irrigated plot caused by access to irrigation is associated with a 54 - 60 percentage point decrease in the probability of irrigating a second command area plot. We find similarly large effects for adoption of horticulture, household labor, and inputs. These results confirm a

> 5This heterogeneity could only exist if there were frictions in at least one other market in addition to labor markets.

> 6The 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.

4
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 30% 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.<sup>7</sup> 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 contribute to inefficient 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 decreased input substitution across plots for larger households. We then estimate differential substitution with respect to household size and wealth to test for labor market failures. households We find exactly this pattern: with two additional members substitute 50% - 94% less than average size households, while one standard deviation wealthier households substitute 41% - 97% more than average wealth households. As these patterns of differential substitution 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 randomized controlled trials with the farmers who have access to irrigation. Two of these trials focus on characteristics peculiar to irrigation systems: usage fees and

> 7With 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).

5
failures of operations and maintenance; we find neither plausibly affects farmers’ adoption decisions in our context. 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 cultivate 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 adoption 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; Adamopoulos et al., 2017; Foster & Rosenzweig, 2017; Adamopoulos & Restuccia, 2018). We document that land misallocation hinders technology adoption, and that frictions in labor markets are 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).<sup>8</sup> Our context allows us to innovate by demonstrating that separation failures induce differential 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; Shenoy, 2017; Restuccia & Santaeulalia-Llopis, 2017).<sup>9</sup> Our test for inefficient technology

> 8The 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.

9Although 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 6
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 productivity 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.

# **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;<sup>10</sup> 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 relatively short, cultivating the primary staple crops is not possible for households not robust to the presence of unobserved heterogeneity across plots or measurement error (Gollin & Udry, 2019).

> 10Staple 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.

7
|Terracing||Irrig<br>constr|ation —_<br>uction|Irrigation const<br>complete|ruction<br>d||
|---|---|---|---|---|---|---|
|:<br>2009<br>2010|2011|2012|2013|2014<br>| 2015|2016<br>fr<br>2017|2018 —_|
|||||Baseline|Midline<br>1|Midline 3|
|||||2014 Dry<br>2015 Rainy 1, 2|2016 Rainy 2, Dry| <br><br>2017 Rainy 1|2018 Rainy 1, 2, Dry|
||||||Midl|ine 2|
||||||2017Rai|ny2,Dry|
secondary pipes run down the terraces from the canal every 200 meters, with valves on the main canal controlling the flow of water into these secondary pipes. Farmers draw water from tertiary 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 made up of all the plots which are below the canal and located within 100 meters of one of these tertiary valves.<sup>12</sup> 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, as the pressure available at an individual valve is determined by the volume of water in the pipe above that valve. The primary cost to farmers of irrigating a plot in this context is the 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 water.<sup>13</sup> As we document in Section 6 there were not significant challenges in operations and maintenance during the sample period, perhaps due to governmental oversight and the youth of these schemes.

We exploit a spatial discontinuity in irrigation coverage to estimate the impacts of irrigation. 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 plots just above the canal fall outside the command area and do not have access to irrigation.<sup>14</sup>

> 12We define clusters of plots that share the same secondary pipe as water user groups. In addition, water user groups can be grouped into zones. The secondary pipes in each zone are located along a single segment of the canal, and the flow of water into each of these segments is regulated by a single large valve located on the canal.

> 13In 2017, an attempt was made to collect taxes _unconditional_ on the use of irrigation, to avoid influencing cultivation decisions. The taxes are small in magnitude compared to potential farmer yields, as they are meant to fund only ongoing operations and maintenance costs, and compliance was very low (4%). The research team conducted a randomized controlled trial to pay these taxes described in Appendix I and found no evidence that farmers responded to these taxes.

> 14One might be concerned that during construction, the command area could be manipulated in order to cover particularly influential or productive farmers. In one of the sites, we have the

9
Figure 2: Karongi 12 hillside irrigation scheme

# **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.<sup>15,16</sup> After each point was sampled, georeferenced engineering layout plan that specifies the command area, in addition to the maps of the actually constructed command area. In results available upon request, our estimates are qualitatively similar when we use either the engineering layout plan or the actual map. This is consistent with the engineering layout plan closely aligning with the actual map, which in turn is consistent with the high costs of construction of these schemes.

> 15This procedure will produce a sample of plots that is more representative of land than of households. In Supplementary Appendix A, we reproduce our analysis in Section 3 but weighting households inversely proportionally to their number of plots, and find that our results are qualitatively similar with this alternative weighting.

> 16In 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

10
we excluded all points within 10m of that point (to avoid selecting multiple points too close together). Enumerators visited each of these points, and identified when a point fell on cultivable land.<sup>17</sup> With the help of a key informant (often the village leader), they then recorded the name of the cultivator of the plot, their contact information, as well as a sufficiently detailed description of the plot. These listed cultivators form our main household survey sample. For each cultivator, one of their identified plots was randomly selected, which we refer to as the _sample plot_ .

# **2.2.2 Survey**

Our baseline survey covered 1,695 spatially sampled cultivators in August - October 2015. The survey includes detailed agricultural production data (season-by-season) for seasons 2014 Dry through 2015 Rainy 2 (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. A panel of plot-level production and input data are maintained for two plots, which were mapped using GPS devices for precise location and area measurement. 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 next most important plot (defined at baseline; we refer to this as the “most important plot” or “MIP”). We also collected data on household characteristics, labor force behavior, and a short consumption 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

> 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.

> 17This was to discard forest, swamps, thick bushes, bodies of water, or other terrain which would make cultivation impossible.

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- 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 household sample for the follow up surveys consists of all the baseline respondents, while the plot sample for the follow up surveys consists of the sample plots and most important plots. To maintain a panel of plots, we ran a “tracking survey”. This survey was triggered whenever a household’s sample plot or most important plot was sold or rented out to another household, or a household stopped renting in that plot if it was not the owner (“transacted”). 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 A8. 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 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 a 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 F.

# **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.

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Table 1: Summary statistics on agricultural production

|||Staples|||Ho|rticultu|re|
|---|---|---|---|---|---|---|---|
||Staples<br>(1)|Maize<br>(2)|Beans<br>(3)|Bananas<br>(4)|All<br>(5)|Rainy<br>(6)|Dry<br>(7)|
|Yield|302|318|285|273|575|588|566|
|Hired labor (days)|37|37|37|9|61|66|57|
|Hired labor expenditures|28|28|28|7|45|49|42|
|HH labor (days)|266|248|260|101|417|414|420|
|Inputs<br>|19|35|16|3|50|50|50|
|Profts||||||||
|Shadow wage = 0 RwF/day|256|255|241|263|481|489|475|
|Shadow wage = 480 RwF/day|128|136|117|214|280|290|273|
|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, hired labor expenditures, 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.

**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._

The mean horticultural plot uses about 420 days/ha of household labor, 60 days/ha 13
of hired labor, and 50,000 RwF/ha of inputs, regardless of the season in which it is planted.<sup>18</sup> 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 agricultural 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 market 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. As a result, ultimately the economic profitability of horticulture relative to bananas will depend critically on the constraints on household labor supply decisions. It is worth noting that both horticulture and bananas appear more profitable than cultivating staples, which would be unprofitable if labor were valued at market wages; the ubiquity of staple cultivation in and around these sites is a first piece of evidence that farmers face a shadow wage below the market wage.<sup>19</sup>

> 18For reference, in the study period, the exchange rate was approximately 800 RwF = 1 USD

> 19Both 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.

