## Abstract

Technology adoption often requires multiple stages of investment. As new information emerges, agents may abandon a technology that was profitable in expectation. We use a field experiment to vary the payoffs at two stages of investment in a new technology: a tree species that provides on-farm fertilizer benefits. Farmer decisions identify the information about profitability that arrives between the take-up and follow-through stages. Results show that this form of uncertainty increases take-up but lowers average tree survival, decreasing the cost-effectiveness of take-up subsidies. Thus, uncertainty offers another explanation for why even costly technologies may go unused or be abandoned.

## I. Introduction

LOW rates of adoption for seemingly beneficial technologies remain a puzzle. Classic examples in developing countries include adoption of fertilizer, hybrid crop varieties, clean stoves, latrines, water purification systems, and mosquito nets. Subsidizing the adoption of these technologies may be justified on a number of grounds, including positive health or environmental externalities, a lack of information about the technology's benefits, and credit constraints. In most cases, subsidies are tied to the initial purchase price. However, these benefits often come from usage or continued investment (follow-through) rather than the initial purchase (take-up). For example, new crop varieties must be cultivated, medicines must be taken on schedule, clean cookstoves must be used in place of older cooking technologies, and gym members must exercise.

The multistaged adoption decisions behind these technologies are inherently dynamic. At the time of take-up, benefits of both the technology and costs associated with the follow-through decision may be unknown to the potential adopter. New information arrives between the take-up and follow-through decisions in the form of learning about the technology (Foster & Rosenzweig, 1995; Conley & Udry, 2010; Beaman et al., 2014) or in the form of shocks to the opportunity cost of follow-through. If the new information contains bad news about the profitability of the technology, then adopters may opt to abandon it (i.e., forgo the follow-through investments). Importantly, if adopters know that they can reoptimize once new information is available, then they are likely to account for this at the time of take-up. Thus, the take-up decision for these technologies amounts to the purchase of an option to follow through.

The dynamics of multistaged adoption decisions complicate the use of subsidies to correct suboptimal rates of adoption. If all of the costs and benefits of the technology are known at the time of take-up, everyone who takes up at a positive price will also follow through. However, take-up may not perfectly predict follow-through for at least two reasons: if there is an intensive margin to the follow-through decision or if the adopter receives new information between take-up and follow-through.1 In these cases, understanding whether subsidizing take-up affects the likelihood and intensity of follow-through by changing the composition of adopters, for example, through a screening effect of the take-up price, has important implications for policy design.2 While the literature has largely focused on the former reason (the intensive margin), our focus is on the latter, which we refer to as uncertainty.3 We highlight two implications of uncertainty for the design of policy. First, the presence of some uncertainty generates imperfect follow-through, but a positive screening effect of the take-up price remains: a higher price induces selection by those who are relatively more likely to follow through. Second, and perhaps counterintuitively, high levels of uncertainty induce high take-up rates. High take-up rates, in turn, dilute the screening effect of the take-up price, creating a disconnect between take-up and follow-through, even at high prices. This last consequence of uncertainty may explain why subsidies have been observed to undermine the screening effect of the take-up price in some cases (Ashraf, Berry, & Shapiro, 2010; Berry et al., forthcoming) but not others (Cohen & Dupas, 2010).4

This paper asks how uncertainty affects take-up and follow-through outcomes and the effectiveness of subsidies for technology adoption. We develop theoretical and analytical frameworks that can be applied in the following very general circumstances: (a) the decision to take up the technology precedes costly follow-through investments that are necessary for the full realization of the technology's benefits, and (b) a failure to follow through is not penalized (there is limited liability). We apply our analytic framework to farmer decisions to adopt agroforestry trees in Zambia. This technology requires both a one-time take-up decision (purchasing seedlings) and follow-through decisions (planting and caring for the trees) that occur in the months after take-up and are necessary for tree survival but can be neglected without penalty.5 In this context, uncertainty at take-up emerges from potential shocks to the opportunity cost of follow-through, including shocks that affect the trees directly (e.g., pests, drought) but also those that affect the value of competing activities (e.g., illness of a household member, crop prices) and therefore the opportunity cost of time. The analytic framework allows estimating the magnitude of the uncertainty that is dissipated before follow-through decisions are made, and thus offers a general framework for analyzing the effectiveness of subsidies under many forms of uncertainty.

We first establish that uncertainty plays a theoretically important role in the effects of subsidies for multistage technology adoption using a simplified model in which individuals make binary take-up and follow-through decisions at two different points in time. The theoretical model generates the clear predictions about the relationship between uncertainty and adoption outcomes. Our conceptual framework borrows heavily from the literature on investment under uncertainty (Pindyck, 1993; Dixit & Pindyck, 1994) and, like Fafchamps (1993), shows that choices that appear to lead to losses (like purchasing a technology that will soon be abandoned) can be rational ex ante if they preserve flexibility.

Next, we generate empirical evidence for these predictions using a field experiment. Farmers choose whether to adopt an agroforestry tree species that generates private soil fertility benefits over the long term but carries short-run costs. We observe whether the 1,314 farmers in the study take up a fifty-tree seedling package at the start of the agricultural cycle. The follow-through decision consists of the number of seedlings that the farmer chooses to plant and care for (which we together refer to as tree cultivation) and, unlike our theoretical model, has an intensive margin. This decision is separated in time from the take-up decision since it occurs over the course of the subsequent year. We orthogonally vary the take-up price (through a random subsidy) and the incentives for follow-through (through a randomly assigned cash prize for the survival of at least 35 trees). This two-stage experimental variation helps identify both reduced-form tests and a dynamic structural model. The reduced-form responses to our treatments are consistent with predicted behavior in the face of substantial uncertainty: while farmers respond to economic incentives—they take up at higher rates under higher subsidies and follow through at higher rates under higher rewards—the randomized take-up subsidies are not predictive of the follow-through outcomes.6 In addition, a large share of farmers who paid a positive price end up abandoning the technology altogether, which is consistent with new information that arrives after take-up.

We use a dynamic structural model to quantify the scale of the uncertainty and its contribution to the screening effect of take-up price separately from that of the intensive margin of adoption.7 We find that in our setting, heterogeneity along the intensive margin of tree survival (the privately optimal number of trees) induces a negative screening effect of prices (i.e., higher prices attract farmers with a lower intensity of follow-through, similar to Suri, 2011), working in the opposite direction of the positive screening effect of prices in the presence of uncertainty. The standard deviation of the unknown component of cost is roughly equal to 10 person-days of agricultural labor, suggesting the scale of uncertainty is large (the average private profit from the trees is equivalent to 9.4 person-days of agricultural labor). In our setting, the flexibility associated with acquiring additional information before making follow-through decisions leads to 26% higher take-up than if farmers had to make follow-through decisions without any additional information.

