metadata: authors: 0: author: Lerva,Benedetta
count: Uganda
docna: 0: docna: The Monetary Value of Externalities :
            Experimental Evidence from Ugandan Farmers
docty: Policy Research Working Paper
abstracts: cdata!: Understanding the value of the
            externalities associated with a technology is crucial to
            correctly estimate the welfare benefits of public policies
            and investments. Suboptimal adoption rates of agricultural
            technologies in low-income countries partly result from
            farmers not fully internalizing the positive externalities
            of adoption. This paper designs an experiment to measure the
            monetary value of the externalities of an agricultural
            pest-control technology; it elicits a farmer&#x2019;s
            willingness-to-pay for another farmer to adopt the
            technology, as a measure of the externalities generated by
            the other farmer. The findings show that externalities are
            large, as mean willingness-to-pay for others is equal to two
            days&#x2019; wage, or half the willingness-to-pay for
            themselves. Willingness-to-pay for another farmer depends on
            social proximity (as it is easier to learn about the
            technology from closer connections), and the distance
            between their two plots (as pest-control is more beneficial
            for plot neighbors). Targeting the technology to farmers
            with geographically central plots and more socially
            connected farmers generates greater positive externalities
            and more social value than targeting farmers with the
            highest willingness-to-pay for themselves.
display_title: The Monetary Value of Externalities
            : Experimental Evidence from Ugandan Farmers
listing_relative_url: /research/2023/07/34122160/monetary-value-externalities-experimental-evidence-ugandan-farmers
topicv3: Agriculture Extension m1325967 1009,Pest Management m1326418 178,Agricultural Technology Adaptation
            m1326424 1951
publishtoextweb_dt: 2023-07-24T00:00:00Z
dois: 10.1596/1813-9450-10521
author_keys: 0: author_key: 1980036
model_extractions: Policy Research Working Paper 10521 The Monetary Value of Externalities Experimental Evidence from Ugandan Farmers _Benedetta Lerva_ Development Economics Development Impact Evaluation Group July 2023
Policy Research Working Paper 10521

# **Abstract**

Understanding the value of the externalities associated with a technology is crucial to correctly estimate the welfare benefits of public policies and investments. Suboptimal adoption rates of agricultural technologies in low-income countries partly result from farmers not fully internalizing the positive externalities of adoption. This paper designs an experiment to measure the monetary value of the externalities of an agricultural pest-control technology; it elicits a farmer’s willingness-to-pay for another farmer to adopt the technology, as a measure of the externalities generated by the other farmer. The findings show that externalities are large, as mean willingness-to-pay for others is equal to two days’ wage, or half the willingness-to-pay for themselves. Willingness-to-pay for another farmer depends on social proximity (as it is easier to learn about the technology from closer connections), and the distance between their two plots (as pest-control is more beneficial for plot neighbors). Targeting the technology to farmers with geographically central plots and more socially connected farmers generates greater positive externalities and more social value than targeting farmers with the highest willingness-to-pay for themselves.

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 author may be contacted at blerva@worldbank.org.

_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
The Monetary Value of Externalities: Experimental Evidence from Ugandan Farmers<sup>_∗_</sup>

**Benedetta Lerva**<sup>_†_</sup>

**JEL Codes: O12, Q12, Q16.**

**Keywords: externalities, technology adoption, agriculture, Becker-DeGrootMarschak, field experiments, social networks.**

> _∗_ I thank the Handelsbankens Research Foundation and Vetenskapsr ̊adet for generous financial support; Charles Angebault and Apollo Tumusiime for their collaborative efforts throughout the project; seminar participants at Bocconi University, Oxford University, Paris School of Economics, Stockholm University, University of California Berkeley, and World Bank for providing useful comments; Ingvild Almas, Tessa Bold, Konrad Burchardi, Jonathan de Quidt, Dahyeon Jeong, Florence Kondylis, John Loeser, Anna Tompsett, Jakob Svensson, Hannah Uckat for their helpful feedback. All errors and omissions are the responsibility of the author alone. The findings, interpretations, and conclusions expressed in this paper are entirely those of the author. They do not necessarily represent the views of the World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent.

- World Bank; E-mail: blerva@worldbank.org
# **1 Introduction**

Technology adoption can generate externalities whose monetary value is difficult to measure: since they are not sold on the market, they lack a price tag. Yet, knowing the value of externalities is crucial for two reasons. First, it helps governments decide _whether_ to intervene: an intervention may be worth it only once its social benefit exceeds a certain threshold. Second, if the threshold is met, knowing how externalities are produced helps governments decide _how_ to intervene: typically governments have a menu of policies to choose from, and may want to prioritize those with the highest social benefits.

Externalities are commonplace, and notably in agriculture. Many of the agricultural technologies available to farmers generate positive externalities, like pest control or wildfire prevention, that cause equilibrium adoption rates to be lower than socially optimal if agents do not internalize the social benefit of adoption (Pigou, 1920); this may contribute to explaining the persistent low adoption rates observed in many lower income countries (Bandiera and Rasul, 2006; Foster and Rosenzweig, 1995; World Bank, 2007).

In this paper I design a field experiment to uncover how much the externalities of one technology are worth and what governments should do to harness their benefits. Specifically, I study the externalities of a new agricultural pest-control technology in Uganda, consisting of a training on pest-control practices for a new pest. I measure the externalities of the training by asking farmers how much they are willing to pay for _only one specific farmer_ in their village to be trained on pest-control practices for the pest fall armyworm. The willingness-to-pay elicitation mechanism, a variant of the Becker-deGroot-Marschak or BDM (Becker et al., 1964), is incentive-compatible and yields a measure of the externalities generated by one trained farmer keeping others’ actions constant.<sup>1</sup> The feature of keeping others’ actions constant is achieved by allowing a maximum of one farmer to receive training per village through a lottery; it allows to shut down complementarities and substitutabilities in demand that would confound the observed willingness-to-pay for others. The upside of such a design choice is that it ensures I measure the externalities produced by one farmer (at the margin) neatly, although at the expense of measuring how externalities change when more than one farmer is trained in a village. I find farmers anticipate substantial positive spillovers from others: the median value a farmer attaches to another farmer receiving the training is equivalent to the wage received from two days of agricultural labor (or $8.6), about half the median willingness-to-pay for themselves (equal to $17.3).

I use my valuation data to show that targeting choices can produce large and quantifiable social gains if they account for externalities. I identify which targeting criterion for the training produces a higher social benefit in two steps. First, I calculate the per capita externality generated by training one farmer - the average willingness-to-pay of

> 1This setup rests on the assumption, supported by the data, that farmers are self-interested and do not engage in altruistic behavior in this setting.

1
others for that farmer - and find it is heterogeneous, hence the data suggests the identity of the trained farmer matters.<sup>2</sup> On average, within a village, the farmer with the highest per capita externality generates double the amount than the farmer with the lowest per capita externality ($7.9 vs $4.5). Second, I use the per capita externality to calculate the social benefit generated by training one farmer<sup>3</sup> and horserace two targeting criteria for the training: one in which the farmer with the highest willingness-to-pay for self receives the training, and one in which the farmer with the highest per capita externality receives the training. I find that the latter criterion outperforms the former; providing training to the highest-externality farmer in a village generates $455 in social benefit, 26% more on average than providing training to the highest-willingness-to-pay farmer (which generates $362).

I implement two randomized interventions to illustrate that the ways externalities originate - their sources - cause some farmers to be more socially valuable than others; innovatively, I embed the interventions in my willingness-to-pay elicitation exercise. I study how two sources of positive externalities, contagion and knowledge, affect willingness-to-pay for others. I introduce randomized variation in farmers’ beliefs over the two sources of externalities and observe how they adjust their willingness-to-pay for others in response. _Contagion externalities_ occur when others face a lower risk of infection due to a farmer reducing the pest population in her own farm; they are a function of distance between plots (the shorter the distance, the higher the contagion externalities (Li et al., 2019; Pannuti et al., 2016). _Knowledge externalities_ occur when knowledge spills over from a trained farmer to others in the village; they are a function of how much farmers interact as the more farmers interact, the likelier the knowledge transfer (Bandiera and Rasul, 2006; Conley and Udry, 2010; Foster and Rosenzweig, 1995; Munshi, 2004).

To identify contagion externalities I introduce a random shock to farmers’ beliefs about plot distance; I randomize whether or not a farmer receives truthful information about the walking distance between own plot and the plot of another farmer before formulating her valuation for the other farmer. In 95% of the cases farmers are wrong about the true distance, typically overestimating it (when farmers overestimate, they do so by 14 minutes on average; when they underestimate, they do so by 8 minutes on average). To identify knowledge externalities I introduce a random shock to farmers’ beliefs about future social interactions; I randomize whether or not a farmer receives an invitation to a one-on-one meeting with another farmer before formulating their valuation for the other farmer. I expect this to induce the participant to update own beliefs over future knowledge spillovers

> 2In the data heterogeneity is both demand-driven (different farmers value training the same person differently) and supply-driven (the same farmer values training different people differently). The coefficient of variation of farmers’ willingness-to-pay for the same person is 74%, while the coefficient of variation of a farmer’s willingness-to-pay for different people is 35%, showing that demand-driven heterogeneity plays a larger role than supply-driven heterogeneity.

> 3Which I define as the per capita externality multiplied by the number of farmers in a community, plus the farmer’s willingness-to-pay for self.

2
between them.

I find participants respond to contagion externalities. When they learn that someone else’s plot is further away - so contagion externalities are lower than believed - they decrease their valuation for that farmer by 11% of a daily wage. This indicates that the spatial distribution of plots indeed matters for targeting. My intervention is instead not conclusive about knowledge externalities, but I provide suggestive evidence that participants place a higher value on training farmers who are more likely to transfer knowledge to them. This indicates that social connections matter for knowledge diffusion, lending further evidence to policies targeting socially central individuals. Taken together, my results indicate that policies aimed at fostering technology adoption should be targeted towards socially central farmers with centrally located plots.

