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.

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