Methodologically, our econometric framework is an example of sequential identification of subjective and objective opportunity cost components in a dynamic discrete choice model (Heckman & Navarro, 2005, 2007). We account for selection into treatment (in our case, take-up) when identifying the distribution of the unobserved opportunity cost determinants by introducing two layers of random variation in economic incentives: one produces a probability of take-up equal to 1 for a randomly selected subpopulation; a second produces an interior solution in tree cultivation outcomes with probability 1 in the limit. Experimental variation in treatments at two different points in time offers an alternative to a panel data structure, since statistically independent samples are exposed to each of the different treatment combinations. To our knowledge, this is the first paper to introduce experimental variation in order to satisfy the exclusion restrictions needed for sequential identification.

Our final step uses the structural model to simulate counterfactuals that vary uncertainty to quantify its importance in adoption dynamics and the response to subsidies. From a policy standpoint, uncertainty lowers adoption outcomes per dollar of subsidy invested but increases the expected private profits to the adopter because the downside risk from taking up is bounded at 0. The simulations also highlight a trade-off associated with take-up subsidies under uncertainty: the negative screening effect of subsidizing the take-up price may be offset by higher rates of take-up, such that a larger number of farmers produce a smaller number of trees each. The policy implications of this trade-off depend on whether the benefits of the technology come from high levels of follow-through by a small number of adopters or from lower levels of follow-through by many adopters. The simulations also point to the benefits of incentivizing follow-through directly. Stronger contracts that force adopters to follow through once they take up (e.g., by liability rules) address the problem of high take-up coupled with low follow-through, but they do so at a clear cost to the adopter. While this paper does not provide a policy prescription on the optimal design of subsidies, it highlights the importance of further research into innovative solutions to encourage both take-up and follow-through in the presence of uncertainty.

## II. A Simple Model of Intertemporal Technology Adoption

This section provides a simplified framework to facilitate intuition on the role of uncertainty in self-selection. We provide formal proofs for the propositions in appendix A.1 for both a bivariate and generic distribution of shocks. Section V extends the simplified version of the model presented here to account for nonbinary follow-through decisions.

Consider a two-period model, where each agent chooses whether to purchase (take up) a single unit of a technology in the first period (time 0) and whether to follow through with implementation of the technology (also a binary decision) in the second period (time 1). The only cost incurred at take-up is $c-A$, where $c$ is the price of the technology and $A$ is an exogenous subsidy. At time 0, individuals have only some information about the costs and benefits of following through. We assume the privately known and unknown components of the net (of benefits) cost of following through, $F0$ and $F1$, respectively, are additively separable. $F0$ is known at all times, and $F1$ is revealed to the agent at time 1. Thus, the private benefit of following through is given by $R-(F0+F1)$, where $R$ is an exogenous reward conditional on following through. Note that because the term $F0+F1$ represents the cost net of benefits, it can be positive or negative. Assume that $c$, $A$, and $R$ are constant across agents, while $F0$ varies according to some cdf $G(f0)$. Assume further that

1. $F0$ and $F1$ are independent.

2. Agents correctly assume $Et=0(F1)=0$.

The first, independence, assumption is essentially a restatement of the information structure: there is no information left in $F0$ that would help the individual predict the realization of $F1$. In other words, $F0$ represents the agent's best guess at $t=0$ about her net cost of following through, and $F1$ represents any new information that emerges after the take-up decision is made. Assumption (b) means that agents have rational expectations.

Following backward induction, the agent decides to follow through at $t=1$ if $R-F0-F1>0$. If this inequality does not hold, the agent does not follow through, which yields a payoff of 0 at $t=1$. At $t=0$, the agent decides to take up by purchasing the technology if
$EF1max(R-F0-F1,0)≥c-Aδ,$
(1)
where $δ$ is the one-period discount factor and the expectation in equation (1) is taken with respect to the density of $F1$.8

To simplify exposition, assume that the distribution of $F1$ is such that $F1∈{fL,fH}$, with $fL and $Pr(F1=fL)=pL$.9 With $pL=12$, this simple distributional assumption on the shocks allows us to represent a mean-preserving increase in uncertainty as a symmetric widening of the distance between $fL$ and $fH$. With this assumption, we can classify individuals into three types: those who always follow through, regardless of the realization of $F1$ (always follow-through types), those who follow through only if the low net cost shock is realized (contingent follow-through types), and those who never follow through (never follow-through types). These three types of agents can be characterized by whether their value of $F0$ is below $R-fH$, between $R-fH$ and $R-fL$, or above $R-fL$, respectively. Figure 1 shows the proportions for each type of agent using areas under a symbolic bell-shaped distribution for $F0$, separated by gray dashed lines. Figure 1 also illustrates two thresholds (along the support of $F0$) for take-up in black dashed lines. The first take-up threshold (labeled $R-E(F1)-c-Aδ$) is binding only if it falls to the left of the threshold that defines always adopters ($R-fH$). When this first take-up threshold binds, only a share of always follow-through types take up. The second take-up threshold (labeled $R-fL-(c-A)δpL$) is perhaps more interesting. When binding, all always-follow-through types take up, but only a share of contingent follow-through types take up (those to the left of the threshold).

Figure 1.

Take-Up and Follow-Through Thresholds as a Function of Agent Type

The figure shows the shares of always-follow-through, contingent-follow-through, and never-follow-through types over a symbolic probability density function of $F0$. The gray thresholds ($R-fH$ and $R-fL$) correspond to the follow-through thresholds, while the black thresholds correspond to the take-up thresholds.

Figure 1.

Take-Up and Follow-Through Thresholds as a Function of Agent Type

The figure shows the shares of always-follow-through, contingent-follow-through, and never-follow-through types over a symbolic probability density function of $F0$. The gray thresholds ($R-fH$ and $R-fL$) correspond to the follow-through thresholds, while the black thresholds correspond to the take-up thresholds.

Proposition 1.

Follow-through conditional on take-up weakly increases as a function of take-up cost, that is, there is a screening effect of the take-up cost.

As take-up cost increases (represented by $c-A$ in figure 1), the second take-up threshold (right black dashed line) moves to the left, reducing the share of contingent follow-through types among the set of individuals who take up. Since contingent types follow through with probability less than 1 ($pL$), this in turn increases the share of individuals who follow through among those who take up.

Proposition 2.

An increase in uncertainty reduces follow-through conditional on take-up.

Widening the distance between $fL$ and $fH$ causes the share of contingent follow-through types to increase (as the two gray dashed lines in figure 1 move farther apart). Note that as uncertainty increases, the position of the second take-up threshold does not change relative to the threshold that determines the upper bound for contingent follow-through types. Thus, this group becomes a larger share of those who take up, reducing average follow-through.

Corollary 1.

Under no uncertainty, everyone who takes up follows through.

This is easy to see from figure 1: under no uncertainty (where $fL=fH$), there would be only always-follow-through types and never-follow-through types. Thus, under no uncertainty, there is also no screening effect of the take-up cost.

Proposition 3.

If a screening effect of the take-up cost exists, that effect dissipates under large amounts of uncertainty.