14
# **3 Impacts of irrigation**

## **3.1 Empirical strategy**

We start our analysis with a regression discontinuity design. We restrict this and subsequent analysis to sample plots within 50 meters of the discontinuity, consistent with our sampling strategy. We regress Where _ykist_ is outcome _y_ for plot _k_ of household _i_ located in site _s_ in season _t_ , CA _kis_ 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 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. Dist1 _is_ 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 _X_ 1 _is_ is the log plot area.<sup>20</sup> Our coefficient of interest is _β_ 1, the effect of the command area on outcome _y_ .

We include controls for distance to the boundary and log plot area to address two primary potential sources of omitted variable bias. First, the canal sits at a particular contour of the hillside. Plots that are positioned relatively higher on the hillside may have different agronomic characteristics; accordingly, farmers may differentially sort into these plots. We therefore follow convention by controlling for the running variable (Dist1 _is_ ) and its interaction with treatment (CA1 _is_ ). Second, as the construction of the canal slices through plots on the hillside, this may differentially change the area of plots that are positioned above or below the canal. 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. We anticipate this will cause plots to be relatively larger just inside the command area. As plots exhibit strong evidence of diminishing returns to scale in this context, this effect would likely bias _β_ 1 downwards absent control.<sup>21</sup>

> 20We calculate distance using the distance of the plot boundary to the command area boundary. 21In Appendix C, we estimate specification (A1) that omits controls for distance to the command area boundary, its interaction with the command area indicator, and log plot area. All our results are qualitatively similar in this alternative specification, suggesting these potential sources of bias do not meaningfully affect our results. In Supplementary Appendix A, we estimate a specification that also includes controls for distance to the command area boundary squared, and its interaction with

15
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.<sup>22</sup> Second, marginal plots which would have been too unproductive to cultivate absent irrigation, and would thus have been left permanently fallow, may now While our be sufficiently productive to be worth cultivating with access to irrigation. 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 annual 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 Goldstein & 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 areas will not have nearby comparison plots outside the command area, and therefore will not contribute to the estimation of the of the command area.<sup>23</sup> effect In practice, we define a set _Nkist_ to be the group of five closest plots to plot _k_ the command area indicator. All our results are qualitatively similar in this alternative specification, suggesting choice of functional form for the distance control does not meaningfully affect our results. 22Typically, 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 _β_ 1 downwards.

> 23Formally, SFE estimators leverage the identification assumption lim _||k−k′||→_ 0 _E_ [ _εkist|Xkist_ ] = _E_ [ _εk′i′st|Xk′i′st_ ], where _||k − k_<sup>_′_</sup> _||_ represents the distance between plot _k_ and plot _k_<sup>_′_</sup> .

16
observed in season _t_ , including the plot itself. Then, for any variable _zkist_ , define _<u>zkist</u>_ = (1 _/|Nkist|_ )<sup>�</sup> _k_<sup>_′_</sup> _∈Nkist_<sup>_zk′i′st_.TheSFEspecificationthenestimates</sup>

where _Vkis_ includes all controls from Equation (1), 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 their nearest 3 plots (self inclusive) within 50 meters, and 87% have 3 plots within 100m; 60% of plots have all their nearest 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 Specification (1), we cluster standard errors at the level of the nearest water user group, the group of plots that can source water from the same secondary pipe.<sup>24</sup> When estimating Specification (2), the spatial fixed effects generate correlation between the errors of close observations. To allow for this, we calculate Conley (1999) standard errors.<sup>25</sup>

# **3.1.1 Balance**

We now use specifications (1) and (2) 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 and 4), and our preferred specifications which we use in our analysis with key controls included (Columns 5 and 6).

First, our sample plots are balanced in terms of ownership and rentals. Additionally, 89% of sample plot owners on both sides of the canal owned the land over

> 24As described in Section 2.1, water user groups are grouped into zones. In Supplementary Appendix A, we report estimates from specification (1) with standard errors clustered at the zone level, instead of the water user group level. The patterns of statistical significance we describe in Section 3 are unaffected by clustering at the zone level.

> 25 _′ ′_ Specifically, we allow plot _l_ managed by household _j_ and plot _l_ managed by household _j_ to have correlated errors if there exists a plot _k_ such that _l ∈Nkist_ or _k ∈Nljst_ , and _l_<sup>_′_</sup> _∈Nkist_ or _k ∈Nl′j′st_ .

17
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.

Table 2: Balance: Sample plot characteristics

||Full sample||R|D sample|||
|---|---|---|---|---|---|---|
||Coef. (SE) [p]|Dep. var.||Coef.|(SE) [p]||
||(1)|(2)|(3)|(4)|(5)|(6)|
|log area|0.045|-2.515|0.425|0.200|||
||(0.077)|(1.179)|(0.121)|(0.128)|||
||[0.554]|969|[0.000]|[0.118]|||
|Own plot|-0.012|0.894|0.004|-0.004|-0.001|-0.006|
||(0.020)|(0.309)|(0.032)|(0.038)|(0.032)|(0.038)|
||[0.535]|969|[0.907]|[0.921]|[0.972]|[0.877]|
|Owned plot _>_5 years|0.045|0.880|0.019|0.012|0.007|0.010|
||(0.019)|(0.326)|(0.037)|(0.035)|(0.036)|(0.034)|
||[0.020]|686|[0.613]|[0.723]|[0.834]|[0.767]|
|Rented out, farmer|0.027|0.032|-0.003|0.009|-0.009|0.007|
||(0.012)|(0.177)|(0.023)|(0.027)|(0.023)|(0.027)|
||[0.022]|969|[0.884]|[0.726]|[0.699]|[0.796]|
|Slope|-0.006|0.290|-0.007|0.007|-0.011|0.007|
||(0.013)|(0.183)|(0.019)|(0.024)|(0.019)|(0.024)|
||[0.655]|969|[0.695]|[0.769]|[0.559]|[0.781]|
|Omnibus F-stat [p]|2.1||2.6|0.5|0.1|0.1|
||[0.066]||[0.025]|[0.756]|[0.971]|[0.993]|
|Site FE|||X||X||
|Distance to boundary|||X|X|X|X|
|log area|||||X|X|
|Spatial FE||||X||X|

_Notes:_ Column 2 presents the mean of the dependent variable and the standard deviation of the dependent variable in parentheses, for sample plots in the main discontinuity sample that are outside the command area, and the total number of observations. Columns 1 and 3 through 6 present regression coefficients on a command area indicator, with standard errors in parentheses, and p- values in brackets. Column 1 uses the full sample, while Columns 2 through 6 use the discontinuity sample. Columns 5 and 6 use specifications (1) and (2), respectively.