This paper makes six contributions. First, I devise a technique to credibly price externalities, a key economic quantity that is not marketed by definition. Studies on the measurement of the monetary value of non-marketed goods have largely relied on contingent valuations. Contingent valuations have been at the center of a long academic debate, mainly due to their vulnerability to _hypothetical response bias_ , which leads respondents to overestimate the value of hypothetical items they have no market experience of (Diamond and Hausman, 1994; Hanemann, 1994; Portney, 1994; Carson, 2012; Hausman, 2012; Kling et al., 2012). My paper overcomes this bias by eliciting valuations that are incentive-compatible and have real stakes. The elicitation technique I adopt is a multipleprice-list (MPL) variant of the standard BDM (Becker et al., 1964)<sup>4</sup> , shown to perform just as well as BDM for demand estimation in the field; Berry et al. (2020) implement a multiple-price-list variant of the BDM mechanism in the field to estimate willingnessto-pay for water filters in Ghana and compare BDM to take-it-or-leave-it (TIOLI) offers experimentally, finding they perform similarly; Burchardi et al. (2021) compare MPL to standard BDM and find comparable and high rates of comprehension and optimal bidding behavior. In my elicitation exercise, I collect valuations from six to nine sampled farmers per village in 103 villages in the Eastern region of Uganda (780 farmers in total), and each sampled farmer formulates one valuation for herself and one for every other sampled farmer in her village<sup>5</sup> (yielding five to eight valuations for others). I use a random lottery incentive to ensure that the valuations formulated by a farmer are independent from each other. I inform farmers that only one among all of the valuations in their village will be randomized for implementation, resulting in maximum one trainee per village. The

> 4Standard BDM requires a participant to formulate her maximum willingness-to-pay for an item and then the researcher to draw a random price. If the willingness-to-pay is at least as large as the random price, the participant has to buy the item paying the random price; if it is lower, the participant cannot buy the item. Just like in a second price auction, it is in the best interest of the participant to state her maximum willingness-to-pay truthfully. In addition, valuations obtained with this technique are equivalent to revealed preferences because they have real stakes.

> 5When formulating willingness-to-pay for another farmer, participants know which other farmers they are making the valuation for.

3
random lottery incentive allows me to measure the willingness-to-pay of a participant to change one farmer’s actions at a time, _ceteris paribus_ ; it rules out complementarities or substitutabilities in demand that would arise if more than one farmer could be trained or the trainee were not selected randomly.<sup>6</sup> Second, I quantify the importance of two specific types of externalities: contagion and knowledge externalities. Contagion externalities have been shown to affect take up of health products such as deworming medications or vaccinations (Miguel and Kremer, 2004; Boulier et al., 2007; White, 2019) and agricultural practices such as wildfire prevention (Crowley et al., 2009); knowledge externalities have been shown to affect take-up of agricultural technology as farmers do not fully internalize the positive effects of their learning on others’ learning when making adoption decisions (Bandiera and Rasul, 2006; Conley and Udry, 2010; Foster and Rosenzweig, 1995; Munshi, 2004). My work complements these findings by showing that individuals attach monetary value to contagion and knowledge externalities, and weigh how the identity of the adopter affects them. Further, I confirm knowledge externalities are important in this setting by comparing the adoption rate of trained versus non-trained farmers living in the same village; if training increases adoption by a similar amount among trained and untrained farmers, we conclude knowledge spills over from trained to untrained farmers. In my setting the random selection of one person to receive the training in a village means training is randomly assigned at the village level, conditional on the willingness-to-pay of the farmer whose valuation is selected. Training takes place in about two thirds of the villages (64 out of 103), and it results in a 15% increase in adoption among the 64 trained farmers and a 14% increase in adoption among non-trained farmers living in the same village, suggesting information Third, I estimate the social benefit of alternative targeting policies and the losses incurred by society if program targeting disregards externalities. A consistent finding in the social learning literature is that targeting matters for diffusion and, in some cases, for adoption; Beaman et al. (2021) show that targeting farmers using a social network model with complex contagion<sup>7</sup> performs better for diffusion and adoption than having extension workers choose who to target in Malawi; Caeiro (2019) finds that weak ties play a major role for diffusion of cultivation practices in Guinea-Bissau, but have small impacts on adoption; targeting farmers who are similar to the average farmer increase diffusion and adoption more than targeting wealthier farmers in Malawi and Uganda (BenYishay and Mobarak, 2018; Vasilaky and Leonard, 2018), but not in Mozambique

> 6Complementarities or substitutabilities in demand are central concepts in the study of externalities, and a key element to guide policies such as optimal subsidies. Gautam (2023) and Guiteras et al. (2019) provide recent evidence on the impact of providing subsidized access to sanitation, a technology with high contagion externalities.

> 7 Complex contagion requires a farmer to be connected to at least two knowledgeable farmers to start a diffusion process, while one connection is sufficient for a diffusion process with simple contagion.

4
(Kondylis et al., 2017). My paper confirms targeting policies are key determinants of social outcomes and adds to the debate by identifying the monetary value attached by society to different targeting policies, showing social benefit is substantially larger when externalities are accounted for (compared to targeting individuals with the highest private benefit).

Fourth, I show that in-person agricultural extension services are valuable to, and valued by, farmers. The traditional agricultural extension approach of “Training and Visit” (T& V) has been criticized for being financially unsustainable and causing at best modest improvements in adoption (Gautam, 2000; Krishnan and Patnam, 2014; Udry, 2010), spurring the growth of cost-effective programs that leverage SMS and phone-based platforms to spread extension messages (Fabregas et al., 2019). My project contributes to the open debate on the extent to which T&V services should be rolled back by backing out demand for extension services at different price points, a valuable exercise for policy makers who need to know whether demand exists before committing public funds. Findings show farmers value individual training substantially but below its cost (training one farmer costs $29.4 in my setting, much less than the average willingness-to-pay), indicating the service is only cost-effective when positive externalities generate large social benefits. An interesting point of comparison with my findings is provided by Cole and Fernando (2020) and Hidrobo et al. (2022), who elicit farmers’ willingness-to-pay for mobile-based extension services. Hidrobo et al. (2022) report the median willingness to pay for a nutrition-sensitive agricultural information service in Ghana for a month is about $0.4; Cole and Fernando (2020) find the average willingness to pay for a 9-month subscription to an advice platform in India is $2, or $0.22 per month, and also note how positive externalities may depress willingness to pay in their setting as farmers can freeride on others. Finally, as mentioned earlier, the random assignment of the training allows me to estimate its positive impacts on adoption among both direct beneficiaries and other farmers in their communities.

Fifth, I use an incentive-compatible mechanism in the field to identify the ideal beneficiaries of a policy. A growing literature on mechanism design exploits truthful reporting mechanisms to target development interventions. Both Rigol and Roth (2016) and Hussam et al. (2021) study the feasibility of truth-telling mechanisms in the field; Rigol and Roth (2016) evaluate the performance of a peer prediction method in which participants are incentivized to report socioeconomic characteristics of their peers (such as health expenditures or risk aversion) and find it yields accurate reports and is empirically incentive-compatible; Hussam et al. (2021) show that such a peer prediction mechanism, called Robust Bayesian Truth Serum (RBTS), can deliver truthful peer reports on who would be the most successful entrepreneur in a community. Similarly, I exploit a labin-the-field methodology to identify the farmers whose adoption decisions generate the highest social benefit.

5
Lastly, I connect a key issue in economics, the measurement of externalities, with a prominent contemporary policy challenge, the low agricultural technology adoption in lower income agrarian economies. The puzzle of underadoption in developing countries has been widely studied and shown to be tied to multiple behavioral or market failures. Bold et al. (2017) provide evidence of input market failures, showing that the low quality of seeds and fertilizer available on the market decreases both returns to technology and adoption in Uganda. Karlan et al. (2014) investigate the role of uninsured risk and liquidity constraints in depressing farm investment, and find that providing insurance increases investment more than cash grants. Duflo et al. (2011) show that behavioral biases induce Kenyan farmers to procrastinate the purchase of fertilizer and miss profitable fertilizer investment opportunities. Burchardi et al. (2019) discuss how sharecropping agreements depress investments in agricultural inputs, and increasing tenants’ shares raises both investment and productivity. In the context of the underadoption puzzle, this paper connects the dots between externalities and missed investment opportunities, ultimately leading to low agricultural productivity.

# **2 Setting**

The America-native fall armyworm ( _Spodoptera Frugiperda_ ) was first recorded in Africa in 2016 and in Uganda in early 2017. The pest feeds on several crops in the Americas and Europe, but in sub-Saharan Africa it mainly affects maize. FAO estimates the fall armyworm caused maize losses of about 1% of national GDP in Uganda in the first cropping season of 2017.<sup>8</sup> Maize is the most cultivated cereal and third-most cultivated crop in the country, and the Eastern region (one of the four regions of Uganda) produces over half of the total yearly maize (UBOS, 2010). Tackling the fall armyworm infestation has been a policy priority among both international and local organizations working in agriculture since the pest was detected in the country.

The fall armyworm is more destructive in tropical rather than temperate climates because of a shorter life cycle allowing the pest to reproduce earlier and its population to grow larger than in cooler climates. It has five development stages: egg, larva, caterpillar, pupa, and moth. The larva and caterpillar stages are the most damaging for the host plant as the pest feeds on both leaves and cob, while in the moth stage the pest spreads geographically (as female moths fly during the night to lay eggs).

By the time of my elicitation exercise farmers in my sample had been exposed to the fall armyworm for three cropping seasons, and reported 41% of their plots had been infected in the latest agricultural season (56% if we restrict the sample to maize plots). The high pest prevalence can be partly explained by the fact that practices to handle the fall armyworm are pest-specific and farmers would not be able to infer them without guidance

> 8www.fao.org

6
from agronomists; at the same time, their execution is mostly labor-intensive and farmers would be able to carry them out on their own once trained. The main practices recommended by the Ugandan government are plant early and uniformly, scout the field every three days, handpick and crush the eggs and caterpillars, pour sand and ash on infected plants, spray pesticide two to three times per season, use fertilizer, deep bury the infected plant residue in soil. Informational interviews carried out before the elicitation suggest farmers did not know which practices would be effective to handle the fall armyworm and had not been in contact with a government extension officer about the issue;<sup>9</sup> some farmers reported adopting practices that had not been recommended by the government, such as spraying their plants with laundry detergent or paraffin.