As uncertainty increases, the take-up threshold (labeled $R-fL-c-AδpL$) and the right contingent follow-through threshold (labeled $R-fL$) move in parallel to the right. The mass between them (the share of contingent adopters that are excluded by a positive take-up cost) becomes a smaller proportion of all those who take up provided that the two thresholds lie sufficiently to the right of the mean. This condition is always met under high enough levels of uncertainty, as we show in appendix A.1.10

Proposition 4.

The option value associated with take-up is increasing in uncertainty, which results in higher take-up at all take-up cost levels.

Intuitively, the option value is the value of reoptimizing once new information (the realization of $F1$) emerges. As the distance between $fH$ and $fL$ increases, the payoff at $t=1$ conditional on a low-cost shock ($fL$) increases for contingent follow-through types. This is because agents can choose not to follow through if the payoff of doing so is negative; thus, the payoff at $t=1$ is bounded at 0 even when $fH$, the high cost, becomes very large. Meanwhile, increasing distance between $fL$ and $fH$ lowers $fL$, increasing the expected payoff of follow-through conditional on $fL$. Thus, the expected value of the contract at $t=0$ is strictly increasing in uncertainty, and this increase emerges solely because of the possibility of reoptimizing (i.e., choosing not to follow-through when the cost is high). A higher expected value of the contract results in higher take-up.

### A. Transitory Shocks and Learning

So far, we have left open the question of whether $F1$ should be interpreted as a persistent or a transitory shock. Our framework is consistent with both interpretations. However, the distinction matters for future take-up decisions. If the $F1$ component of the returns to the technology has a persistent component, future take-up decisions will occur under a lower level of uncertainty since individuals will have learned its realization. If $F1$ is completely transitory, future take-up decisions will look similar to the first take-up decision since individuals will receive a new draw of the shock next time.11

## III. Context and Experimental Design

To test the relevance of our conceptual framework, a technology adoption decision requires two key ingredients: investment decisions at two or more points in time and no penalty associated with abandoning the technology. We study the adoption of agroforestry trees, which requires an initial investment in planting inputs and subsequent investment in tree care but carries no penalty if abandoned. In the context of an ongoing project to encourage the adoption of agroforestry trees (Faidherbia albida), we introduce exogenous variation in the payoffs to farmers at the time of their take-up and follow-through decisions.

The study was implemented in coordination with Dunavant Cotton Ltd., a large cotton-growing company in Zambia, and a nongovernmental organization (NGO), Shared Value Africa. The project, based in Chipata, Zambia, targeted 1,314 farmers growing cotton under contract with Dunavant, alongside other subsistence crops.

### A. The Technology

Faidherbia albida is an agroforestry species endemic to Zambia that fixes nitrogen, a limiting nutrient in agricultural production, in its roots and leaves. The relatively wide spacing recommended between the trees (10 meters), together with the fact that the tree sheds its leaves at the onset of the cropping season, means that planting Faidherbia does not displace other crop production. Agronomic studies show yield gains from Faidherbia of 100% to 400% relative to production without fertilizer (Saka et al., 1994; Barnes & Fagg, 2003). However, these private benefits take seven to ten years to reach their full value and may be insufficient to justify the front-loaded investment costs.

In the first year after trees are planted, the farmer has to invest time to weed, water, and protect the trees from pests and other threats. We refer to these investments collectively as tree cultivation. Survey data indicate that farmers in our study devoted around 2.4 hours per tree, on average, to cultivation in the first year. Once a seedling survives the first dry season, the costs of cultivation diminish substantially. Our study ends after one year, which means that farmers acquire new information about the opportunity cost of cultivation, but not long-run fertilizer benefits.12 The opportunity cost of the first-year investments may vary substantially across farmers and contain many components that are hard to measure directly. Consequently, one major objective of this paper is to estimate the heterogeneity in opportunity costs by revealed preference. Nevertheless, we conduct a rough back-of-the-envelope calculation of benefits and costs (see appendix A.6 for details) that suggests that private costs are on the order of US$0.75 per tree, while the present value of private benefits is about US$0.04 per tree over a twenty-year time horizon. The trees also provide public benefits through carbon sequestration worth around US$17.76 of external benefits per tree, which more than covers the calculated private cost of adoption. ### B. Experimental Design and Data Collection The field experiment was implemented between November 2011 and December 2012 with 125 farmer groups and 1,314 farmers. Implementation of the study relied on Dunavant's existing farmer groups, each of which includes ten to fifteen farmers and a lead farmer. Implementation was concentrated at two points in the agricultural season.13 First, farmer training, program enrollment, and a baseline survey occurred at the beginning of the planting season. Second, the end-line survey, tree survival monitoring, and reward payment occurred at the end of our study period, one year after program enrollment. At the training, farmers were provided with instructions on planting and caring for the trees, information about the private fertilizer benefits and public environmental benefits of the trees, and details on eligibility for the program.14 All farmers who attended the training received a show-up fee of ZMK 12,000 and lunch. Farmers were told that the show-up fee, which was equivalent to about a day's agricultural wages, was compensation for their time and was theirs to keep. The fee was intended to reduce the effect of immediate liquidity constraints on take-up. Since it may also have generated experimenter demand effects, we allow for a homogeneous positive demand shock in the take-up decision when we estimate the structural model. Enrollment occurred at the end of the training. Study enumerators explained the details of the enrollment choice: a take-it-or-leave-it offer of a fixed number of seedlings (fifty, or enough to cover half a hectare) to be planted and managed by the farmer. The study design varied two major margins of the farmer's decision to adopt Faidherbia albida. First, the size of the take-up subsidy ($A$) varied between 0, ZMK 4,000, ZMK 8,000, and ZMK 12,000. At 0 subsidy, farmers paid ZMK 12,000 (approximately US$2.60 or around a day's agricultural wages) for inputs, which is the cost recovery price for the implementing organization, but falls below farmers' full cost of accessing seeds or seedlings outside the program. Groups were randomly assigned to one of four take-up subsidy treatments with equal probability using the min-max T approach, balanced on Dunavant shed, farmer group size, and day of the training. The subsidized price of the inputs was announced to all farmers in the group at the end of training, before the take-up decision was made.