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 18
poorly here; we find significant imbalance on half of our variables, and the omnibus test rejects the null of balance. However, balance improves substantially in our two preferred specifications (Columns 5 and 6, 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. For Specification (1) in Column (5), we reject the null of balance at the 10% significance level, as there is a significant difference in whether the household head has completed primary schooling or not and an almost significant difference in the number of household members (15-64). In Supplementary Appendix A, we estimate specifications (1) and (2) with controls included for household head completed primary schooling and number of household members (15-64), and our results are unaffected by the inclusion of these controls. We also note that 1 out of 10 variables significant at the 10% level is what one would expect due to chance.<sup>26</sup> 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 3 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 at the time of 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 B; consistent with this low adoption, we do not find significant impacts of access to irrigation on inputs or output in these seasons. Second, starting

> 26That the coefficient on household head primary completion in our test for balance is positive might be particularly concerning if education strongly predicted decisions to adopt irrigation, as this would be suggestive of endogenous selection rather than sampling noise. In contexts where information is a first order constraint to adoption, more educated farmers have been shown to be significantly more likely to adopt new technologies (Foster & Rosenzweig, 1996). Throughout this paper, we argue that information is unlikely to be a first order constraint to adoption of irrigation in this context; consistent with this, in results available upon request we find that household head primary completion is weakly negatively correlated with adoption of irrigation. To the extent that more educated household heads have a higher shadow wage, this is also consistent with our argument that labor market failures drive heterogeneous decisions to adopt irrigation in this context.

19
Table 3: Balance: Household characteristics

||Full sample||R|D sample|||
|---|---|---|---|---|---|---|
||Coef. (SE) [p]|Dep. var.||Coef.|(SE) [p]||
||(1)|(2)|(3)|(4)|(5)|(6)|
|HHH female|0.041|0.221|0.045|0.044|0.043|0.041|
||(0.025)|(0.416)|(0.046)|(0.050)|(0.046)|(0.050)|
||[0.094]|969|[0.326]|[0.378]|[0.345]|[0.412]|
|HHH age|0.5|47.5|2.1|0.7|1.4|0.3|
||(0.8)|(14.5)|(1.4)|(1.8)|(1.4)|(1.9)|
||[0.497]|967|[0.127]|[0.694]|[0.298]|[0.863]|
|HHH completed primary|0.069|0.287|0.128|0.102|0.119|0.099|
||(0.025)|(0.453)|(0.047)|(0.062)|(0.047)|(0.062)|
||[0.005]|966|[0.006]|[0.097]|[0.012]|[0.111]|
|HHH worked of farm|0.023|0.410|-0.039|-0.019|-0.024|-0.011|
||(0.027)|(0.493)|(0.051)|(0.064)|(0.050)|(0.064)|
||[0.392]|969|[0.441]|[0.763]|[0.631]|[0.868]|
|# of plots|0.61|5.19|0.20|0.35|0.36|0.40|
||(0.18)|(3.38)|(0.36)|(0.46)|(0.36)|(0.46)|
||[0.001]|969|[0.582]|[0.448]|[0.319]|[0.382]|
|# of HH members|0.17|4.89|-0.00|-0.03|-0.01|-0.03|
||(0.11)|(2.16)|(0.21)|(0.25)|(0.22)|(0.25)|
||[0.104]|969|[0.985]|[0.917]|[0.971]|[0.908]|
|# who worked of farm|0.10|0.77|0.01|0.03|0.01|0.04|
||(0.05)|(0.85)|(0.08)|(0.10)|(0.08)|(0.10)|
||[0.039]|969|[0.909]|[0.799]|[0.906]|[0.722]|
|# of HH members (15-64)|0.20|2.60|0.26|0.17|0.24|0.15|
||(0.08)|(1.45)|(0.15)|(0.16)|(0.16)|(0.16)|
||[0.007]|969|[0.090]|[0.300]|[0.128]|[0.349]|
|Housing expenditures|-2.3|49.2|-5.6|-16.7|-6.5|-18.6|
||(6.9)|(127.4)|(14.9)|(19.0)|(14.7)|(19.1)|
||[0.739]|962|[0.707]|[0.380]|[0.658]|[0.328]|
|Asset index|0.11|-0.12|0.15|0.06|0.13|0.04|
||(0.05)|(0.99)|(0.12)|(0.13)|(0.12)|(0.13)|
||[0.034]|967|[0.215]|[0.647]|[0.291]|[0.738]|
|Omnibus F-stat [p]|3.9||2.1|0.9|1.7|0.9|
||[0.000]||[0.028]|[0.536]|[0.073]|[0.514]|
|Site FE|||X||X||
|Distance to boundary|||X|X|X|X|
|log area|||||X|X|
|Spatial FE||||X||X|

_Notes:_ Column 2 presents the mean of the dependent variable and the standard deviation of the dependent variable in parentheses, for sample plots in the main discontinuity sample that are outside the command area, and the total number of observations. Columns 1 and 3 through 6 present regression coefficients on a command area indicator, with standard errors in parentheses, and p- values in brackets. Column 1 uses the full sample, while Columns 2 through 6 use the discontinuity sample. Columns 5 and 6 use specifications (1) and (2), respectively.

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.

20
<!-- Start of picture text --> ¢ Outside command area ? Command area<br>|III<br>I<br>B 0.3 I| 1II 1II | 1II<br>— I I I I<br>SD | I I I<br><= 0.2 ! ' ! !<br>|III<br>c | I I I<br>D 0.1 I II ; II 7 II<br>0.0 et II : e¢ II e@ e 1| @ ; bd || e) r)4 e<br>d, 0, d, d, SO, Sd, Sd, Sd, 0, d, Sd, 0, SO,<br>%y oN oN Oy Onn Onn On ~~’ ~s “~O Pr Or %<br>Lt % %®W LT Be Bet BWW SF WW G<br>LZ Z ZZ LZ LZ LZ ZZ ZZ<br>VY © V © 4V © q ©<br><!-- End of picture text -->
<!-- Start of picture text --> Cultivated Irrigated Horticulture Banana<br>os fT Tht “Lag 0.4 T 5 0.4 H 2 “ve t<br>04) ° « epee 03 oe 03 ile" _t os TTT<br>© e@ J---s! ©<br>2034-7 . ig Ea 7 . re oe © —— “4<br>sg ! © rm © °° © oo es!<br>Q 0.2 !1 7)S02 cr' 7)Bo2 vi nog ia*\-7 -!kK<br>o1 ' 0.1 ontgl 014, oe--- 2-41 o4 aleeee<br>0.0 } 0.0L“ | 0.01_-* 0.0 } ><br>40 -20 0 20 40 40 -20 0 20 40 40 -20 0 20 40 40 -20 0 20 40<br>Meters to boundary Meters to boundary Meters to boundary Meters to boundary<br>HH labor Input exp. Hired labor exp.<br>| - A” 25 | mr)<br>£w 200 is + 20 ‘a % | | 4<br>2 150 Le e =< 1 ’ & 20 f /<br>Ooo t e- weoot 45= 1°|, —_ | &S |1,? Pi<br>© 100 a © rZ--78 Cs r<br>fo}a5 _——_e—eee so fo)oOSs a ca iS© 10 eeaee--- se<br>0 ct ' 0 e- a= 2ee 0 a je ae F 1<br>40 -20 0 20 40 40 -20 0 20 40 40 -20 0 20 40<br>Meters to boundary Meters to boundary Meters to boundary<br>Yield Sales Profits (w* = 0) Profits (w* = 800)<br>|<br>300 a Fa 250 i ° 7° 300 1 a 128 1 °,<br>w ' 4 ' ’ 1 ‘ 1004 * 1 se<br>££= 1 ‘ ’ ££® 200 1 y : £© \ ‘ ‘ £o N N 1 i" ‘<br>S 200 1 ve’ = = 150 1— , --| iE3 200 !14 a --| iL3 75 s N 1toy y<br>ao ~.|ets harYe e iiao 100 ~S tA---ea7 oOx ~Seys, hanYe- «o 50 eS terTf<br>S 100 ve S ~. © 100 ate} Ss iw<br>s ae---77e-4eek Tiy S 5 oeCin- tienof4 S --7 77 Bsgii S 055 - Jott. <¢ : Decnee<br>0 0 0 0 *<br>40-20 0 20 40 40 -20 0 20 40 40 -20 0 20 40 40 -20 0 20 40<br>Meters to boundary Meters to boundary Meters to boundary Meters to boundary<br><!-- End of picture text -->
Table 4: Access to irrigation enables transition to dry season horticulture from perennial bananas, causes large increases in dry season labor and input use, yields, and sales; profitability depends on household’s shadow wage