# **3 Conceptual Framework**

This section develops a simple model to highlight the parameters that determine willingnessto-pay for self and for others. A farmer _i_ chooses whether to take or not a binary action _li ∈{_ 0 _,_ 1 _}_ to maximize net utility of avoiding a pest infestation. In an economy with no externalities farmer _i_ solves where _Ui_ is the utility of avoiding infection, _c_ is the cost of acquiring the knowledgebased technology and _ki_ is the individual cost of implementing the recommended pestmanagement techniques. Information and contagion externalities allow _i_ to learn from other farmers and face lower infection risk. All farmers in the village take adoption decisions simultaneously.

The parameter governing _knowledge_ externalities is _p_<sup>_L_</sup> , the probability that _i_ learns from at least another farmer in the village, where _p_<sup>_l_</sup> _ij_<sup>istheprobabilitythat</sup><sup>_i_learnsfrom</sup><sup>_j_.Theutilityvalueoftheknowledge</sup> externality is measured by ( _Ui − ki_ ) _p_<sup>_L_</sup> , the product of the net utility of avoidance times the probability of learning.

The parameter governing _contagion_ externalities is (1 _− p_<sup>_T_</sup> ), the probability that _i_ is not infected by any other farmer _j_ ,

> 9In general farmers reported they seldom have contact with government extension officers, whose activities had almost exclusively consisted of seeds distribution in their area.

7
where _p_<sup>_t_</sup> _ij_<sup>isthereduced-formprobabilitythat</sup><sup>_i_isinfectedby</sup><sup>_j_,andtrivially(1-</sup><sup>_pt_</sup> _ij_<sup>)is</sup> the probability that _i_ is not infected by _j_ . Every adopting farmer _j_ generates a positive contagion externality for _i_ by reducing the pest load of the environment and increasing the probability that _i_ avoids infection (or equivalently, decreasing the probability that _i_ is infected). The utility value of the contagion externality is measured by _Ui_ (1 _− p_<sup>_T_</sup> ). It is the product of avoidance utility _Ui_ times the probability that farmer _i_ does not get infected by any other farmer _j_ . If _lj_ = 0, _i_ avoids infection from _j_ with probability (1 _− p_<sup>_t_</sup> _ij_<sup>).</sup> If _lj_ = 1, _i_ avoids infection from _j_ with probability 1.

I make the two following assumptions. First, the technology works perfectly.

# **A1: If a farmer implements the technology, her plots are immune from the pest.**

Second, once a farmer has learned the technology from another farmer, the utility from implementing the technology is higher than the utility from contagion externalities.

# **A2: The utility of implementing the technology is larger than the utility of contagion externalities**

Trivially, if no _j_ = _i_ farmer adopts the technology in the village,<sup>�</sup> _j_ = _i_<sup>_lj_= 0, there are no</sup> externalities and farmer _i_ ’s problem is just (1). If at least another farmer in the village chooses to adopt, such that<sup>�</sup> _j_ = _i_<sup>_lj≥_1,farmer</sup><sup>_i_’sproblemis</sup> where the farmer can choose to adopt _li_ = 1 and have profit ( _Ui − c − ki_ ), or not adopt. If _i_ does not adopt she can learn from others at no cost with probability _p_<sup>_L_</sup> and not benefit from contagion externalities, yielding profit ( _Ui − ki_ ), or not learn and benefit from contagion externalities with probability (1 _− p_<sup>_T_</sup> ), yielding profit _Ui_ .

In the experiment, the setting above is modified in the following ways:

1. There is a set of farmers _F_ = ( _i, j, . . . , N_ ).

2. A maximum of 1 farmer can acquire the technology.

3. A participant _i_ is either in a state of the world in which only _i_ can acquire the technology ( _l−i_ = 0), or in a state of the world in which only _j_ can acquire it ( _l−j_ = 0).

8
4. A participant _i_ decides whether to acquire technology for herself in the state of the world _l−i_ = 0; she decides whether to acquire technology for _j_ in the state of the world _l−_ = 0. _j_ 5. A participant chooses her maximum willingness-to-pay for herself to adopt, _wii_ , in the state of the world _l−i_ = 0, or chooses her maximum willingness-to-pay for _j_ to adopt, _wij_ , in the state of the world _l−j_ = 0.

6. There is no cost to acquiring the technology, _c_ = 0.

Then equations 1 and 4 become Suppose the state of the world is _l−i_ = 0. Then, a rational farmer will set her _wii_ equal to the difference between the profits she would obtain if she chooses to adopt Π1( _li_ = 1 _|lj_ = 0) and the profits she would obtain if she chooses not to adopt Π1( _li_ = 0 _|lj_ = 0), yielding

which shows _wii_ is equal to the utility of avoiding infection minus the cost of implementing the techniques.

Suppose the state of the world is _l−j_ = 0. Then a rational farmer will set her _wij_ equal to the difference in profits if she chooses that _j_ should adopt versus not adopt, where<sup>�</sup> _m_ = _i,j_<sup>(1</sup><sup>_−p_</sup> _im_<sup>_t_) describes the background infection environment.Setting �</sup> _m_ = _i,j_<sup>(1</sup><sup>_−_</sup> _p_<sup>_t_</sup> _im_<sup>) =</sup><sup>_E_andsubstituting(7)into(8)yields</sup> Which shows that willingness-to-pay of _i_ for _j_ depends on the parameters governing knowledge and contagion externalities, respectively _p_<sup>_l_</sup> _ij_<sup>and</sup><sup>_pt_</sup> _ij_<sup>, willingness-to-pay for self,</sup> implementation cost _ki_ , and the background infection environment _E_ . My empirical approach is designed to shed light on four key parameters in (9); the willingness-to-pay 9
elicitation exercise measures _wii_ and _wij_ , while the belief update interventions identify the impact of _p_<sup>_l_</sup> _ij_<sup>and</sup><sup>_pt_</sup> _ij_<sup>on</sup><sup>_wij_.</sup> Finally, it is important to notice that (9) embeds a selfish assumption: agents are only willing to pay for others to acquire the technology as long as it benefits them. I interpret a participants’ willingness-to-pay for another farmer as the total value to the participant of the externalities produced by the other farmer; as a result, the selfish assumption is crucial to identify spillovers. If participants had altruistic preferences, their willingnessto-pay would also include the value a participant attaches to providing the technology to others. I will further discuss the selfish assumption in the results section to provide evidence in its favor.

# **4 Data and Sample**

The sample includes 780 farmers from 103 villages located in the districts of Manafa, Mbale, and Tororo in Eastern Uganda. This sample had been selected for a field experiment carried out in previous years by a research team that included the author (Burchardi et al., 2022). The three contiguous districts were selected for their high suitability to maize cultivation according to the FAO GAEZ data.<sup>10</sup> The 103 villages<sup>11</sup> were selected by a randomization algorithm from the pool of villages in the 2010 national census with a population density lower than 100 households per square kilometer (to ensure they were in rural areas), stratifying by population density. In each village, we enlisted all residing households through a researcher-run census survey. We selected six to nine research participants (maximum one per enlisted household, always the head of the household) according to the following criteria: _i)_ engaging in commercial farming; _ii)_ having cultivated or planning to cultivate maize; _iii)_ reporting land holdings from two to six acres; _iv)_ having a mobile money account. The participants in the Burchardi et al. (2022) experiment were enrolled at the end of 2016 and had participated in up to four survey interviews and one willingness-to-pay elicitation by the time the field work for the experiment in this paper started; all research activities connected to Burchardi et al. (2022) were completed by 2017.

The data I use come from four surveys: an in-person baseline survey, an in-person willingness-to-pay elicitation survey, a phone follow-up survey, an in-person follow-up survey. All surveys have been written by the research team and approved by the Ugandan ethics authorities. The enumerators who administered the survey have at least a high school diploma, speak the Eastern local languages (Ateso, Japadhola, Luganda, Lugisho, Swahili) and were recruited through a local research firm. The timeline of data collection is summarized in Figure A.1, while Appendix F provides details about each variable used

> 10www.gaez.fao.org

> 11Villages are commonly referred to as LC1 (Local Council 1) in Uganda, and they are the smallest administrative unit, governed by a chairperson (LC1 chairperson) and nine executive committee members.

10
in the analysis.

# **5 Experimental Design**

## **5.1 Willingness-to-Pay Elicitation**

Enumerators carried out home visits to elicit participants’ willingness-to-pay for a threehour training session about Fall Armyworm. During the home visit, each participant formulates her willingness-to-pay to receive training herself, and also her willingness-topay for each other sampled farmer in her village to receive the training. These valuations are elicited in a way that makes it clear they are mutually exclusive events: only one farmer can actually receive training.

The elicitation technique I employ is a multiple-price list variant of that proposed by Becker et al. (1964), in which a participant formulates a bid _b_ for an item and the bid is compared with a random price draw _p_ . If the bid is equal to or larger than the random price, the participant has to buy the item; if the bid is lower than the random price, the participant cannot buy the item.

Before the exercise, enumerators ask participants if they know what the Fall Armyworm is and inform them it spreads by proximity, so that the closer a plot is to pest-infected plants, the likelier it is that the pest spreads to the plot.<sup>12</sup> We also inform participants that one decision maker would be randomly selected in their village. The decision maker is the one who actually gets the opportunity to purchase the training, and participants do not know the identity of the decision maker before the elicitation. We inform participants they will make _N_ bids, _N_ = [6 _,_ 9], choosing their willingness-to-pay for themselves and for up to eight other farmers to receive the training in their village, but only one of these _N_ choices will be actually implemented if they are the decision maker. If they are not the decision maker, none of their choices will be implemented.

In the multiple-price list variant I employ, the participant is presented with 21 amounts, ranging from 0 to 40,000 UGX ($ 34.6) and increasing in steps of 2,000 UGX ($ 1.7): (0, 2,000, 4,000, ..., 40,000).<sup>13</sup> At every step, the participant is asked if she would be willing to pay amount _x_ to purchase the training. If the respondent accepts to pay _x_ , she is asked if she would be willing to pay _x_ + 2 _,_ 000. If she does not accept to pay _x_ , the enumerator stops and records her bid as _b_ = _x −_ 2 _,_ 000. Note that negative prices and prices above 40,000 are not allowed in the experiment. There are no participants who refuse to pay 0, and if a participant is willing to pay 40,000 or higher the enumerator records _b_ = 40 _,_ 000.