Second, the program offered a threshold payment conditional on follow-through (tree survival) after one year. The payment varied randomly at the individual level. Farmers received the reward if they kept 70% (35) of the trees alive through the first dry season (for one year). The threshold reward, as opposed to a per tree incentive, allows us to draw a sharper distinction between private incentives and external incentives to cultivate the trees, which aids identification of the structural model.15 To implement the individual-level randomization of the rewards and allow participants to make their take-up decision in private, study enumerators called the farmers aside one by one and described the reward. The farmer then drew a scratch-off card from a bucket, which revealed the individual reward value, after which the take-up decision was recorded. The size of the threshold performance reward ($R$) was varied in increments of ZMK 1,000, ranging from 0 to ZMK 150,000, or a little over US$30.16 Variation in the reward was introduced using a random draw at the time of the take-up decision. One-fifth of all draws were for ZMK 0, with the remaining four-fifths distributed uniformly over the range. Treatment assignment is shown in appendix figure A.7.2. We also varied whether this reward was known to the farmer before the take-up decision; if it was not, farmers drew a reward conditional on take-up. Following the take-up decision, all farmers were given a baseline survey. After the survey, participating farmers signed a contract indicating their agreement with the program terms, paid the take-up cost, and collected their seedlings. To preempt an effect of seedling choices on tree survival, farmers were not allowed to pick their seedlings. One year after the training, all farmers in the study sample were given an end-line survey. Approximately one week after the end-line survey, farmers with contracts were visited for field monitoring, during which the farmer and a study enumerator examined each tree and recorded whether it was sick, healthy, or dead. Monitors also recorded indicators of activities likely to affect survival outcomes: weeding, watering, constructing fire breaks, and field burning (which, in contrast to the other three, threatens tree survival). All surviving trees counted toward the reward threshold. Shortly after the monitoring visit, farmers with 35 or more surviving trees received their reward payment. ## IV. Summary Statistics and Reduced-Form Results In the study sample, the average household includes around five members and owns around three hectares of land spread across just under three fields, which are an average of around twenty minutes away from their dwelling. Around 10% of households state that soil fertility is one of the major challenges that their household faces. Households have worked with Dunavant Cotton for an average of over four years. Almost 70% of respondents report familiarity with the technology, but only around 10% had adopted prior to the program. Appendix table A.7.1 shows the balance on these and other farmer characteristics. We also examine whether nonrandom attrition at any stage of data collection affects internal validity (appendix table A.7.2).17 The baseline survey covered over 98% of trained farmers, while the end-line survey included over 95% of baseline respondents. For the tree survival monitoring, over 95% of the 1,092 households that took up the program were located.18 Finally, appendix table A.7.3 shows no evidence that the randomized rewards affected the behavior of other farmers in the same group. ### A. Reduced-Form Evidence of Uncertainty Table 1 displays means and standard deviations for several program outcomes: take-up, follow-through (tree survival $≥$ 35), zero surviving trees, and the number of trees conditional on positive survival rates. These statistics are broken down by treatment and show clear patterns of responses to the incentives offered in the experiment. We also estimate a linear relationship between the administrative outcomes and the treatments, shown in table 2. Panel A shows results for all relevant farmers, and panel B shows results conditional on take-up. In panel A, specifications that include the reward are restricted to the subtreatment that drew reward values prior to making a take-up decision (the “no-surprise group”). Table 1. Summary Statistics and Mean Comparisons (1) Take-Up(2) 35-Tree Threshold(3) # Trees $|$ # Trees $>$ 0(4) Zero Trees A. Full Sample Mean 0.83 0.25 27.42 0.36 SD 0.38 0.44 14.31 0.48 B. By Take-Up Subsidy Treatment A $=$ Mean 0.71 0.26 27.60 0.37 SD 0.46 0.44 14.31 0.48 A $=$ 4,000 Mean 0.76 0.29 28.86 0.36 SD 0.43 0.45 13.67 0.48 A $=$ 8,000 Mean 0.86 0.27 29.30 0.38 SD 0.35 0.44 14.19 0.49 A $=$ 12,000 Mean 0.97 0.22 24.93 0.33 SD 0.17 0.41 14.52 0.47 C. By Reward Treatment R $=$ Mean 0.90 0.13 22.00 0.49 SD 0.31 0.34 14.70 0.50 R $=$ (0,70,000] Mean 0.90 0.21 25.45 0.40 SD 0.30 0.41 14.62 0.49 R $=$ (70,000,150,000] Mean 0.93 0.32 29.53 0.30 SD 0.25 0.47 13.67 0.46 (1) Take-Up(2) 35-Tree Threshold(3) # Trees $|$ # Trees $>$ 0(4) Zero Trees A. Full Sample Mean 0.83 0.25 27.42 0.36 SD 0.38 0.44 14.31 0.48 B. By Take-Up Subsidy Treatment A $=$ Mean 0.71 0.26 27.60 0.37 SD 0.46 0.44 14.31 0.48 A $=$ 4,000 Mean 0.76 0.29 28.86 0.36 SD 0.43 0.45 13.67 0.48 A $=$ 8,000 Mean 0.86 0.27 29.30 0.38 SD 0.35 0.44 14.19 0.49 A $=$ 12,000 Mean 0.97 0.22 24.93 0.33 SD 0.17 0.41 14.52 0.47 C. By Reward Treatment R $=$ Mean 0.90 0.13 22.00 0.49 SD 0.31 0.34 14.70 0.50 R $=$ (0,70,000] Mean 0.90 0.21 25.45 0.40 SD 0.30 0.41 14.62 0.49 R $=$ (70,000,150,000] Mean 0.93 0.32 29.53 0.30 SD 0.25 0.47 13.67 0.46 Means and standard deviations of take-up (column 1) and followthrough (columns 2–4) outcomes, by experimental treatment. Column 1 includes all farmers ($N=1,314$). Columns 2–4 are conditional on take-up ($N=1,092$). Column 2 reports the number of farmers who reached the performance reward threshold. Table 2. Effects of Treatments on Take-Up and Follow-Through Take-UpFollow-Through# Trees $|$ Trees $>$ 01.(Zero Trees) (1)(2)(3)(4)(5)(6)(7)(8) A. Unconditional on take-up Take-up subsidy 0.022*** 0.002 −0.229 −0.016*** (0.005) (0.004) (0.200) (0.005) Reward 0.001* 0.001*** 0.047*** −0.001*** (0.000) (0.000) (0.017) (0.000) Knew reward at take-up Dependent variable mean 0.83 0.84 0.21 0.21 27.42 27.11 0.47 0.47 $N$ 1,314 624 1,314 624 701 333 1,314 624 B. Conditional on take-up Take-up subsidy −0.004 −0.229 −0.003 (0.004) (0.200) (0.005) Reward 0.001*** 0.044*** −0.001*** (0.000) (0.013) (0.000) Dependent variable mean 0.25 0.25 27.42 27.42 0.36 0.36 $N$ 1,092 1,092 701 701 1,092 1,092 Take-UpFollow-Through# Trees $|$ Trees $>$ 01.(Zero Trees) (1)(2)(3)(4)(5)(6)(7)(8) A. Unconditional on take-up Take-up subsidy 0.022*** 0.002 −0.229 −0.016*** (0.005) (0.004) (0.200) (0.005) Reward 0.001* 0.001*** 0.047*** −0.001*** (0.000) (0.000) (0.017) (0.000) Knew reward at take-up Dependent variable mean 0.83 0.84 0.21 0.21 27.42 27.11 0.47 0.47 $N$ 1,314 624 1,314 624 701 333 1,314 624 B. Conditional on take-up Take-up subsidy −0.004 −0.229 −0.003 (0.004) (0.200) (0.005) Reward 0.001*** 0.044*** −0.001*** (0.000) (0.013) (0.000) Dependent variable mean 0.25 0.25 27.42 27.42 0.36 0.36 $N$ 1,092 1,092 701 701 1,092 1,092 OLS regressions of outcomes on treatment variables. The reward and take-up subsidy are both measured in thousand ZMK. Columns 1 and 2 show effects on take-up, columns 3 and 4 on follow-through at the 35-tree threshold, columns 5 and 6 on the number of surviving trees conditional on positive tree survival, and columns 7 and 8 on the probability of zero surviving trees. Panel A includes farmers who do not take up and assumes they have no surviving trees. Even columns restrict the sample to farmers in the “no-surprise group” (knew the reward before take-up) so that reward values are nonmissing for all observations. Panel B is conditional on take-up. We use the means and standard deviations presented in table 1 and the linear regression results in table 2 to examine the predictions of our conceptual model. First, take-up rates are increasing in the take-up subsidy (table 1), with a ZMK 1,000 increase in the subsidy leading to a 2 percentage point increase in the probability of take-up (column 1, table 2). Take-up rates are high, on average, even in the zero subsidy condition, where over 70% of farmers take up. Without further evidence, this could be due to high known net-benefit from follow-through on average or high expected values driven by option value, or both (proposition 4). Second, follow-through rates vary considerably within treatment and are low, on average, with only 25% of farmers reaching the 35-tree threshold (column 2, table 1). This holds even in the zero subsidy condition, ruling out that the high take-up was due to farmers being certain about high payoffs associated with cultivating a large number of trees. Instead, low follow-through conditional on take-up is consistent with large amounts of uncertainty (proposition 2). At the same time, follow-through is responsive to the value of the reward (column 4, table 2), which indicates that farmers had control over tree survival outcomes. Third, many farmers abandon the technology altogether (no trees survive) even conditional on taking up with no subsidy (37%, column 4, table 1). This rules out the no-uncertainty scenario (corollary 1 of our conceptual model). At the same time, the likelihood of no surviving trees is decreasing in the value of the reward (column 8, table 2). We also see no reduced-form effect of the subsidy treatment on the likelihood of reaching the 35-tree threshold or of abandoning the technology, conditional on take-up (panel B, table 2). This is consistent with proposition 3 (the screening effect of subsidies is diminished by high levels of uncertainty in the net benefits of follow-through). The variation in the timing of the reward announcement offers a separate test for farmers' ability to self-select at take-up based on information about their net costs of follow-through. Conditional on take-up, the effect of the reward on follow-through does not depend on whether the farmer factored it into the take-up decision (see appendix table A.7.4). Finally, observable characteristics of the farmer are very poor predictors of follow-through: the $R2$ from a regression of tree survival on observables is 0.042. In comparison, the experimental treatments deliver an $R2$ of 0.077. Observables are also poor predictors of take-up, which means that even the known component of follow-through costs is hard to measure directly.19 The low explanatory power of observables further motivates our structural model. ### B. Additional Results and Confounds This section provides additional evidence supporting our results and interpretation. First, liquidity constraints are ruled out by our research design and by a lack of response to variation in the timing of the reward. Second, measures of farmers' investments in tree cultivation are also responsive to our treatments. A higher reward increases weeding, fire breaks, and watering and decreases field burning, which threatens tree survival (appendix table A.7.7). Third, because we observe no effect of the exogenous variation in take-up subsidies on follow-through, we are able to rule out three potential psychological explanations: sunk-cost effects, quality signaling through the NGO's decision to subsidize, or crowding out of intrinsic motivation to take up the technology. Finally, an alternative explanation for our reduced-form results is procrastination or hyperbolic time preferences. We collect and analyze survey data to test whether measures of procrastination are correlated with take up or tree survival, or whether procrastinators are more likely to take up when the upfront costs are low. Our measures of procrastination have little explanatory power (see appendix table A.7.8). ## V. Model, Identification, and Estimation The results in section IV suggest that uncertainty in the opportunity cost of follow-through shapes adoption decisions. However, other sources of heterogeneity in costs may explain the lack of screening effect of the subsidy. For instance, a 0 or even negative correlation between take-up prices and follow-through rates could emerge if there is a negative correlation between the privately optimal number of trees and the total profit farmers derive from them.20 In addition, the reduced-form results do not offer any insight into the magnitude of the uncertainty that farmers face, which is important for interpreting responses to the adoption subsidies. To address these remaining questions, we adapt the simple theoretical model in section II to our empirical setting and explicitly estimate the distribution of random parameters governing a quasi-profit function (a “reduced-form” profit function). The two main sources of experimental variation we introduce (the subsidy for take-up and the reward for follow-through) allow us to quantify the importance of uncertainty in farmers' adoption decisions by estimating the joint distribution of expected and realized profits from the trees. In