# (a) Dry season

|Culti-<br>vated|Irri-<br>gated|Horti-<br>culture|Banana|HH<br>labor/<br>ha|Input<br>exp./ha|Hired<br>labor<br>exp./ha|Yield|Sales<br>/ha|Prof<br>Shado<br>= 0|ts/ha<br>w wage<br>= 800|
|---|---|---|---|---|---|---|---|---|---|---|
|(1)<br>|(2)<br>|(3)<br>|(4)|(5)|(6)|(7)|(8)|(9)|(10)|(11)|
|RDD (Site-by-season FE, Spe|cifcation|1)|||||||||
|CA<br>0.005|0.162|0.137|-0.133|70.8|6.3|3.7|73.1|55.5|63.9|9.3|
|(0.041)|(0.024)|(0.024)|(0.037)|(17.5)|(1.5)|(2.1)|(23.2)|(14.5)|(21.0)|(16.5)|
|[0.909]|[0.000]|[0.000]|[0.000]|[0.000]|[0.000]|[0.082]|[0.002]|[0.000]|[0.002]|[0.573]|
|SFE (Spatial FE, Specifcatio|n 2)||||||||||
|CA<br>0.022|0.171|0.156|-0.142|76.9|4.3|3.2|55.0|49.3|49.1|-3.0|
|(0.044)|(0.030)|(0.029)|(0.035)|(20.7)|(1.8)|(2.6)|(28.5)|(19.2)|(25.7)|(20.8)|
|[0.610]|[0.000]|[0.000]|[0.000]|[0.000]|[0.019]|[0.221]|[0.054]|[0.010]|[0.057]|[0.886]|
|# of observations<br>2,537|2,537|2,536|2,536|2,523|2,527|2,527|2,402|2,527|2,402|2,400|
|# of clusters<br>196|196|196|196|196|196|196|196|196|196|196|
|Control mean<br>0.391|0.058|0.065|0.245|59.5|2.5|3.7|82.3|49.7|76.1|32.8|

# (b) Rainy seasons

|Culti-<br>vated|Irri-<br>gated|Horti-<br>culture|Banana|HH<br>labor/<br>ha|Input<br>exp./ha|Hired<br>labor<br>exp./ha|Yield|Sales<br>/ha|Prof<br>Shado<br>= 0|ts/ha<br>w wage<br>= 800|
|---|---|---|---|---|---|---|---|---|---|---|
|(1)<br>|(2)<br>|(3)<br>|(4)|(5)|(6)|(7)|(8)|(9)|(10)|(11)|
|RDD (Site-by-season FE, Spe|cifcation|1)|||||||||
|CA<br>-0.092|0.035|0.016|-0.158|8.5|1.1|3.7|-22.6|-13.3|-26.4|-31.8|
|(0.025)|(0.009)|(0.018)|(0.038)|(23.1)|(2.9)|(3.4)|(30.8)|(18.5)|(28.5)|(26.4)|
|[0.000]|[0.000]|[0.371]|[0.000]|[0.714]|[0.710]|[0.276]|[0.462]|[0.472]|[0.354]|[0.228]|
|SFE (Spatial FE, Specifcatio|n 2)||||||||||
|CA<br>-0.053|0.059|0.048|-0.168|9.9|2.1|3.1|-15.4|5.6|-19.4|-27.3|
|(0.027)|(0.012)|(0.025)|(0.034)|(24.7)|(3.1)|(4.5)|(30.8)|(21.6)|(27.5)|(31.9)|
|[0.051]|[0.000]|[0.056]|[0.000]|[0.689]|[0.511]|[0.490]|[0.617]|[0.793]|[0.480]|[0.393]|
|# of observations<br>4,236|4,236|4,235|4,235|4,215|4,223|4,223|4,085|4,223|4,085|4,078|
|# of clusters<br>196|196|196|196|196|196|196|196|196|196|196|
|Control mean<br>0.838|0.016|0.073|0.274|226.7|16.1|15.9|271.5|85.1|239.8|59.5|

_Notes:_ Regression coefficients on a command area indicator for the sample plot (“CA”) are presented above. Specifications control for distance to the command area boundary, its interaction with CA, and log area of the sample plot. RDD specification includes site-by-season fixed effects, and SFE specification includes spatial fixed effects. Standard errors are in parentheses, and p-values in brackets.
First, in line with results from Section 3.2.1, command area plots are 16pp - 17pp 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 - 14pp in the command area, and as a consequence we observe no impacts on overall cultivation in the dry season.<sup>29</sup> 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 intensive. 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 irrigation. Doing so, we find that adoption of irrigation increases household labor use, input expenditures, and hired labor expenditures by 440 - 450 person-days/ha, 25,000 - 39,000 RwF/ha, and 19,000 - 23,000 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 350,000 - 360,000 RwF/ha, an order of magnitude larger than the effects on input expenditures or hired labor expenditures. 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 320,000 - 450,000 RwF/ha, 51 - 72% of annual agricultural production. As horticulture is primarily commercial: each 1 RwF/ha increase in yields is associated with a 0.76 - 0.90 RwF/ha increase in sales. Once again, these results on outputs are consistent with differences between bananas

> 29As 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 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%.

24
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 290,000 - 390,000 RwF/ha, a 53 - 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 labor at 800 RwF/personday, 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.<sup>30</sup> We anticipate three categories of spillovers in our context: across household spillovers, within plot (across season) spillovers, and within household (across plot) spillovers. First, the across household spillovers we anticipate are general equilibrium effects, as the increased demand for labor and increased production of horticulture caused by the sample plot shock drive up wages and down horticultural prices. We test for these effects in Appendix E and find no evidence that wages or staple prices changed over time, though prices of horticultural crops did decrease in one of the sites, reducing our estimated effects on revenues. Second, 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. However, we failed to find strong evidence of impacts on rainy season labor, inputs, yields, or profits. Third, 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. To address this spillover, 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.

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

> 30In Appendix D, 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.