The enumerator follows this procedure to obtain a participant’s willingness-to-pay for

> 12Figure A.2 shows that, one year after this exercise, farmers believe that the closer a plot is to an infected plot, the likelier it is to be infected. Farmers’ beliefs are dispersed but decrease linearly with distance.

> 13All US Dollar amounts are expressed in PPP terms. I calculate amounts in $PPP using the 2018 conversion rate of $1=1157.27 LCU (Local Currency Units), retrieved by the World Bank Databank. Numbers in $PPP are rounded to the first decimal digit.

11
herself to receive the training, _b_ 1, and then to obtain a participant’s willingness-to-pay for each of the other sampled farmers in the village to receive the training, _b_ 2 _, b_ 3 _, . . . , bN_ . After the respondent has made _N_ willingness-to-pay bids, the enumerator gives her a sealed plastic card. The card contains a random price _p_ drawn from a uniform distribution, _p ∼U_ (0 _,_ 40 _,_ 000). The card also indicates if the participant is the decision maker or not. If the respondent is the decision maker, the card also indicates which of the _N_ choices made binds, so which of the _b_ 1 _, . . . , bN_ bids matters. The enumerator does not know _p_ or any other information included in the card. Suppose a participant is the decision maker and her card says that choice 3 is the one that binds. Then if her bid for farmer 3 is larger than the random price, _b_ 3 _≥ p_ , she buys the training for farmer 3 at price _p_ . If _b_ 3 _< p_ , she does not buy the training. Note that if the decision maker does not manage to buy the training, no other farmer can purchase the training for anyone else in the village. All participants from the same village are interviewed over the course of one day to minimize the chance that the identity of the decision maker becomes known in the village before the elicitation exercise is completed.

**_Design Rationale of the Elicitation_** In the experiment I exploit a random-lottery design and perform three lotteries,

1. a _price lottery_ that assigns a price _p ∈{_ 0 _,_ 2 _,_ 000 _, . . . ,_ 40 _,_ 000 _}_ to each participant;

2. a _choice lottery_ that determines which of the _N_ choices should be implemented; 3. a _decision maker lottery_ that determines which of the _N_ participants in the village has the opportunity to buy the training for the choice selected in 2).

This design implies that a maximum of one farmer can receive the training in each village.

The _price_ lottery ensures that a participant’s valuation is truthful; the _choice_ and _decision maker_ lotteries rule out strategic complementarities or substitutabilities between farmers. To further clarify why strategic complementarities and substitutabilities need to be ruled out in this setting, assume it was possible for a participant to purchase training for two or more farmers. Then, when making a choice, the participant would have to weigh the pros and cons of each n-person combination of farmers (unobservable to the econometrician), their joint decision processes, and how their efforts would complement or substitute each other. Such considerations could distort a participant’s valuations and add a layer of complexity that compromises the tractability of the problem for both the participant and the researcher. The same reasoning applies if the experiment allowed for two or more decision makers. If another person’s choice were to be implemented together with her own in a two decision maker scenario, a participant would have to consider a much larger set of states of the world than if she was the only decision maker, potentially distorting her choices to exploit the complementarity or substitutability with the other 12
decision maker’s choices (or expectations over them). Obviously, if information is made available outside of a controlled experimental setting, more than one person per village can obtain it and demand complementarities or substitutabilities kick in. This makes the decision over the value of others’ learning much more complex. While my experiment cannot speak to this by design, it also provides a scenario in which adoption is bounded from below and the valuation decision has high stakes. If none of the participants buys the training, no one in the village will adopt the techniques.

# **5.2 Belief Update Intervention**

My willingness-to-pay elicitation survey included a belief update experiment to understand how concerns for _i)_ knowledge externalities and _ii)_ contagion externalities affect how much a farmer values training one other farmer.

Knowledge externalities between two farmers depend on the probability that the two farmers share agricultural information with each other _p_<sup>_L_</sup> (I restrict my analysis to direct communication between farmers and exclude indirect communication that involves other members of the community). The enumerator induces the participant to update her belief over _p_<sup>_L_</sup> by informing her that the research team would organize a meeting between the participant and that specific farmer after training had taken place, if the participant is the decision maker and their valuation for that specific farmer is selected by the choice lottery. I call this the “meeting treatment”.

Contagion externalities between two farmers depend on the physical distance between their plots, because the pest spreads by proximity. The enumerator induces the participant to update her belief over _p_<sup>_T_</sup> _ij_<sup>followingatwo-stepprocedure.Firsttheenumeratorasks</sup> the participant how long it would take to walk from her largest maize plot to the closest plot of a specific farmer _j_ , _d_<sup>_P_</sup> _ij_<sup>.Thentheenumeratorinformstheparticipant</sup><sup>_i_ofthe</sup> true as-the-crow-flies walking distance between those plots, _d_<sup>_T_</sup> _ij_<sup>.Icallthisthe“distance”</sup> treatment. Appendix G reports the exact wording used in the experiment. Figure A.4 shows the joint distribution of perceived distance _d_<sup>_P_</sup> _ij_<sup>andtruedistance</sup><sup>_dT_</sup> _ij_<sup>inwalking</sup> minutes. From the figure one can see that in most cases the true and perceived distances are within 20 walking minutes, and never above 100. This means that the plots considered lay within a distance of five miles or eight kilometers from each other. Figure A.5 shows the distribution of the difference between true and perceived distance in the control group, _d_<sup>_T_The median difference is close to zero (equal to -4), so farmers’ beliefs are roughly</sup> _ij_<sup>_−dP_</sup> _ij_<sup>.</sup> correct on average. In addition, the distribution is well-behaved. This is encouraging, as it suggests that farmers are familiar with plot distances. It also suggests that farmers are putting effort into answering plot distance questions that were not incentivized.

Both types of belief update interventions are a within-individual experiment; I generate random variation in contagion and knowledge externalities _within-participant_ at the _valuation level_ . For each farmer, I assign each of her five to eight valuations for others 13
to one of three experimental conditions: control, meeting treatment, distance treatment. This implies that each participant is exposed to all three conditions. The randomized assignment rule specifies that a maximum of four valuations should be assigned to control, a maximum of two to the meeting treatment, and a maximum of two to the distance treatment.

**_Rationale of Belief Update Intervention_** The ideal experiment to study knowledge externalities consists in randomly adding a new node - a person - to a participant’s social network, where the new node is a farmer who has either received training or not, and study how much the participant values information held by the new node. This would exploit the _extensive margin_ of a participant’s social network. The context of my experiment does not allow me to add a new node to a participant’s network, but I can exploit the _intensive margin_ of a social network manipulation by increasing the likelihood that the participant interacts with another farmer. The meeting treatment tries to achieve exactly that. _Ceteris paribus_ , I expect the meeting treatment to increase a participant’s willingness-to-pay for the farmer she is going to meet.

For the meeting treatment to affect willingness-to-pay for another farmer, the participant needs to know that she is going to meet the other farmer before formulating her willingness-to-pay. Additionally, for the meeting treatment to be exogenous, whether the meeting happens needs to be independent from a participant’s willingness-to-pay for that farmer.<sup>14</sup> Hence, before the elicitation, the enumerator informs the participant that the meeting will take place i) regardless of her willingness-to-pay; ii) if the participant is the decision maker; iii) if that choice is selected by the choice lottery.

The ideal experiment to study contagion externalities consists in randomly adding a new node - a plot - to a participant plot’s network, where the new plot is at random distance. By comparing the valuation of participants for farmers with identical plots at a different random distance, one could gauge the importance of contagion spillovers. This would exploit the _extensive margin_ of a participant plot’s network. The context of my experiment does not allow me to add a new node to a participant plot’s network, but I can exploit the _intensive margin_ of the current plot network by increasing the perceived likelihood that a plot is infected by another plot. This is what my distance treatment achieves by revealing the true distance to randomly selected plots. _Ceteris paribus_ , I expect the distance treatment to increase a participant’s willingness-to-pay for a farmer whose plot is surprisingly closer and decrease a participant’s willingness-to-pay for a farmer whose plot is surprisingly further away.

Similarly to the meeting treatment, for the distance treatment to affect the willingnessto-pay for another farmer, the participant needs to learn the true distance to a farmer’s

> 14If the participant could reduce the meeting probability by reducing her willingness-to-pay for that farmer, treatment would be endogenous.

14
plot before formulating her willingness-to-pay for that farmer. Hence, before the elicitation, the enumerator asks the participant what she thinks is the walking distance between her plot and the other farmer’s plot, and then informs her of the true distance. An important caveat is that the enumerator reveals the true as-the-crow-flies distance between any two plots in the experiment - the most relevant because the pest spreads by flying during the moth stage - and not the true walking distance.

### **5.2.1 Training and Researcher-Organized Meeting**

One week after the elicitation exercise, a team of three agronomists visited the villages in which the decision maker had managed to buy the training. In each village, one agronomist collected payment from the decision maker and trained the farmer for whom training was bought. The agronomists were recruited for the project and had not had previous interactions with the participating farmers before this project. Training was carried out in 64 out of 103 experimental villages; all 64 farmers who committed to pay (five for themselves and 59 for another farmer) did, in fact, pay. Each individual training session lasted about three hours and took place at a respondent’s homestead. A training session included a theory module and a practice module. Agronomists taught the theory module with the aid of a color-printed leaflet (available upon request) that they developed together with the author. The leaflet contains basic information about how to recognize, prevent, monitor and control a Fall Armyworm infestation, and the trainee is encouraged to keep it for future reference. The practice module was typically taught in the respondent’s closest maize plot. The (marginal) cost of providing training to one farmer in the experiment is 34,000 UGX or $29.4. If the government were to implement the training, marginal costs would most likely be lower (government wages are typically lower than in the experiment, and government operations have larger economies of scale). Fixed costs of training are negligible in the experiment and would be so if a larger organization were to implement the training as well; the only fixed costs in my experiment consist in a 3-day training of the agronomists.

Once all training sessions had been carried out, the research team arranged meetings for the farmers who had been selected to be decision makers and whose randomly selected valuation involved a meeting treatment (this was the case for 24 farmers). Meetings took place at a location agreed upon by both farmers, and a member of the research team attended the meeting as a facilitator.