other words, the experimental variation permits estimating the magnitude of uncertainty relative to other forms of farmer heterogeneity.21 This is among the first papers to introduce multiple dimensions to the experimental design to distinguish between adoption decisions and returns to investment (see Karlan & Zinman, 2009, and extensions of their design by Ashraf et al., 2010; Cohen & Dupas, 2010; and others), and the first to use this research design to explore time-varying returns to investment. ### A. Farmer Net Benefits We define a quadratic quasi-profit function that uses our experimental variation to characterize farmer heterogeneity along two dimensions of the farmer's profit maximization problem: the interior solution to the maximization problem and the profit level evaluated at the privately optimal number of trees. Farmer quasi-profits, $Π(N)$, at time $t=1$ are $Π(N)=N-12TiN2-Fi×1(N>0)+1(N≥N¯)Ri,$ (2) where $N¯=35$ is the threshold that triggers the reward and $Ri$ is the reward. The quasi-profit function in equation (2) allows for two sources of ex ante heterogeneity across farmers, parameterized as $Ti$ and $Fi$. $Ti$ corresponds to the interior solution, and $Fi$ determines the scale of profits. We nest this quasi-profit function in a more traditional profit function in appendix A.3, in which fixed and variable costs to trees are defined explicitly, along with private benefits. The heterogeneous parameters, $Ti$ and $Fi$, are thus “reduced form” in the sense that they are themselves functions of heterogeneous parameters of a structural profit function. A free correlation structure is key to their interpretation as reduced-form parameters, since each is potentially a function of common structural parameters. Even in the absence of uncertainty, a negative or zero correlation between them could generate the type of selection patterns we observe in the data: zero correlation between the take-up cost and reaching the tree survival threshold. An advantage of this parameterization is that the joint distribution of farmer heterogeneity is identified from experimental variation. ### B. Dynamics and Take-Up Decision As in the conceptual model, we assume the farmer makes adoption-related decisions in two periods: $t=0,1$. The random parameter $Fi$ largely determines the magnitude of optimized profits and is divided into two additive components, $F0i$ and $F1i$, where $F0i$ is known at all periods and $F1i$ is known at $t=1$ but not at $t=0$ (i.e., the unknown component of profit). We assume that $Ti$ is known to the farmer at all times. This amounts to assuming uncertainty about the net costs of tree cultivation but not about the optimal scale of the technology. This information structure allows us to nest a model without uncertainty (i.e., $Var(F1i)=0)$ that could also deliver no screening effects (or even negative screening effects) within our more general model. Moreover, because $Fi$ is the main determinant of the maximum profit attainable, take-up decisions are driven by uncertainty in $Fi$ rather than $Ti$; assuming $Ti$ is unknown at the time of take-up would therefore have little impact. At $t=0$, the farmer decides whether to take up the technology. At this time, the farmer has partial information about her net benefits from the contract. Assuming the farmer knows the distribution of $F1i$ conditional on the realizations of $F0i$ and $Ti$ at $t=0$, the farmer chooses to take up if $EF1i|F0i,TimaxNΠ(N|Ti,F0i,F1i,Ri)≥c-Aiδ,$ (3) where $c$ is the cost of the seedlings, $Ai$ is the randomly determined subsidy, and $δ=11+r$ and is assumed equal to 0.6.22 Note that this representation of the net present value of the farmer's profits from trees maintains risk neutrality (see section II).23 The three main takeaways of the model in section II hold when we allow for this intensive margin of follow-through (e.g., the number of trees cultivated in our empirical application or the frequency of usage in the case of other technologies and products). However, incorporating the intensive margin allows us to differentiate the role of heterogeneity in optimal scale from the role of uncertainty as explanations for the disconnect between take-up and follow-through. Implicitly, testing for a positive correlation between the optimal scale and the profit level has been the objective of much of the literature on the screening effects of price, which has focused on the adoption of technologies with an intensive margin of use or follow-through (Ashraf et al., 2010; Cohen & Dupas, 2010). ### C. Identification and Estimation Identification of the structural model consists of uniquely identifying the joint distribution of unobservables $Ti$, $F0i$, and $F1i$. In addition to the assumptions on the timing of information, we maintain assumptions a and b on the components of $Fi$ from section II and add: 1. No common shocks: $F1i⊥F1j$$∀i≠j$ 2. Normality: $F0i∼nμF,σF02,$$F1i∼n0,σF12$ 3. Joint normality: ($Fi,lnTi)∼n(μ,Σ)$ Below we explain the role that each of these assumptions plays in identification. In what follows, we denote the randomized values of $Ai$ and $Ri$ as $ai$ and $ri$ to emphasize their role as known (to the farmer and researcher) and exogenous. With no assumptions other than profit-maximizing behavior on behalf of the farmer and a quadratic profit function that allows for corner solutions, the joint distribution of $Fi$ and $Ti$ can be nonparametrically identified in the subset of the support such that $N¯. To see this, consider the follow-through decision of the subset of the sample for which $lima→A1PrEmaxNΠ(N|Ti,F0i,F1i,r)F0i,Ti≥c-aiδ=1,$ such that there is no self-selection on take-up. Within this subset, variation in $ri$ identifies the joint distribution of $(Fi,Ti)$. For this group, the probability of cultivating $N*=n>N¯$ trees when $R=ri$ can be written as $Pr(N*=n;R=ri)=PrFi (4) Because the left-hand side of equation (4) is empirically observable, increments in $ri$, holding $n$ constant, trace out the conditional distribution of $Fi$ given $Ti$. The same expression recovers the marginal distribution of $Ti$ by varying $n$ and dividing by the conditional distribution of $Fi$. Since nonparametric identification of the joint distribution of $Fi$ and $Ti$ occurs only in the subset of the support such that $N¯, additional parametric assumptions are required to fully characterize these distributions. We therefore adopt assumption e for the estimation. We use farmers' take-up decisions in combination with assumptions a to d in order to separately identify the distributions of $F0i$ and $F1i$ once the joint distribution of $Fi$ and $Ti$ has been identified. Under these assumptions, the decision to take up in response to $ri$ and $ai$ provides independent identification of the distribution of the known component of $Fi$, $F0i$. More formally, identification of the distribution of $F0i$ is obtained from the decision to take up, which is characterized by the inequality in equation (3). The left side of equation (3) is a known function of the random variable $F0i$: note that parameters $μF,σF2,μT,σT2,andρT,F$ can be treated as known since they are identified from tree survival as already described. Denote this function $ψ(F0i;ri)$, so we can rewrite equation (3) as $ψ(F0i;ri)≥c-aiδ.$ (5) The right side of equation (5) can take one of four known values: $ai∈{0,4,000,8,000,12,000}$. The left-hand side of equation (5) is known up to $F0i$ and varies across individuals in response to $ri$. Provided that $ψ(F0i;ri)$ is invertible,24 we can identify the distribution of $F0i$ from the random variation in $ai$ and $ri$: $PrF0i≤ψ-1c-aiδ,ri|μF,σF2,μT,σT2,ρT,F=Pr(TakeUpi|ai,ri).$ (6) #### Common shocks and mean shift model. Assumption c plays an important role for identification, as it implies that the variance of $Fi$ across farmers is the sum of the variances of its two components: $σF02+σF12$.25 The variance of shocks is thus partially identified from subtracting the variance estimate of $F0i$, identified from equation (6), from the variance of $Fi$, identified from tree choices. Shocks that are common across farmers do not translate into variation in tree choices and would lead to an underestimate of $σF1i2$. In our context, much of the uncertainty farmers face appears to be from idiosyncratic shocks.26 However, given that farmers are also likely affected by common shocks, we estimate a variant of our model that allows for a specific type of common shock—one that is completely unforeseen at the time of take-up and is common across all farmers. This model variant can be estimated by relaxing assumption b, allowing for subjective and objective expectations about the mean of the shock to differ. We refer to this as the mean shift model. The mean shift—or difference between the subjective mean of the shock distribution at take-up and its objective mean—is identified because the random variation in $ri$ and $ai$ allows us to identify $μF$ in equation (6) from the take-up decisions independent of the estimate from tree choices. The mean shift also captures overoptimism, experimenter demand effects, or other behavior where the subjective and objective means of the opportunity cost distribution diverge and are common across farmers. #### Estimation. We estimate the model using simulated maximum likelihood. The log-likelihood function uses the observed number of trees, $N=0,…,50$, and the participation decision, $DP=0,1$. The sample includes the 1,314 farmers who made a take-up decision. Because the farmer cultivates no trees whenever she chooses not to participate, the support of this bivariate vector is given by the 52 $(DP,N)$ pairs: $(0,0),(1,0),(1,1),(1,2),…,(1,50)$. Thus, the likelihood function is given by: $l(ξ;DP,N)=∑i=1M{(1-DPi)ln(1-πP,i)+DPiln(πP,i)+DPi∑j=0501(Ni=j)lnPr(N=j)},$ (7) where $ξ=(μF,σF02,σF12,μT,σT2,ρT,F)$. We use numerical methods to minimize the negative of the simulated log likelihood and calculate standard errors from the inner product of simulated scores (see appendix A.4 for details). ## VI. Structural Estimates, Simulation Results, and Interpretation ### A. Structural Estimates and Model Fit Table 3 shows the point estimates for the main parameters described in section VC. Panel A shows the estimates of our baseline model, which assumes that farmers' expectations about $F$ are correct and consistent over time. Panel B shows the results of the mean shift model. Because point estimates are somewhat hard to interpret (e.g., the $μT$ and $σT$ parameters do not correspond to the mean and standard deviation of the log-normal distributed parameter $T$), we convert the estimated parameters into more easily interpretable outcomes using simulation. The estimated joint distribution of $T$ and $F$ shown in panel A is such that the mean ex post privately optimal number of trees is 8.46 (SD 14.64), with about 59% of farmers choosing to cultivate no trees. Table 3. Structural Parameter Estimates Parameters in $T$Parameters in $F$ $μT$$σT$$ρ$$μF$$σF0$$σF1$$αs$$αm$$μFs$ A. No mean shift 3.539 1.401 0.818 107.58 307.87 211.42 −91.79 −238.40 – (0.057) (0.066) (0.066) (11.822) (93.278) (49.953) (16.222) (73.887) – B. Allowing for mean shift 3.579 1.392 0.835 74.48 290.06 193.05 −54.42 −229.53 53.29 (0.071) (0.075) (0.073) (15.47) (84.622) (45.427) (20.47) (74.444) (26.761) Parameters in $T$Parameters in $F$ $μT$$σT$$ρ$$μF$$σF0$$σF1$$αs$$αm$$μFs$ A. No mean shift 3.539 1.401 0.818 107.58 307.87 211.42 −91.79 −238.40 – (0.057) (0.066) (0.066) (11.822) (93.278) (49.953) (16.222) (73.887) – B. Allowing for mean shift 3.579 1.392 0.835 74.48 290.06 193.05 −54.42 −229.53 53.29 (0.071) (0.075) (0.073) (15.47) (84.622) (45.427) (20.47) (74.444) (26.761) Parameters fitted by simulated maximum likelihood using 1,500 draws of the random vector ($F0i,F1i,Ti$), with smoothing (lambda is 0.5) and tolerance (1e-15). The baseline model (panel A) restricts the mean of $Fi$ to be the same in both time periods. The mean shift model (panel B) allows the mean of $Fi$ to differ between the two periods and the parameter $FS$ to capture this difference. The log-likelihood value for the baseline model is 11,142.064 and 11,138.996 for the mean shift model. This joint distribution also implies that the average ex post private profit from the optimal number of trees is ZMK 108,390 (about US$24, equivalent to about 9.4 person-days of agricultural labor). However, ex post private profits vary widely across farmers: the standard deviation is ZMK 185,470. Importantly, the model estimates that about 39% of the variance in ex post profits is due to new information that emerges after the take-up decision is made. Thus, the standard deviation of new information corresponds to about 10 person-days of agricultural labor. To put the importance of the flexibility associated with waiting for new information into perspective, our model results imply that relative to a scenario in which the farmer acquired no new information before making the follow-through decision, 26% more farmers are willing to take up and 68% of farmers end up growing a different number of trees than initially planned when the number can be adjusted based on new information.