25
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 53 - 71% increases in yields net of expenditures that we document from just three months of cultivation. At the same time, we observe a minority (30%) of farmers ultimately making use of the irrigation system. These results suggest that the shadow wage, and therefore labor market frictions, are likely to be important for the decision to cultivate horticulture.<sup>31</sup> Building on this result, we next adapt the classical agricultural household model (Singh et al., 1986; Benjamin, 1992) to develop formal tests for the role of market failures in adoption of irrigation.

# **4 Testing for binding constraint**

In this section, we describe a model of a farmer household that chooses input and household labor allocations across multiple plots, subject to constraints in markets for labor, inputs, and risk. We use this model to generate testable predictions of the farmer household’s responses to the sample plot shock for the presence of constraints and the nature of the constraints the farmer household faces. The formal setup of the model, motivating assumptions, and additional details are in Appendix G.

The farmer household has two plots: consistent with our data, we call these their sample plot and their most important plot. Production on each plot is a function of input and household labor allocations on that plot, of the plot’s productivity, and of a common productivity shock. While we abstract from the choice of crops or decision to irrigate in this framework, we interpret this production function as the envelope of production functions from cultivating different fractions of bananas and irrigated horticulture during the dry season, with cultivating horticulture as optimizing at a high labor and input intensity.<sup>32</sup> The household maximizes expected utility over consumption and leisure, choosing its off-farm labor supply and its allocations of inputs and household labor on each plot.

> 31Testing the role of the shadow wage, by estimating the impacts of access to irrigation on profits under different assumed shadow wages, has a number of limitations. First, all results above could be fully explained by heterogeneity in the returns to adoption of irrigation (Suri, 2011). Second, person days may be a clumsy measure for comparing hired labor and household labor, as household labor may be less intense, require fewer hours per day, or be preferred by households to working for others.

32We formalize this interpretation by extending the model to feature crop choice in Supplementary Appendix B.

26
We build on Benjamin (1992) and allow farmers to face three crucial constraints that cause deviations from expected profit maximization. First, access to insurance may be limited, so farmers may reduce labor and input use to avoid basis risk. Second, credit or access constraints may limit input use. Third, farmers’ off farm labor allocations may be constrained from above, resulting in overutilization of labor on the household farm.<sup>33,34</sup> We model access to irrigation on the sample plot (the “sample plot shock”) as a labor- and input-complementing increase in the productivity of the sample plot. This offers predictions consistent with our results in Section 3: the sample plot shock increases production, labor allocations, and input allocations on the sample plot.

Next, we consider the impacts of the sample plot shock on production decisions on the most important plot in this framework.

**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._

In the absence of the three constraints listed above, households maximize expected profits. As access to irrigation on the sample plot does not impact marginal products or prices on the most important plot, labor and input allocations on the most important plot do not respond to the sample plot shock.

**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._

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. 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 labor on the most important plot

> 33These 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).

> 34We model labor constraints as a constraint on off farm labor allocations from above because this generates a shadow wage that is below the market wage, and we note this generalizes a model without an off farm labor market. Agness et al. (2020) provide evidence in Kenya that households’ shadow wages are almost always below the market wage. In addition, as we discuss in Section 3.2.2, our results on profits are consistent with a shadow wage that is below the market wage.

27
and leisure. Third, absent insurance, the increase in agricultural production caused by access to irrigation reduces the marginal utility from agricultural production relative to the marginal utility from consumption. In turn, this causes labor and input allocations on the most important plot to fall.

An implicit assumption we make that generates this result is the absence of functioning 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 the most important plot would flow to the household with the highest willingness-topay for them. In practice, land transactions do occur; as discussed in Section 2.2.2, our survey tracks plots across transactions 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.

Rejecting separation with the test suggested by Proposition 2 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 of the three constraints above interacts with land market frictions to generate separation failures.

To shed light on which other constraints generate separation failures, we consider how households with different characteristics should _differentially_ respond to the sample plot shock. We focus on two important household characteristics: household size, which determines the availability of household labor, and wealth, which determines the ability to purchase inputs.<sup>35</sup>

**Proposition 3.** _If input 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._

The intuition for this result is that both insurance and input constraints are ultimately financial constraints, which causes household size and wealth to enter the problem symmetrically. Under insurance constraints, both household size (by increasing the amount of labor income) and wealth increase household consumption. 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

> 35In Section 5.1, we further discuss the choice of household size and wealth as shifters of availability of household labor and ability to purchase inputs, respectively.

28
maximizing expected profits, and therefore allocations on the most important plot will be less responsive to the sample plot shock. Second, 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. Similarly, if larger households could finance input purchases from labor income, larger households would be less likely to see the constraint bind. Therefore, their allocations on the most important plot would be less responsive to the sample plot shock.

**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 sample 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._

When labor constraints bind, the household responds to the sample plot shock by allocating additional labor to the sample plot, but they may withdraw labor from either the most important plot or from leisure. In general, the differential responses of wealthier and larger households cannot be signed. However, we focus on the case where larger households have more elastic on farm labor supply, while wealthier households have less elastic labor supply; this relationship has been posited as far back as Lewis (1954), and is discussed in depth in Sen (1966). These differences in on farm labor supply generate the prediction that larger households should be less responsive to the sample plot shock, as they draw labor to the sample plot primarily from leisure, while wealthier households should be more responsive to the sample plot shock, as they draw labor primarily from the most important plot.

These four propositions, summarized in Table 5, generate two sets of tests. First, Propositions 1 and 2 imply that substitution away from the most important plot in response to the sample plot shock allows us to reject the absence of constraints. Second, Propositions 3 and 4 produce a test of the absence of labor constraints. If the input and labor allocations of larger households are less responsive to the sample plot shock, while those of wealthier households are more responsive to the sample plot shock, then we would reject the absence of labor constraints.

29
We note that while it is unambiguous that constraints on selling labor would lead to inefficient adoption of irrigation, it is not clear whether they would result in adoption which is inefficiently low or inefficiently high. That result will depend on how wages would respond to the removal of those constraints. We return to this point in the conclusions.

Table 5: Model predictions

||_dL_2|_d_<br>_dL_2|_d_<br>_dL_2|
|---|---|---|---|
||_dA_1|_d_<br>_L_<br>_dA_1|_d_<br>_M_<br>_dA_1|
|No constraints|0|0|0|
|Constraints||||
|Insurance|_−_|+|+|
|Inputs|_−_|0_/_+|+|
|Labor|_−_|+<sup>_∗_</sup>|_−_<sup>_∗_</sup>|

_Notes:_ Predicted signs from the model for key comparative statics of interest are presented in this table. _<u>dL</u>_ <u>2</u><sup>theeffectofthesampleplotshockonlaborallocationsonthemostimportantplot,</sup> _dA_ 1<sup>is</sup> and _<u>d dL</u>_ <u>2</u> _<u>d dL</u>_ <u>2</u><sup>theimpactofincreasedhouseholdsizeandwealth,respectively,on</sup> _dL dA_ 1<sup>and</sup> _dM dA_ 1<sup>are</sup> this effect. Predictions in the no constraints case correspond to Proposition 1. Predictions on _dA_<sup>_<u>dL</u>_</sup><sup><u>2</u></sup> 1 correspond to Proposition 2. Predictions on _ddL dAdL_ <u>21</u><sup>and</sup> _dMd dAdL_ <u>21</u><sup>when insurance or input constraints</sup> 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.