# **6 Results**

## **6.1 The Training Program Is Beneficial**

I start by providing evidence that the training increases adoption of pest-control practices. To this end, I exploit the random variation in training provision at the village level 15
generated by the elicitation exercise.

Whether training takes place in a village is a random event, conditional on the willingnessto-pay of the decision maker _D_ for randomly selected potential trainee _z_ . The _price_ , _choice_ , and _decision maker_ lotteries are such that a decision maker cannot affect the price she pays for training, the identity of the recipient, and the likelihood that she herself is the decision maker. But her willingness-to-pay choice can affect the probability that a recipient _z_ , selected via _choice-lottery_ , receives training; the higher the willingness-to-pay of a decision maker for _z_ , the more likely it is that _z_ receives training. Whether training takes place in a village is therefore a random event, conditional on the willingness-to-pay of the decision maker _D_ for randomly selected potential trainee _z_ . This allows me to employ the following empirical specification to evaluate the impact of training one farmer on the adoption of other sampled farmers in the village<sup>15</sup> : The dependent variable is a dummy equal to 1 if farmer _i_ in village _v_ has adopted the following recommended practices to control the Fall Armyworm: spraying pesticides, pouring ash (or sand or soil) on infected plants, crushing eggs or caterpillars. _Trainingv_ is a dummy equal to 1 if training has taken place in village _v_ . _Trained Farmeri_ is equal to 1 if _i_ has received training. _Spillover Farmeri_ is equal to 1 if _Trained Farmeri_ is zero. Indicator 1 ( _wDz,v_ = _p_ ) is equal to 1 if the willingness-to-pay of decision maker _D_ for potential trainee _z_ is equal to _p_ , where _p ∈{_ 0 _,_ 2 000 _, . . . ,_ 40 000 _}_ .<sup>16</sup> Results from estimating 10 are presented in Table 1 and based on responses to a phone follow-up survey carried out in December 2018. In the survey we only ask adoptionrelated questions to farmers who say at least one of their plots had a Fall Armyworm infection during the current season; for this reason, the analysis in Table 1 focuses on practices included in the training module and only applicable once a plot is infected. Before getting to the discussion of results, the reader should have an important caveat in

> 15An alternative way to investigate the relationship between training and adoption is to use the random price assigned by the _price_ lottery to the decision maker as an instrument for training. When I implement this IV specification (not reported) I find that coefficient magnitudes are quite similar to those obtained estimating Eq. 10 but, predictably, noisier.

> 16The OLS estimator _β_ 1 in this case is a weighted estimator, where weights are given by the conditional variance of the treatment variable. The conditional variance of _Trainingv_ (conditional on each possible value of _wDz,v_ ) is highest when, within a bin of _wDz,v_ , the share of treated and untreated is equal. So bins of _wDz,v_ in which everyone is treated or everyone is not treated are going to receive lower weights than bins in which treated and non-treated have similar shares, and hence higher conditional variance (see Chapter 3 in Angrist and Pischke (2009)). In the data, bins such that _wDz,v ∈_ [6 _,_ 000 _,_ 12 _,_ 000] are the ones with the most similar treatment shares and hence are weighted more; if _wDz,v <_ 6 _,_ 000 most or all villages are untreated; if _wDz,v >_ 12 _,_ 000 most or all villages are treated.

16
Table 1: Effects on Adoption

||(1)<br>Any Action|(2)<br>Spray|(3)<br>Pour Ash|(4)<br>Crush<br>Eggs/Worm|
|---|---|---|---|---|
|Trained Farmer|0.15|0.13|-0.01|0.03|
||(0_._08)<sup>_∗_</sup>|(0_._09)|(0_._03)|(0_._03)|
|Spillover Farmer|0.14|0.12|-0.00|0.01|
||(0_._06)<sup>_∗∗_</sup>|(0_._06)<sup>_∗_</sup>|(0_._02)|(0_._01)|
|Control Mean|0.42|0.40|0.04|0.01|
|Observations|739|739|739|739|

**Notes:** The table reports estimates based on specification (10). _Trained Farmer_ is a dummy variable equal to 1 if a farmer has received training on the Fall Armyworm as part of the experiment. _Spillover Farmer_ is a dummy variable equal to 1 if a farmer lives in a village where training was provided to another farmer. The dependent variable in Column (1) is a dummy equal to 1 if the farmer reported having adopted any of the following recommended practices: spraying their field, pouring ash (or sand or soil) on infected plants, crushing the eggs or caterpillars. In the remaining columns the dependent variable is a dummy for each recommended practice. All specifications include fixed effects for the willingness to pay of the Decision Maker for the potential trainee in the village. Robust standard errors are clustered at the village level and given in round brackets; *** (**) (*) indicates significance at the 1% (5%) (10%) level.

mind with respect to estimates in Table 1. The training is randomized at the village level among 103 villages and takes place in 64 villages (translating into 64 trained farmers). Under standard assumptions, this sample size is not adequate to detect effects of the training on adoption. Powering this part of my experiment was not a first-order concern since adoption is not the main outcome of my analysis, but an identical program could fail to replicate these results.

The first column of Table 1 shows adoption of any of the three recommended practices, and the remaining columns show the contribution of each individual practice to overall adoption. The omitted comparison group in this case is that of spillover farmers in villages where training did not take place. Adoption increases by 14% among spillover farmers in villages in which training took place, while it increases by 15% among farmers who received training themselves. This result is driven by higher take-up of pesticides, which increases by a similar magnitude among trained and spillovers farmers. The fourth column shows that trained farmers are much more likely to adopt the practice of crushing eggs and caterpillars by hand, but the practice does not transfer to spillover farmers (their adoption rate is identical to farmers in control villages). These results suggest that only the practice of spraying pesticides diffuses, while the practice of crushing eggs and worms does not diffuse, a pattern that is qualitatively confirmed by two metrics I collected at follow-up. First, when spillovers farmers are asked which practices the trained farmer recommended, most of them mention spraying pesticides and few of them mention any other practice (see top panel of Figure A.9). Second, in July 2019 I administered an 17
incentivized knowledge test to all farmers in the sample<sup>17</sup> and find that while trained farmers are overall not more knowledgeable than spillover farmers or farmers in control villages (see Figure A.8), they are more likely to know that crushing eggs or caterpillars is advisable (the bottom panel of Figure A.9 shows the share of farmers who answered correctly in the knowledge test in each group).

The estimates reported in Table 1 provide causal evidence that when one farmer learns about the technology, others adopt it. This behavior could be triggered by several factors, including lower adoption costs due to a decrease in information barriers or larger value of adoption due to the decrease in pest population generated by adopters. Evidence of the effects of the training program, by itself, is not informative of whether farmers value neighbors’ information. Investigating the value placed by farmers on neighbors’ knowledge, and understanding which factors affect it, is the objective of the next section.

# **6.2 Farmers Value Training Others**

After having established that training is beneficial to village adoption, the next step is to verify whether farmers are aware of the benefits of the training, both for themselves and for others. To do so, I collect farmers’ valuations for themselves to receive the training, and for others to receive the training. I elicit willingness-to-pay for the training using an incentive-compatible mechanism that farmers have already experienced in the past and that they understand well, as shown by measures of optimal bidding behavior and overall comprehension in Appendix B. Figure 1 shows the distribution of willingness-to-pay for self (blue) and one other farmer (orange).

Figure 2 shows the demand for training if the recipient is oneself (blue) or one other farmer (orange). In both cases, demand for training is non-negligible. A useful benchmark to interpret these curves is the median agricultural daily laborer wage in local markets, UGX 5,000 or $ 4.3. At the daily wage price, more than 90% of farmers would buy the training for themselves and more than 60% would buy the training for another farmer.

In the sample, median willingness-to-pay for self _wii_ is UGX 20,000 or $ 17.3, so about four days of work as a daily farm laborer. The median willingness-to-pay for another farmer _wij_ is UGX 10,000 or $ 8.6, the equivalent of two days of work as a farm laborer. Figure 3 plots the joint distribution of willingness-to-pay for self and others; _wii_ on the y-axis against _wij_ on the x-axis, and the 45-degree line is added for reference. Bubble size is proportional to frequencies. As Figure 3 shows, nearly all farmers display _wii > wij_ . This is in line with an implication of the main assumption of the model. In the model,

> 17The test consists of 15 multiple-choice questions about the FAW and how to prevent an infestation. After the respondent has answered all questions, one of them is randomly selected and if the answer is correct, the respondent is awarded a small prize (a pack of salt). On average, respondents answer correctly nine times out of 15, with no difference if they received training themselves (left bar, _Trained Farmer_ ), someone else in the village received training (center bar, _Spillover Farmer_ ), or no training took place in their village (right bar, _Non-trained Village_ ).

18
Figure 1: WTP Distribution <!-- Start of picture text --> WTP For Self<br>WTP For Other<br>Frequency<br>0 10,000 20,000 30,000 40,000<br><!-- End of picture text --> _Notes:_ The figures depicts the distribution of willingness-to-pay for self and others in the sample among the 21 possible prices; blue bars indicate willingness-to-pay for self and orange bars indicate willingnessto-pay for another farmer.

Figure 2: Training Demand Curves <!-- Start of picture text --> 40,000<br>WTP For Self<br>WTP For Other<br>30,000<br>Price in UGX 20,000<br>10,000<br>0<br>0 .2 .4 .6 .8 1<br>Share of Farmers Who Buy<br><!-- End of picture text --> _Notes:_ The figures depicts the demand curves for training, showing the share of participants (on the x-axis) that would purchase training for each of the 21 possible prices (on the y-axis) for themselves and for another farmer in blue and orange respectively.

a farmer values learning positively and always prefers to learn than benefit from contagion externalities, which imply that a farmer always prefers to learn for sure than benefit from externalities. The average value of the ratio<sup>_w_</sup> _w_<sup>_i_</sup> _ii_<sup>_<u>j</u>_is58%,soafarmervaluesanother</sup> farmer’s learning almost two-thirds of her own.