Panel B of table 3 explores the robustness of our estimates to the no-common-shocks assumption. The variance of shocks to information about costs is partially identified out of the difference in the variances of expected profits at take up ($t=0$) and ex post profits at the time the follow-through decision is made ($t=1$) and partially identified out of its nonlinear effect on the mean level of the expected profits at take-up. The presence of common shocks generates a tug-of-war between these two sources of identification: the expected value of the profits pulls up the variance of shocks parameter, $σF1$, while the ex post variance in profits, which does not reflect the variance of common shocks, pulls $σF1$ down. The mean shift model helps explore the importance of the bias in $σF1$ generated by the presence of common shocks by allowing the mean level of profits to be different at $t=0$ and $t=1$.

Results from the mean shift model are presented in panel B of table 3. The estimated difference in means between the two periods, the mean shift, is given by parameter $μFS$. A nonzero value for this estimated parameter has two plausible interpretations. First, it can represent a single common shock whose possibility was unknown at the time of take-up and affected all farmers equally. Second, it can pick up a common update in the value of the technology that occurred after the take-up decision was made. The latter interpretation is a useful test for the presence of experimenter demand effects on take-up: the perceived obligation of potential adopters to take up in the presence of the experimenter. Our estimate of the value for $μFS$ is positive but small and not significantly different from 0 at standard confidence levels. The positive value is consistent with either the presence of a common shock of the specific type described or an experimenter demand effect; however, it is small compared to the standard deviation of the shocks, $σF1$. Importantly, allowing for this effect induces only a small change in the variance of the shocks: $σF1$ falls moderately from 211.42 to 193.05, consistent with a positive bias in our baseline model stemming from the presence of common shocks.27 This suggests that uncertainty in the form of idiosyncratic shocks is important and that experimenter demand effects are not driving our results.