# **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).

Equation 3 also includes controls CA2 _is_ , an indicator for whether the most important plot is in the command area, and _X_ 1 _is_ and _X_ 2 _is_ , the log area of the sample plot and the most important plot, respectively. We report _β_ 1, the effect of the sample plot shock 30
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 CA1 _is ∗_ CA2 _is_ to test for this. In these specifications, we also report this difference in differences coefficient. For both this coefficient and _β_ 1, in line with the model predictions in Table 5, we interpret negative coefficients on labor, inputs, irrigation use, and horticulture, as evidence of separation failures.<sup>36</sup> As in Section 3 , we include a specification with spatial fixed effects.<sup>37</sup> Specifically, we estimate 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.<sup>38</sup> We estimate where _Wi_ is a vector of household characteristics, which includes household size and an asset index in our primary specifications.<sup>39</sup> We focus on _β_ 3: the heterogeneity,

> 36Although we do not explicitly model the location of the most important plot in Section 4, in Supplementary Appendix B.1 we provide an extension of the model featuring crop choice and demonstrate these predictions hold for heterogeneity of substitution with respect to the location of the most important plot.

> 37Note that all differencing in this specification is done using the location of sample plot. 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.

> 38For parsimony, we only present the specification of the interaction for the specification without spatial fixed effects; all tables also present results with interactions included with spatial fixed effects, similar to Equation 4.

> 39Through the lens of our model, household size and the asset index act as shifters of the household’s availability of labor and the household’s ability to purchase inputs, respectively. First, this requires that we have meaningful variation in household size and wealth in the cross-section. In our sample, household size has a standard deviation of 2.2 members (see Table 3), and a one standard deviation increase in the asset index corresponds to an additional 30,000 RwF of liquid assets (goats and chickens). For comparison, our estimates in Section 3.2 suggest that 1.3 members worth of labor and 10,000 RwF of inputs are necessary to cultivate median household landholdings with horticulture during the dry season. Second, it requires that household size and the asset index are not correlated with other household or plot characteristics that might affect patterns of substitution. In Appendix H, we justify our choice of shifters by showing that household size and asset index explain agricultural production decisions in the expected manner, and that this correlation is unaffected by

31
with respect to household characteristics, of the impacts of the sample plot shock on outcomes on the most important plot. The signs on _β_ 3 produce our main test of which market failures cause separation failures; Table 5 presents which signs map to which market failures.

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.<sup>40</sup>

# **5.1.1 Balance**

We now use specifications (3) and (4) 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 and 4), and our preferred specifications which we use in our analysis with key controls included (Columns 5 and 6). Balance tests for most important plots are reported in Table 6. 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 also located in the command area, as households’ plots tend to be located near each other. In contrast, our preferred specifications (Columns 5 and 6) which restrict to the discontinuity sample correct for this imbalance. For both specifications, the omnibus test fails to reject the null of balance.

As an additional check, in Appendix B, we estimate for 2014 Dry specifications (3) and (4), and specifications with heterogeneity following Equation 5. 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 the inclusion of key household covariates. In addition, in results available upon request, we have included other household and plot characteristics in the interaction that might affect these patterns – number of plots and number of command area plots (if households with more land are more price risk averse), and plot area (as a proxy for quality, if smaller plots are typically higher quality). None of these added controls affect the significance of our results.

> 40Results for the rainy seasons and with output as an outcome are available upon request.

32
Table 6: Balance: Most important plot characteristics

||Full sample||R|D sample|||
|---|---|---|---|---|---|---|
||Coef. (SE) [p]|Dep. var.||Coef.|(SE) [p]||
||(1)|(2)|(3)|(4)|(5)|(6)|
|log area|-0.108|-2.381|0.094|0.074|||
||(0.068)|(1.041)|(0.128)|(0.136)|||
||[0.114]|784|[0.460]|[0.588]|||
|Own plot|0.025|0.875|0.040|0.033|0.039|0.029|
||(0.019)|(0.331)|(0.033)|(0.039)|(0.032)|(0.037)|
||[0.174]|784|[0.226]|[0.392]|[0.232]|[0.436]|
|Owned plot _>_5 years|0.005|0.960|0.012|0.033|0.011|0.030|
||(0.014)|(0.197)|(0.024)|(0.024)|(0.023)|(0.025)|
||[0.728]|585|[0.617]|[0.175]|[0.617]|[0.233]|
|Rented out, farmer|0.013|0.033|-0.026|-0.040|-0.029|-0.041|
||(0.010)|(0.179)|(0.022)|(0.025)|(0.023)|(0.026)|
||[0.224]|784|[0.249]|[0.114]|[0.222]|[0.116]|
|Slope|0.024|0.268|0.011|-0.004|0.011|-0.006|
||(0.009)|(0.144)|(0.016)|(0.018)|(0.015)|(0.018)|
||[0.012]|784|[0.497]|[0.806]|[0.496]|[0.730]|
|Command area|0.187|0.399|-0.053|-0.079|||
||(0.032)|(0.491)|(0.058)|(0.059)|||
||[0.000]|784|[0.360]|[0.183]|||
|Omnibus F-stat [p]|7.1||0.7|1.4|0.9|1.3|
||[0.000]||[0.627]|[0.220]|[0.458]|[0.279]|
|Site FE|||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:_ Column 2 presents the mean of the dependent variable and the standard deviation of the dependent variable in parentheses, for sample plots in the main discontinuity sample that are outside the command area, and the total number of observations. Columns 1 and 3 through 6 present regression coefficients on a command area indicator, with standard errors in parentheses, and p- values in brackets. Column 1 uses the full sample, while Columns 2 through 6 use the discontinuity sample. Columns 5 and 6 use specifications (3) and (4), respectively.

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. First, we present graphical evidence of this substitution in Figure 5. As in earlier figures, distance of the sample plot to the canal in meters is represented on the horizontal 33
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 7 and 8. 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.

Table 7: Sample plot shock causes households to substitute labor and input intensive irrigated horticulture away from most important plot

||Culti-<br>vated|Irri-<br>gated|Horti-<br>culture|Banana|HH<br>labor/<br>ha|Input<br>exp./ha|Hired<br>labor<br>exp./ha|
|---|---|---|---|---|---|---|---|
||(1)<br>|(2)<br>|(3)<br>|(4)|(5)|(6)|(7)|
|RDD (Site-by-seas|on FE, Sp|ecifcatio|n 3)|||||
|CA|0.038|-0.044|-0.038|0.092|-32.2|-6.0|-1.8|
||(0.040)|(0.026)|(0.024)|(0.032)|(20.0)|(2.7)|(2.1)|
||[0.344]|[0.087]|[0.110]|[0.004]|[0.107]|[0.028]|[0.404]|
|Sample plot efect|0.005|0.162|0.137|-0.133|70.8|6.3|3.7|
|SFE (Spatial FE,|Specifcati|on 4)||||||
|CA|0.004|-0.036|-0.037|0.065|-33.2|-6.7|-0.5|
||(0.049)|(0.033)|(0.029)|(0.036)|(23.8)|(2.8)|(2.3)|
||[0.930]|[0.270]|[0.206]|[0.072]|[0.162]|[0.017]|[0.825]|
|Sample plot efect|0.022|0.171|0.156|-0.142|76.9|4.3|3.2|
|# of observations|2,179|2,179|2,179|2,179|2,166|2,169|2,169|
|# of clusters|182|182|182|182|182|182|182|
|Control mean|0.368|0.114|0.109|0.199|66.8|5.6|3.9|

_Notes:_ Regression coefficients on a command area indicator for the sample plot (“CA”) are presented above. Specifications control for distance to the command area boundary, its interaction with CA, log area of the sample plot and the most important plot, and a command area indicator for the most important plot. RDD specification includes site-by-season fixed effects, and SFE specification includes spatial fixed effects. Standard errors are in parentheses, and p-values in brackets. “Sample plot effect” estimates are from Table 4.