**Altruistic behavior and warm-glow** In the conceptual framework I noted how a selfish assumption is necessary to interpret a participant’s willingness-to-pay for others as the

19
Figure 3: Joint Distribution of WTP for Self and Other <!-- Start of picture text --> WTP For Self<br>0 10,000 20,000 30,000 40,000<br>WTP For Other<br>40,000<br>30,000<br>20,000<br>10,000<br>0<br><!-- End of picture text --> _Notes:_ The figures depicts a scatterplot of the joint distribution of the willingness-to-pay for self against willingness-to-pay for another farmer to receive the training, for each of the 21 possible training prices.

total value to the participant of the externalities produced by the other farmer. In line with this assumption, the willingness-to-pay data suggest that participants do not internalize the social benefit of training. If they did, we would expect to observe two patterns in the data. First, valuations would be uniform within villages - both within and across participants. The previous paragraph disproves that valuations are uniform within participant, as it shows that willingness-to-pay for self is substantially higher than willingness-to-pay for others; in addition, the average coefficient of variation of willingness-to-pay for others at the participant level is 35%. Having uniform valuations across participants means that different participants have a similar willingness to pay for the same farmer; in the data, the average coefficient of variation of willingness-to-pay for the same farmer is equal to 74%, pointing to high dispersion. Second, if participants internalized the social benefit of the training, their willingness-to-pay would increase with village size or with the number of maize farmers in a village. I find that willingness-to-pay for others is not positively correlated with village size and number of maize farmers in a village (the correlation is negative, -11% and -7% respectively), and willingness to pay for self is not meaningfully correlated with either (0 and 2% respectively). Figure A.7 plots willingness to pay (for self or others) against number of households engaged in maize farming in the village at baseline, and bubble size measures frequency. Participants appear to have similar valuations irrespective of the number of households engaged in maize farming in their village. My experiment is not designed to identify or rule out altruism, but I can quantify warm 20
glow (Andreoni, 1990) as the willingness-to-pay for another farmer whom the participant does not know and who produces no spillovers from the participant’s standpoint. I assume that spillovers related to either contagion or knowledge externalities decay to zero beyond a certain plot or home distance threshold respectively. At the 95th percentile in plot and home distance (for a home distance larger than 1.7 miles and an average plot distance larger than 35 walking minutes), the median willingness-to-pay for a farmer whom the participant does not know is zero, pointing to a lack of warm-glow giving behavior; the same holds true at the 90th percentile.

# **6.3 The Social Benefit of the Training Is Large and Heterogeneous**

The willingness-to-pay data allow me to evaluate three policy-relevant objects: the value of the per capita externality generated by training one farmer; the social benefit of the training; and how different targeting criteria for the training generate different levels of social benefit. In what follows I will show how to calculate the per capita externality and social benefit of training one farmer, and then compare two targeting criteria. The first allocates the training according to a _price criterion_ : the farmer with the highest willingness-to-pay gets the training. The second allocates the training according to an _externality criterion_ : the farmer producing the highest per capita externality gets the training. While it is trivial to foresee that the externality criterion will produce a higher social value than the price criterion, farmers’ valuations allow us to fine tune this intuition by quantifying the change in social benefit when externalities are accounted for in targeting decisions.

I use farmers’ willingness-to-pay for others to calculate the externality generated by a trained farmer _t_ in village _v_ : Where _Nj_ is the number of sampled farmers _j_ = _t_ in village _v_ .

Column (2) in Table 2 shows the mean, standard deviation, median, maximum and minimum value of the per capita externality, calculated using equation (11); it ranges from 500 to 24,250 UGX and has a median value of 6,750 UGX.

The social value of _t_ ’s training is then the _Per Capita Externality_ in (11) scaled up by the relevant population size (excluding _t_ ) plus _t_ ’s willingness-to-pay for self. Indicating the relevant population in _t_ ’s village as _Nv_ yields 21
Table 2: Social Value Generated by Different Targeting Criteria

||(1)|(2)|(3)<br>Social Value if|(4)<br> Targeting Criterion is:|
|---|---|---|---|---|
||WTP for Self|Per Capita Ext.|Highest WTP|Highest Ext.|
|Mean|15,226|7,392|419,174|526,434|
||(8_,_721)|(4_,_469)|(535_,_303)|(630_,_738)|
|Median|12,000|6,750|246,857|359,714|
|Max|38,000|24,250|3,252,250|3,786,750|
|Min|0|500|59,500|103,333|
|N|274|274|37|37|

**Notes:** The table shows summary statistics for four quantities indicated by columns (1)-(4). The first is willingness-to-pay for self, calculated at the farmer level. The second is the per-capita externality calculated at the farmer level using equation 11. The third is the social value produced by the farmer with the highest willingness-to-pay in a village, calculated at the village level using equation 12. The fourth is the social value produced by the farmer with the highest per-capita externality in a village, calculated at the village level using equation 12. The figure only includes villages where farmers reported willingness-to-pay values ranging from 0 to 38,000 UGX.

Columns (3) and (4) in Table 2 display statistics for the social value generated by training the farmer willing to pay the highest price (column 3) or the farmer producing the highest externality (column 4). The table excludes villages in which any farmer reports willingness-to-pay equal to 40,000 UGX, the maximum price, because in that case the true willingness-to-pay may have been higher than the maximum price. The social values are calculated at the village level, assuming commercial maize farmers are the relevant population in each village - this seems reasonable since the farmers in my sample are a random draw from the population of commercial maize farmers in a village and almost all of them are willing to pay a positive price to train another farmer in their village. Typically the two targeting criteria select different farmers: in 85% of the villages the farmer with the highest willingness to pay is not the farmer producing the highest per capita externality. The table shows that targeting the training according to the externality criterion leads to a 107,000 UGX gain in mean social value (26%) and a 113,000 UGX gain in median social value (46%) relative to the price criterion. Table E.1 replicates the analysis including villages in which farmers report willingness-to-pay values for self or others equal the maximum (40,000 UGX).

While the assumption on the relevant population affects my estimates in columns (3)(4), the general pattern that the social value generated by the highest-externality farmer is higher than that generated by the highest-willingness-to-pay farmer holds across the range of the distribution of population sizes. In Figure 4 I estimate the social value of the two targeting policies at different population sizes using the per capita externality calculated in the data; I also include two counterfactual analyses: the social value generated by training the most socially connected farmer and the social value generated by training the farmer 22
with the most central plot. Finally, I include the social benefits generated by the farmer producing the lowest per capita externality to illustrate the cost of wrong targeting. Like Table 2, the figure excludes villages in which any farmer reported willingness-to-pay values for self or others equal the maximum (40,000 UGX). Figure 4: Social Value By Population Size and Targeting Criterion <!-- Start of picture text --> Social Value 1000000<br>Highest WTP<br>Highest Externality<br>Lowest Externality<br>800,000 Socially Central<br>Geographically Central<br>600,000<br>400,000<br>200,000<br>0<br>0 10 20 30 40 50 60 70 80 90 100<br>Maize Farmers per Village<br><!-- End of picture text --> _Notes:_ The figure depicts the mean social value produced by five types of farmers when the population of commercial maize farmers ranges from 1 to 100. The social value is calculated at the village level using equation 12 and averaging across villages. The five types of farmers are: the farmer with the highest willingness-to-pay in the village (red line), the farmer producing the highest per capita externality in the village (dark blue line); the farmer producing the lowest per capita externality in the village (light blue line); the most socially connected farmer (orange line), or the farmer with the highest _Connectedness_ (see Appendix F); the farmer with the most geographically central maize plot (green line). The mean value of the commercial farmer population size in my sample is equal to 54 and marked by a dashed vertical gray line. All valuations equal to 40,000 UGX are excluded from the sample.

The figure shows that training the highest-externality farmer (dark blue line) always generates a higher social value than training the highest-willingness-to-pay farmer (red line) for a farmer population size larger than four (a threshold that all villages in my sample meet, as the commercial maize farmer population ranges from 11 to 164). At the maize farmer population sample mean, equal to 54 and marked by the vertical dashed line, the values of the lines in the figure correspond to the values reported in the first line of Table 2. The figure also anticipates the findings I will discuss in the next section 23
on the importance of knowledge and contagion externalities. The orange line reports the social value of targeting the most socially connected farmer (the farmer with the highest _Connectedness_ , see Appendix F), while the green line reports the social value of targeting the farmer with the most centrally located maize plot in the village. Interestingly, both lines lay between the red and the dark blue lines, illustrating that farmers value more socially and geographically central farmers rather than farmers who have a large willingness to pay for themselves. The same pattern emerges if we include villages in which any farmer reported WTP values of 40,000 UGX for themselves or others (Figure E.2).

# **6.4 Valuations Respond to Changes in Externalities**

This section first presents the empirical strategy to evaluate the impacts of the belief update intervention on willingness-to-pay for others, and then comments on results. The outcome of interest is the willingness-to-pay of farmer _i_ for farmer _j_ , _wij_ . A farmer’s willingness-to-pay can take 21 monetary values that are multiples of 2,000 Ugandan Shillings, _wij ∈{_ 0 _,_ 2 000 _,_ 4 000 _, . . . ,_ 40 000 _}_ .

I conjecture that the distance treatment should negatively affect _wij_ if the distance information is _good news_ for _i_ , meaning that _j_ ’s plot is surprisingly _further away_ from _i_ ’s plot. Conversely, the distance treatment should positively affect _wij_ if the distance information is _bad news_ , meaning that _j_ ’s plot is surprisingly closer than expected. The rationale is that if _j_ ’s plot is further away than _i_ expected, the benefit accruing to _i_ of _j_ ’s adoption is lower, and the other way around. The key metrics are when _i_ learns that _j_ is surprisingly further away, and when _i_ learns that _j_ is surprisingly closer. Variable _d_<sup>_T_</sup> _ij_<sup>isthetruedistancebetween</sup><sup>_i_’s</sup> largest plot and _j_ ’s closest plot in walking minutes. Specifically, _d_<sup>_T_</sup> _ij_<sup>istheas-the-crow-</sup> flies distance in miles between the GPS coordinates of the centroids<sup>18</sup> of the two plots, converted to walking minutes by assuming that the average adult takes 20 minutes to walk one mile. The variable _d_<sup>_P_</sup> _ij_<sup>isaparticipant</sup><sup>_i_’sanswerwhenaskedhowlongittakes</sup> to walk from her largest plot to _j_ ’s closest plot (exact question wording can be found in

> 18If a plot of land is a two-dimensional plane, its centroid is the arithmetic mean position of all points of the plane.