We now turn to the interpretation of the parameters that govern the distribution of known (at the time of take-up) sources of heterogeneity across farmers. We estimate a high, positive correlation between $F$ and $lnT$, $ρT,F=0.81$ ($ρT,F=0.83$ in the mean shift model).28 Because $F$ and $T$ are reduced-form parameters, the positive correlation between them could stem from two sources: a positive correlation between farmers' fixed costs and farmers' interior solution to the maximization problem, or a high mean and high variance of net marginal returns (see appendix A.3 for the exact relationship between reduced form and structural parameters in the profit function).

Because $F$ enters negatively in the profit function, the positive correlation between $T$ and $F$ translates into a negative correlation between the privately optimal number of trees and the level of profits. This negative correlation generates low follow-through rates (as in low numbers of trees cultivated) among farmers whose expected value from the contract is high and thus take up under a high price. In other words, the static heterogeneity identified by the model induces a negative screening effect of high prices at take-up. In the reduced-form results, we find no statistically significant screening effect of take-up prices on follow-through. Given our results so far, this close-to-zero screening effect is the result of both the large scale of uncertainty, which our model shows results in a positive but small screening effect, and a negative screening effect stemming from time-invariant heterogeneity in the intensive margin. Without further analysis, it is hard to assess the importance of uncertainty in driving the statistically insignificant screening effect. After all, it could be that given the other forms of heterogeneity in our model, the level of uncertainty exerts little influence on self-selection in our particular context. In order to better understand the role of uncertainty on self-selection in our outcomes, section VI B conducts several simulations of take-up and follow-through outcomes where we hold constant the parameters that define the static heterogeneity in our data and vary the level of uncertainty.2

Before turning to model simulations, we assess the fit of our model. Our model does well predicting some simple observations in the data. For example, our baseline model predicts that 1,104 farmers (1,112 under the mean shift model), out of a total of 1,314, will take up; our data show 1,092 participants. Our model also predicts that 173 out of the 963 farmers who faced a strictly positive take-up cost (a subsidy less than ZMK 12,000) will choose to cultivate no trees (180 in the mean shift model), while the observed number of farmers in this category is 112. That is, the dynamics in our model replicate an observation that seems at odds with rationality in a static framework: some farmers who purchase the trees choose not to cultivate them. In this sense, our result parallels the result by Fafchamps (1993) in that individuals make costly choices to maximize future flexibility.