First, consistent with the presence of separation failures, we find households substitute labor and inputs away from their most important plot. Households decrease allocations of household labor (32 - 33 person-days/ha) and inputs (6,000 - 6,700 34
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Table 8: Sample plot shock causes households to substitute labor and input intensive irrigated horticulture away from most important plot

||Culti-<br>vated|Irri-<br>gated|Horti-<br>culture|Banana|HH<br>labor/<br>ha|Input<br>exp./ha|Hired<br>labor<br>exp./ha|
|---|---|---|---|---|---|---|---|
||(1)<br>|(2)<br>|(3)<br>|(4)|(5)|(6)|(7)|
|RDD (Site-by-seas|on FE, Sp|ecifcatio|n 3)|||||
|CA|0.076|-0.004|-0.004|0.096|-13.6|-3.3|0.2|
||(0.043)|(0.020)|(0.018)|(0.041)|(14.1)|(1.8)|(2.1)|
||[0.079]|[0.836]|[0.813]|[0.019]|[0.338]|[0.070]|[0.922]|
|CA * MIP CA|-0.089|-0.094|-0.080|-0.009|-44.1|-6.3|-4.7|
||(0.052)|(0.035)|(0.035)|(0.042)|(23.5)|(3.2)|(2.5)|
||[0.089]|[0.007]|[0.021]|[0.824]|[0.060]|[0.044]|[0.066]|
|Joint F-stat [p]|2.1|3.6|2.7|4.5|1.8|2.6|1.8|
||[0.122]|[0.028]|[0.070]|[0.013]|[0.164]|[0.078]|[0.175]|
|Sample plot efect<br>|0.005|0.162|0.137|-0.133|70.8|6.3|3.7|
|Average efect|0.038|-0.044|-0.038|0.092|-32.2|-6.0|-1.8|
|SFE (Spatial FE,|Specifcati|on 4)||||||
|CA|0.059|0.010|-0.007|0.087|-15.4|-3.8|1.5|
||(0.048)|(0.026)|(0.023)|(0.044)|(19.2)|(2.1)|(2.6)|
||[0.215]|[0.686]|[0.771]|[0.047]|[0.422]|[0.076]|[0.546]|
|CA * MIP CA|-0.121|-0.103|-0.066|-0.048|-39.7|-6.5|-4.5|
||(0.056)|(0.045)|(0.044)|(0.044)|(31.2)|(3.7)|(3.1)|
||[0.030]|[0.021]|[0.133]|[0.275]|[0.204]|[0.079]|[0.146]|
|Joint F-stat [p]|2.7|2.7|1.3|2.0|1.1|3.0|1.1|
||[0.070]|[0.069]|[0.286]|[0.139]|[0.324]|[0.050]|[0.345]|
|Sample plot efect<br>|0.022|0.171|0.156|-0.142|76.9|4.3|3.2|
|Average efect|0.004|-0.036|-0.037|0.065|-33.2|-6.7|-0.5|
|# of observations|2,179|2,179|2,179|2,179|2,166|2,169|2,169|
|# of clusters|182|182|182|182|182|182|182|
|Control mean|0.368|0.114|0.109|0.199|66.8|5.6|3.9|

_Notes:_ Regression coefficients on a command area indicator for the sample plot (“CA”) and its interaction with a command area indicator for the most important plot (“CA * MIP CA”) are presented above. Specifications control for distance to the command area boundary, its interaction with CA, log area of the sample plot and the most important plot, and a command area indicator for the most important plot (“MIP CA”). RDD specification includes site-by-season fixed effects, and SFE specification includes spatial fixed effects. Standard errors are in parentheses, and p-values in brackets. “Sample plot effect” estimates are from Table 4, and “Average effect” is the coefficient on CA from a specification that omits CA * MIP CA.

power by including most important plots outside the command area, which are almost never irrigated and have small allocations of labor and inputs36during 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.
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, 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 - 17pp increase in irrigation use on sample plots in the command area coincides with a 9 - 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 Table A6, we present results of the sample plot shock on sample plots and most important plots, controlling for cultivation and crop choice.<sup>42</sup> Table A6 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. Shifting to most important plots, Table A6 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 23% - 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 household 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

> 42As 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.

37
of the impacts of irrigation 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 irrigation would include reduced farming intensity on non-irrigated plots. However, the substitution of inputs we estimate from most important plots outside the command area is generally not significantly different from zero, and the largest point estimate implies it is 37% as large as substitution away from command area plots.<sup>43</sup> We therefore conclude that the dominant within-household spillover is a reduced intensity of cultivation on irrigated plots. This suggests any bias in our estimates caused by spillovers onto plots outside the command area is likely to be small, and that spillovers onto plots inside the command area decreases our estimates in Section 3.

# **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).

we calculate Specifically, First, ( _β_ 1 + _β_ 3 _,_ CA) (from Equation 5) 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.<sup>44</sup> Third, in the numerator, we apply the

> 43We calculate this using _β_ 1 _/_ ( _β_ 1 + _β_ 3 _,_ CA) from Equation 5, the impact of the sample plot shock on input allocations on most important plots outside the command area divided by the impact on most important plots inside the command area. Estimates come from Table 8.

> 44We implicitly ignores households’ other plots; we do so because our research design has little to

38
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 4.8pp higher under this counterfactual, which represents a 30% increase.<sup>45</sup> This counterfactual relates to land market fric– tions absent these frictions, we would expect that the increased adoption of irrigation caused by this reallocation would be achieved by 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 of the sample plot shock on outcomes on the most important plot. Recall that for this analysis, the model makes two key predictions. First, if only insurance or input constraints bind, wealthier households and larger households should be less responsive. Second, if only labor constraints bind, the differential responsiveness of wealthier households and larger households cannot in general be signed. However, under additional assumptions, households with more elastic on farm labor supply (likely poorer households 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 Table 9. First, larger households are less

> 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.

> 45The p-value on this estimate is 0.077, which we calculate using block bootstrapped standard errors at the nearest water user group level to account for uncertainty in both the numerator and denominator of Equation 6.

39
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, 74% - 103% for horticulture, 63% - 75% for household labor, and 20% - 21% for inputs, with all but the input coefficient statistically significant. In contrast, 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, 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. In this section, we provide evidence from randomized controlled trials on the presence of other competing constraints to adoption of irrigation: management challenges of irrigation schemes, and financial and informational constraints. Additional details on the motivation, treatment assignment protocols, and logistics of implementation of each of these experiments are presented in Appendix I.