24
Appendix G). Variable _Tij_<sup>_d_isadummyequalto1ifparticipant</sup><sup>_i_istoldthetruedistance</sup> to farmer _j_ ’s plot. The estimating equation for the distance treatment is: The coefficients of interest are _β_ 1, for which I expect a negative sign, and _β_ 2, for which I expect a positive sign. The coefficient of _β_ 1 measures the change in _wij_ for every minute that _j_ ’s plot is surprisingly further away from _i_ ’s plot; it proxies the change in the value that _i_ attaches to _j_ ’s adoption when _j_ ’s plot is less important in determining _i_ ’s infection status. The opposite is the case for _β_ 2, it measures the change in _wij_ for every minute that _j_ ’s plot is surprisingly closer to _i_ ’s plot. Specification 13 includes fixed effects _αi_ for participant _i_ . Notice how, for clarity of exposition, (13) does not include the coefficient of _Tij_<sup>_d_alone:thisimplicitlyassumesthattreatmenteffectsarenullforfarmerswithcorrect</sup> beliefs about distance (I present an alternative specification that includes _Tij_<sup>_d_in appendix).</sup> The distance treatment I implement allows me to estimate the local average treatment effect (LATE) of a change in _i_ ’s perceived plot distance between farmer _i_ and _j_ and _i_ ’s willingness-to-pay for _j_ to receive training. The size of the treatment, which is the difference between true and perceived distance in absolute value _|d_<sup>_T_</sup> _ij_<sup>_−dP_</sup> _ij_<sup>_|_,isafunctionof</sup> perceived distance _d_<sup>_P_</sup> _ij_<sup>.Themore afarmer’s perception</sup><sup>_dP_</sup> _ij_<sup>is off,the larger the treatment</sup> she receives. This implies that there is self-selection in the treatment and I can only estimate the effect on those who have wrong beliefs.

The purpose of the meeting treatment is to _ceteris paribus_ increase the perceived probability that _i_ learns the information from _j_ . During the elicitation exercise, participant _i_ is told that the research team is going to organize a meeting with _j_ , to take place after _j_ has received training. Participant _i_ is also told that the meeting takes place regardless of whether _j_ receives training or not, to keep the meeting treatment truly exogenous (if the participant could determine whether the meeting happens or not through her willingnessto-pay decision, the meeting treatment would be endogenous). The estimating equation for the meeting treatment is where _Tij_<sup>_m_is a dummy equal to 1 if participant</sup><sup>_i_is invited to a researcher-organized meet-</sup> ing<sup>19</sup> with _j_ . The exact words used to administer the meeting treatment are reported in Appendix G.

> 19The meeting treatment is similar to Lowe (2021) since both treatments are aimed at increasing the probability that individuals interact with each other. But Lowe (2021) introduces economic incentives to communicate with cricket players of a different social caste and looks at how this type of contact affects discrimination, while the meeting treatment of my study is not (and should not) be incentivized.

25
Table 3 presents results from estimating specification 13. Estimates are at the dyad level, and a dyad is composed by a farmer _i_ stating her valuation and a farmer _j_ for which the valuation is made. Out of 3,566 dyads for which the distance variables are not missing, the last line of column (1) shows that in 939 dyads farmer _i_ would potentially receive good news and in 2,435 dyads she would receive bad news (in 192 dyads she would receive no news because she has correct beliefs). The coefficients of interest are _Good News_ and _Bad News_ , which measure the change in willingness-to-pay of _i_ for _j_ for a 1-minute increase in absolute net distance, or _|d_<sup>_T_</sup> _ij_<sup>_−dP_</sup> _ij_<sup>_|_.Thecoefficienton</sup><sup>_GoodNews_incolumn</sup> (1) is negative as expected. It should be interpreted as the decrease in _i_ ’s willingness-topay for _j_ ’s information for every extra minute that _j_ ’s plot is surprisingly further away than _i_ believed. The coefficient size is 68 UGX and at the mean of _Potential Good News_ (equal to 8) it implies a decrease of 544 UGX, $0.14 or about 11% of the daily wage of a local agricultural laborer. The coefficient on _Bad News_ is surprisingly negative but small and insignificant at conventional levels. Overall, results in column (1) show that farmers reduce their willingness-to-pay for farmers that generate lower contagion externalities.

Theory does not predict the difference between the coefficient size of _Bad News_ and _Good News_ that column (1) in Table 3 displays. An experimental feature that would explain this difference is that a _Good News_ treatment is _actually_ good news, while a _Bad News_ treatment is not necessarily bad news, for the following reason. Farmers are asked about the walking distance between plots, so their answer may take into account rural paths, obstacles or differences in altitude. The distance the enumerator treats them with, _d_<sup>_T_</sup> _ij_<sup>,istheas-the-crow-flieswalkingdistance(betweenplotcentroids)assuminga</sup> farmer walks at three miles per hour (20 minutes per mile). As-the-crow-flies is the relevant distance metric for pest spread because the pest spreads by flying to other plots during the moth stage. Hence, the walking distance stated by farmers _d_<sup>_P_</sup> _ij_<sup>canonlybe</sup> larger than the true walking distance between plots if the farmer has perfect information and walks at a speed of three miles/hour. For this reason, when the true distance is larger than the perceived distance, _d_<sup>_T_</sup> _ij_<sup>_>dP_</sup> _ij_<sup>,thefarmerisundoubtedlyreceivinga</sup> _Good News_ type of shock. When instead _d_<sup>_T_</sup> _ij_<sup>_<dP_</sup> _ij_<sup>,itmaybethatthefarmerdoes</sup> not actually receive bad news because she knows that the walking path is actually much longer than the as-the-crow-flies path. I address this issue by making four different assumptions about the relationship between true and perceived distance in the data, and re-estimating specification 13. In columns (2)-(5) I replace the perceived distance _d_<sup>_P_</sup> _ij_<sup>, used</sup> to calculate _Bad News_ , _Good News_ , _Potential Bad News_ and _Potential Good News_ , with _λd_<sup>_P_where0</sup><sup>_≤λ ≤_1isascalingfactor.Incolumn(2)Iset</sup><sup>_λ_suchthatthemeans</sup> _ij_<sup>,</sup> of the distance variables equalize, _λ_ =<sup>_E_(</sup><sup>_dT_)</sup> _/E_ ( _d_<sup>_P_</sup> ), while in column (3) I set _λ_ so that medians equalize, _λ_ =<sup>_Med_(</sup><sup>_dT_)</sup> _/Med_ ( _d_<sup>_P_</sup> ). In column (4) _λ_ is set such that true distance is the hypothenuse of an isosceles right triangle and the perceived distance _d_<sup>_P_</sup> _ij_<sup>istwiceeach</sup> 26
Table 3: Effects of Belief Update Intervention

||Unscaled||S|caled||
|---|---|---|---|---|---|
|||Equa|lity of|Pat|h Shape|
||(1)|Means<br>(2)|Medians<br>(3)|Triangle<br>(4)|Half Circle<br>(5)|
|Potential Good News|-10.74|-34.24|-30.59|-28.65|-32.48|
||(20_._97)|(20_._43)<sup>_∗_</sup>|(20_._57)|(20_._65)|(20_._53)|
|Good News|-68.01|-54.30|-56.22|-58.10|-55.43|
||(36_._80)<sup>_∗_</sup>|(26_._85)<sup>_∗∗_</sup>|(28_._40)<sup>_∗∗_</sup>|(29_._44)<sup>_∗∗_</sup>|(27_._69)<sup>_∗∗_</sup>|
|Potential Bad News|-10.14|-21.60|-18.07|-16.53|-19.68|
||(8_._82)|(16_._79)|(14_._65)|(13_._55)|(15_._60)|
|Bad News|-14.55|-27.82|-24.61|-23.06|-26.14|
||(9_._66)|(18_._09)|(15_._86)|(14_._70)|(16_._85)|
|Scaling Factor _λ_|-|_E_(_d_<sup>_T_ </sup>)_/E_(_d_<sup>_P_ </sup>)|_M_(_d_<sup>_T_ </sup>)_/M_(_d_<sup>_P_ </sup>)|1_/_<br>_√_<br>2|2_/π_|
|_Control Means_||||||
|_wij_|11,772|11,772|11,772|11,772|11,772|
|Potential Good News|8|7|7|7|7|
|Potential Bad News|14|8|9|9|9|
|Observations|3,566|3,566|3,566|3,566|3,566|
|Of Which Pot. Good/Bad News|939_/_2435|1764_/_1802|1596_/_1824|1566_/_2000|1759_/_1807|

**Notes:** The table reports ordinary least squares estimates based on specification (13). The dependent variable _wij_ is the willingness-to-pay of the participant _i_ for another farmer _j_ . _Potential Good News_ is equal to the absolute value of the difference between true and rescaled perceived distance in walking minutes if the difference is positive, _|d_<sup>_T_</sup> _ij_<sup>_−λdP_</sup> _ij_<sup>_|_if</sup> _d_<sup>_T_</sup> _ij_<sup>_λ −dP_</sup> _ij_<sup>_>_0.</sup><sup>_PotentialBadNews_isequaltotheabsolutevalueofthedifferencebetweentrueandrescaledperceived</sup> distance in walking minutes if the difference is negative, _|d_<sup>_T_</sup> _ij_<sup>_−λdP_</sup> _ij_<sup>_|_if</sup><sup>_dT_</sup> _ij_<sup>_−λdP_</sup> _ij_<sup>_<_0.</sup><sup>_Good(Bad)News_is equal to</sup><sup>_Potential_</sup> _Good (Bad) News_ multiplied by a treatment indicator _Td_ equal to 1 if the true distance was revealed to the participant. Column (1) reports unscaled estimates (or _λ_ = 1). In column (2) _λ_ solves _E_ ( _d_<sup>_T_</sup> _ij_<sup>)=</sup><sup>_λE_(</sup><sup>_dP_</sup> _ij_<sup>);sotheperceiveddistanceis</sup> rescaled to have mean equal to the true distance. In column (3) _λ_ solves _Median_ ( _d_<sup>_T_</sup> _ij_<sup>)=</sup><sup>_λMedian_(</sup><sup>_dP_</sup> _ij_<sup>);sotheperceived</sup> distance is rescaled to have median equal to the true distance. In column (4) _λ_ solves _d_<sup>_T_</sup> _ij_<sup>=</sup><sup>_λdP_</sup> _ij_<sup>,</sup><sup>_dT_</sup> _ij_<sup>isthehypotenuseof</sup> an isosceles right triangle and _d_<sup>_P_</sup> _ij_<sup>istwiceeachcathetus,(</sup><sup>_dT_</sup> _ij_<sup>)2=(</sup><sup><u>1</u></sup> 2<sup>_dP_</sup> _ij_<sup>)2+ (</sup><sup><u>1</u></sup> 2<sup>_dP_</sup> _ij_<sup>)2.Incolumn(5)</sup><sup>_λ_solves</sup><sup>_dT_</sup> _ij_<sup>=</sup><sup>_λdP_</sup> _ij_<sup>,</sup> _d_<sup>_T_</sup> _ij_<sup>isthediameterofacircleand</sup><sup>_dP_</sup> _ij_<sup>ishalfofacircumference,2</sup><sup>_dP_</sup> _ij_<sup>=2</sup><sup>_π_</sup> _d_ 2<sup>_T_</sup> _ij_<sup>.Then</sup><sup>_λ_=2</sup><sup>_/π_.ValuesareinUgandan</sup> Shillings. All specifications include participant fixed effects. Robust standard errors are given in round brackets; *** (**) (*) indicates significance at the 1% (5%) (10%) level.