First, we test whether failures of scheme management limit farmers’ adoption of irrigation. If farmers faced limited access to water due to problems in the centralized operations and maintenance (O&M) system, this could constrain adoption of irrigation. We sought to alleviate 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 be40
Table 9: Larger and poorer households do not substitute away from most important plot in response to sample plot shock

||Culti-|Irri-|Horti-|Banana|HH|Input|Hired|
|---|---|---|---|---|---|---|---|
||vated|gated|culture||labor/<br>ha|exp./ha|labor<br>exp./ha|
||(1)<br>|(2)<br>|(3)|(4)|(5)|(6)|(7)|
|RDD (Site-by-season FE,|Specifca|tion 5)||||||
|CA|-0.069|-0.097|-0.107|0.052|-82.7|-9.1|-4.5|
||(0.086)|(0.048)|(0.046)|(0.065)|(34.8)|(4.2)|(3.6)|
||[0.424]|[0.046]|[0.020]|[0.418]|[0.018]|[0.031]|[0.216]|
|CA * # of HH members|0.021|0.011|0.014|0.008|10.1|0.6|0.5|
||(0.013)|(0.007)|(0.007)|(0.011)|(4.5)|(0.5)|(0.5)|
||[0.112]|[0.155]|[0.061]|[0.485]|[0.025]|[0.237]|[0.273]|
|CA * Asset index|-0.013|-0.018|-0.015|-0.003|-12.4|-2.5|0.3|
||(0.027)|(0.016)|(0.017)|(0.023)|(10.2)|(1.6)|(1.4)|
||[0.620]|[0.277]|[0.384]|[0.900]|[0.226]|[0.117]|[0.856]|
|Joint F-stat [p]|1.5|1.5|1.8|3.1|2.0|1.9|0.6|
||[0.213]|[0.214]|[0.147]|[0.026]|[0.122]|[0.128]|[0.592]|
|Average efect|0.038|-0.044|-0.038|0.092|-32.2|-6.0|-1.8|
|SFE (Spatial FE, Specifc|ation 5)|||||||
|CA|-0.188|-0.121|-0.129|-0.052|-94.6|-10.3|-2.1|
||(0.098)|(0.051)|(0.047)|(0.083)|(38.9)|(4.1)|(3.5)|
||[0.056]|[0.017]|[0.006]|[0.532]|[0.015]|[0.013]|[0.551]|
|CA * # of HH members|0.039|0.017|0.019|0.023|12.5|0.7|0.3|
||(0.014)|(0.008)|(0.007)|(0.015)|(4.5)|(0.5)|(0.5)|
||[0.007]|[0.030]|[0.012]|[0.110]|[0.006]|[0.185]|[0.539]|
|CA * Asset index|-0.043|-0.035|-0.030|-0.012|-24.0|-3.9|-0.3|
||(0.032)|(0.020)|(0.021)|(0.026)|(12.7)|(1.7)|(1.4)|
||[0.181]|[0.077]|[0.156]|[0.661]|[0.060]|[0.025]|[0.813]|
|Joint F-stat [p]|3.5|2.3|2.6|2.1|2.9|2.6|0.1|
||[0.015]|[0.079]|[0.050]|[0.094]|[0.033]|[0.051]|[0.937]|
|Average efect|0.004|-0.036|-0.037|0.065|-33.2|-6.7|-0.5|
|# of observations|2,176|2,176|2,176|2,176|2,163|2,166|2,166|
|# of clusters|182|182|182|182|182|182|182|
|Control mean|0.368|0.114|0.109|0.199|66.8|5.6|3.9|

_Notes:_ Regression coefficients on a command area indicator for the sample plot (“CA”) and its interaction with W (“CA * W”) are presented above. Specifications control for distance to the command area boundary, its interaction with CA, log area of the sample plot and the most important plot, a command area indicator for the most important plot (“MIP CA”), and all W. RDD specification includes site-by-season fixed effects, and SFE specification includes spatial fixed effects. Standard errors are in parentheses, and p-values in brackets. “Average effect” estimates are from Table 8.

41
cause 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 O&M in the schemes. To test whether these taxes limit farmers adoption of irrigation, we randomized tax subsidies for farmers. 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 I.2, and conclude here that these issues were not relevant in this context.

Third, we test whether financial and informational constraints limit adoption of irrigation. 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 and facilitate experimentation if information is a constraint. 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). 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.<sup>46</sup>

# **6.1 Empirical strategy and results**

We estimate the impact of minikits using the specification

> 46Each 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 characteristics 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 and conclusions are qualitatively unaffected.

42
Primary outcomes _y_ are whether households used a minikit (in 2017 Rainy 1 or in 2017 Dry) and adoption of horticulture. Assigned minikit _i_ is an indicator for whether household _i_ was randomly assigned to receive a minikit, Minikit saturation _i_ is the probability of receiving a minikit for households in the water user group of household _i_ ’s sample plot, and _X_ 1 _is_ 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 minikit,<sup>47</sup> and in some specifications 2016 Dry horticulture adoption. For precision, we restrict to command area plots, and for plot level outcomes we focus on the 2017 and 2018 Dry seasons; these are the plots and seasons in which we expect households receiving minikits to adopt horticulture. As minikit saturation is assigned at the water user group level, robust standard errors are clustered at the water user group level.

We present the results of this analysis in Table 10. 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 receive 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 reject estimates from other contexts of the effect of minikits on technology adoption (Emerick et al., 2016; Jones et al., 2018). Third, 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 water 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 constraints 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

> 47After 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.

43
Table 10: Minikits do not cause increased adoption of horticulture, strong positive selection into minikit takeup

||Minikit|takeup|Hortic|ulture|
|---|---|---|---|---|
||(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.

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.<sup>48</sup> 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.

> 48That 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.

44
# **7 Conclusion**

This paper provides evidence that irrigation has the potential to be a transformative technology in sub-Saharan Africa. Using data from very proximate plots which receive differential access to irrigation, we show the construction of an irrigation system leads to a 53% - 71% increase in cash profits. These profits are generated by a switch in cropping patterns from perennial bananas towards a more input-intensive rotation of dry-season horticulture and rainy-season staples.

At the same time, we observe only a minority of farmers adopting this technology four years after introduction. We further document that frictions in land and labor markets cause inefficient adoption of irrigation. 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. This result has stark policy relevance: without greater adoption, these irrigation systems will not be able to generate sufficient revenue to be sustainable.

While our results highlight the presence of constraints on land and labor markets and demonstrate those constraints generate inefficiencies in an important technology adoption context, they can not provide evidence as to whether those inefficiencies lead to too much or too little adoption of irrigation. If farmers faced no constraints in the amount of labor they could sell at the market wage, the model would suggest they would irrigate even less; indeed, based on the stylized facts in Section 2.3, the model would predict nearly all of these farmers would either cultivate low-intensity bananas or exit farming altogether. Of course, a labor supply shift of this magnitude is likely to put downward pressure on the wage. If the ability to sell labor without frictions led to a substantial reduction in the wage rate, we may see many more farmers hiring labor and cultivating horticulture on more of their plots: this shift could allow irrigation systems to realize their transformative potential.

These results underscore 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 limit the effectiveness of financial and information interventions in improving agricultural 45
productivity. This is a fruitful area for future research.

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