cathetus: _λ_ =<sup>1</sup> _/√_ 2. This allows me to examine the scenario depicted in Figure A.3, where the solid line between A and B is the as-the-crow-flies distance and the dotted line is the walking path a farmer has in mind. Similarly, in column (5) I set _λ_ such that the true distance is the diameter of a circle and the perceived distance _d_<sup>_P_</sup> _ij_<sup>ishalfacircumference:</sup> _λ_ =<sup>2</sup> _/π_ . In this case, the farmer has in mind a semi-circular walking path between two plots, while the as-the-crow-flies distance is the diameter.

Scaling results in more dyads having potential good news and fewer dyads having potential bad news relative to the unscaled analysis; in the last row of columns (2) - (5) 27
the number of dyads with potential good news is much closer to the number of dyads with potential bad news. As a result, the point estimates of _Good News_ are smaller and have tighter confidence intervals, while those of _Bad News_ are larger and have wider confidence intervals. These results further confirm that farmers decrease their willingnessto-pay with lower contagion externalities, but do not increase their willingness-to-pay with higher contagion externalities.

As noted earlier, specification (13) does not include _Tij_<sup>_d_alone,assumingimplicitlythat</sup> telling a farmer her beliefs are correct will not have any effect on her _wij_ . About 5% of the dyads have a distance error equal to zero, and half of those are treated. Table D.1 in appendix B estimates specification (13) including _Tij_<sup>_d_;itshowstheeffectoftelling</sup> a farmer her beliefs are correct is statistically indistinguishable from zero, albeit with a positive point estimate, and other estimates are not affected by the inclusion of _Tij_<sup>_d_.</sup> Figure A.6 displays the average willingness-to-pay for another farmer if a participant is invited to meet the other farmer (right bar) or not (left bar). The willingness-to-pay for the other farmer is not significantly affected by the meeting treatment: coefficient _δ_ in specification (14) is negative and insignificant (the point estimate is -230.8, the standard error 153.9). The meeting treatment did not seem to work as intended by design, overall, which is surprising because encouraging farmers to interact is a common approach to disseminate information in rural areas in lower-income countries. Previous work has shown that it has some positive effects on adoption and yields (BenYishay and Mobarak, 2018; Vasilaky and Leonard, 2018). If the behavior observed in my experiment replicates in other contexts, uncovering its causes will help identify when we can and cannot leverage human interaction to disseminate knowledge. One element that emerged during the elicitation exercise, and that is relevant here, is that 92% of all farmer dyads know each other already. It may be that farmers prefer to exchange information on their own, outside of a structured social interaction mediated by an enumerator; or it may be that farmers anticipate costs in term of lost labor or transport without any added benefits, given that they are anyway able to reach the recipient independently from the research team. Another option is that farmers are particularly adverse to meeting farmers that they do not know very well, while attaching a positive value to them receiving training. Or still, farmers may be unwilling to meet someone who is more knowledgeable than them for reputation purposes or because they anticipate feeling shameful. They may also be willing to pay for someone’s training for reciprocity purposes (to give back to someone, or to trigger a symmetric reaction from them) which are orthogonal to the information content of the training. Finally, another potential explanation is that a participant infers that, because meetings will happen, the information content of the training is going to circulate in the village. This realization can trigger a free-riding behavior, where the participant decreases her willingness-to-pay for all the farmers she is asked about after learning that researchers will organize meetings.

28
While the belief shock on knowledge externalities did not affect valuations as anticipated, it is possible to exploit the richness of the elicitation data to shed some light on what drives farmers’ valuations for others. To do so, I let four parsimonious model selection algorithms choose which variables out of 16 best explain _wij_ . The results of this exercise are displayed in Figure 5. The 16 variables I feed to the algorithms are: true plot distance, perceived plot distance, home distance, whether _i_ knows _j_ , whether _i_ visits (or receives visits from) _j_ , whether _i_ and _j_ are relative, whether _i_ and _j_ socialize, whether _i_ borrows (or lends) money from _j_ , whether _i_ borrows (or lends) goods from _j_ , whether _i_ receives (or gives) advice to _j_ , whether they speak about agriculture, whether they pray together (see Appendix F for variable definitions). These variables measure the extent of social connection between two individuals in different life domains, and are identical to the measures used by Banerjee et al. (2013) to quantify social connection between Indian villagers (but adapted to the Ugandan context). The model selection algorithms used in this exercise are three Lasso (adaptive, plugin, and minimum BIC) and Forward Stepwise. I adopt the following procedure: i) standardize regressors; ii) residualize both _wij_ and each regressor on fixed effects for _i_ and _j_ , such that the remaining variation is specific to the _ij_ dyad; iii) run the algorithms such that each selects the model with the highest explanatory power; iv) regress _wij_ on the four selected models. Figure 5 shows the coefficient sizes of regressors in each selected model, expressed in standard deviations. Whether farmers know each other is the predictor with the largest coefficient and is picked up by three out of four selection algorithms; it is followed by receiving advice from, paying visits to, and lending money to the other farmer, which are picked up by all four algorithms. Socializing also matters but is only picked up by the Adaptive and BIC Lasso, and borrowing money and receive visit are only picked up by the Forward Stepwise. I interpret the selected coefficients as providing some suggesting evidence that farmers value training another farmer if that person is accessible, trustworthy, and has a record of sharing information.

29
Figure 5: Correlates of Willingness To Pay <!-- Start of picture text --> Know<br>Pay Visit<br>Related<br>Socialize<br>Lend Money<br>Receive Advice<br>Borrow Money<br>Receive Visit<br>-.2 -.1 0 .1 .2<br>Lasso Adaptive Lasso Plugin<br>Lasso Bic Forward Stepwise<br><!-- End of picture text --> _Notes:_ The figure depicts the standardized coefficients of a regression of _wij_ on subsets of regressors generated by Lasso and Forward Stepwise. In each case, the algorithm is fed a set of 16 variables: _True Distanceij_ , _Perceived Distanceij_ , _Home Distanceij_ , _Knowij_ , _Receive V isitij_ , _Pay V isitij_ , _Relativeij_ , _Socializeij_ , _Borrow Moneyij_ , _Lend Moneyij_ , _Borrow Goodsij_ , _Lend Goodsij_ , _Receive Adviceij_ , _Give Adviceij_ , _Speak Agricultureij_ , _Prayij_ . Each algorithm returns a subset of the 16 variables. The willingness-to-pay _wij_ is then regressed on each subset, including fixed effects for participant _i_ and recipient _j_ .

30
# **7 Conclusion**

This paper investigates how externalities affect farmers’ decisions to adopt agricultural technology. I study a new technology, namely a training on pest-control techniques to manage the outbreak of a new pest in Uganda; the training is beneficial and increases adoption of the practices by 15% among training participants. I set out to measure the monetary value of the externalities of the training, calculate the social benefit of the training if it is targeted to farmers producing high externalities versus not, and identify from where externalities originate.

To measure externalities, I carry out a lab-in-the-field experiment and elicit how much participants are willing to pay for a farmer in their village to receive the training, conditional on only one of them being able to do so. Willingness to pay for others measures the net spillovers that each participant anticipates as a consequence of training another farmer in their community. I find that farmers anticipate substantial spillovers from the training, as they are willing to pay two days’ wages on average ($8.6) to have a farmer in their community receive the training.

To calculate the social benefit of training a farmer, I calculate the per capita externality the farmer produces (how much others are willing to pay for that farmer on average) and scale it up by community size. This allows me to compare the social benefit obtained from training a farmer others value highly (a farmer producing high positive externalities) to the social benefit obtained from training a farmer with high individual valuation of the training (high willingness to pay for self). Results show that the social benefit gain from targeting farmers who produce high positive externalities rather than farmers with high private valuation of the technology is substantial, a 26% difference on the mean and 46% on the median, which demonstrates externalities should be taken into account when defining targeting criteria.

To understand where externalities originate from, I examine two sources that would matter theoretically in this context - _contagion_ and _knowledge_ externalities - and evaluate whether they affect farmers’ valuations. I introduce randomized variation in externalities by inducing some farmers to update (i) their belief over the probability of infection from another farmer’s plot to theirs (the perceived _contagion_ externality between the two farmers), (ii) their beliefs over the probability that knowledge of the pest-control techniques spills over from another farmer to them (the perceived _knowledge_ externality between them). I find that farmers respond to contagion externalities by decreasing their willingness-to-pay for farmers whose plots are further away. My experimental approach does not pick up knowledge externalities, but I provide evidence that farmers value training those who are more accessible to them and from whom they have received advice.

Taken together, my results show the importance of accounting for externalities to optimize social policies. In my specific context, externality considerations indicate the ideal 31
adopters are farmers who are socially central in the social network and whose plots are centrally located. Adapting these conclusions to other contexts will require incorporating a careful analysis of the positive and negative externalities connected to a technology before a targeting decision is made, and weighing the maximization of social benefits against alternative considerations such as equity or inclusivity.

32