In appendix table A.4.3, we compare reduced-form treatment effects estimated from the observed data and model-generated simulated outcomes. Most of the magnitudes and signs on estimates from observed behavior are well matched by model estimates. The effect of the subsidy and the reward on take-up and whether the farmer reached the 35-tree threshold are particularly close, as is the effect of the reward on no tree survival. There are, however, some discrepancies between model predictions and observed data. For example, the sign of the effect of the take-up subsidy on tree survival is different between the observed and simulated data (though estimates are imprecise). We also see evidence that the take-up subsidy selects for farmers more likely to keep no trees alive in the simulated than the observed data, indicating some screening effect of take-up prices on abandoning the technology altogether in the simulated data only. We explore whether these discrepancies are due to our assumptions on deterministic tree survival conditional on effort and find little to no improvement when we introduce stochasticity into tree survival (see appendix A.5 for these results and a discussion of alternative parameterizations).

### B. Uncertainty, Farmer Profit, and Program Outcomes

To better understand the effects of uncertainty on adoption, we use estimates from the structural model to simulate farmer profits and program outcomes (take-up and tree survival) under different levels of uncertainty. For these analyses, we use the results from the mean shift model (panel B in table 3) but set the mean shift for $t=1$, $μFs$, equal to 0 for the following simulations in order to equate the expected benefits with the true average discounted benefits from the program.29 The simulations deliver five main results, the first three of which echo the findings from the conceptual model: (a) take-up is increasing in uncertainty, (b) higher take-up prices screen for high follow-through rates in the presence of uncertainty, and (c) this screening effect dissipates at high levels of uncertainty. We also describe two additional policy-relevant results: (d) subsidizing take-up affects total trees through its effect on take-up and on follow-through via any screening effect, and (e) rewarding follow-through directly may be more effective than subsidizing take-up.

We begin by examining the effect of uncertainty on the average per farmer expected private profit (the left-hand side of inequality 3) implied by the empirical model. To do so, we simulate the value of the expected profit for each farmer at different values of $σF1$. The relationship between the mean expected profit and $σF1$ corresponds to the solid black curves in figure 2. Panel A shows the relationship for a reward of 0 and panel B for the largest reward offered (ZMK 150,000). Both are shown at a full subsidy, so that take up is 100% (there is no self-selection based on take-up price).

Figure 2.

Farmer Expected Profit as a Function of Uncertainty

This figure shows a simulation of farmers' mean expected profit as we vary the level of uncertainty (the standard deviation of $F1$). For the simulations, we use the estimated parameters from panel B of C, except for $σF1$, which we vary along the horizontal axis. The mean per-farmer profit is shown in a solid black line for low (panel A, $R=0$) and high (panel B, $R=150$) reward values. Profits, the subsidy ($A$), and the reward ($R$) are expressed in thousand ZMK. The dashed lines show the mean option value for the two reward levels. We define the option value as the value of reoptimizing the number of trees to cultivate after $F1$ is realized relative to the value of a static choice.

Figure 2.

Farmer Expected Profit as a Function of Uncertainty

This figure shows a simulation of farmers' mean expected profit as we vary the level of uncertainty (the standard deviation of $F1$). For the simulations, we use the estimated parameters from panel B of C, except for $σF1$, which we vary along the horizontal axis. The mean per-farmer profit is shown in a solid black line for low (panel A, $R=0$) and high (panel B, $R=150$) reward values. Profits, the subsidy ($A$), and the reward ($R$) are expressed in thousand ZMK. The dashed lines show the mean option value for the two reward levels. We define the option value as the value of reoptimizing the number of trees to cultivate after $F1$ is realized relative to the value of a static choice.

#### a. Expected farmer profits are increasing in uncertainty.

This result is analogous to proposition 4: the option value from the contract increases with uncertainty and drives a positive relationship between the expected profit and uncertainty. The option value, as defined in appendix A.1, is shown by the dashed lines in figure 2 for different reward values. The option value is always nonnegative and is also the only component of the expected private profit that varies with uncertainty. This result stems from free disposal of the technology (bounding profit realizations at 0). This optimizing behavior turns the high variance of the shocks into an asset of the contract, which leads to higher take-up. The positive relationship between expected private profit and uncertainty has implications for take-up decisions: under higher uncertainty, more farmers are ex ante attracted to the contract, even though its ex post expected value is unchanged.

Next, we turn to program outcomes. Figure 3 plots average take-up at low and high subsidies (dashed and solid lines) and low (panel A) and high (panel B) rewards as a function of uncertainty ($σF1$). Panels C and D show the share of individuals who reach the 35-tree threshold conditional on take-up for the same combinations of subsidies and rewards. Figure 4 shows the effects of uncertainty on the average number of trees for different values of the subsidy ($A$) and reward ($R$). Panels A and B show average tree survival, unconditional on take-up (nonparticipants have no surviving trees). Panels C and D show average tree survival conditional on take-up. Because take-up is 100% with a full subsidy (A $=$ 12), the solid lines in panels C and D coincide with those in panels A and B, respectively.

Figure 3.

Take-Up and Threshold Outcomes as a Function of Uncertainty

This figure shows a simulation of farmers' average take-up and 35-tree reward threshold outcome as we vary the level of uncertainty (the standard deviation of $F1$). For the simulations, we use the estimated parameters from panel b of table 3, except for $σF1$, which we vary along the horizontal axis. Take-up and threshold (trees $≥$ 35) outcomes are shown for different combinations of the reward value and take-up subsidy, both shown in thousand ZMK.

Figure 3.

Take-Up and Threshold Outcomes as a Function of Uncertainty

This figure shows a simulation of farmers' average take-up and 35-tree reward threshold outcome as we vary the level of uncertainty (the standard deviation of $F1$). For the simulations, we use the estimated parameters from panel b of table 3, except for $σF1$, which we vary along the horizontal axis. Take-up and threshold (trees $≥$ 35) outcomes are shown for different combinations of the reward value and take-up subsidy, both shown in thousand ZMK.

Figure 4.

Tree Survival as a Function of Uncertainty

This figure shows a simulation of farmers' mean number of surviving trees as we vary the level of uncertainty (the standard deviation of $F1$). For the simulations, we use the estimated parameters from panel B of table 3, except for $σF1$, which we vary along the horizontal axis. The mean number of surviving trees is shown for different combinations of the external threshold reward and the subsidy for take-up, both shown in thousand ZMK. The top panels show per farmer tree survival for all farmers (those who did not take up have no trees); the bottom panels show tree survival conditional on take-up.

Figure 4.

Tree Survival as a Function of Uncertainty

This figure shows a simulation of farmers' mean number of surviving trees as we vary the level of uncertainty (the standard deviation of $F1$). For the simulations, we use the estimated parameters from panel B of table 3, except for $σF1$, which we vary along the horizontal axis. The mean number of surviving trees is shown for different combinations of the external threshold reward and the subsidy for take-up, both shown in thousand ZMK. The top panels show per farmer tree survival for all farmers (those who did not take up have no trees); the bottom panels show tree survival conditional on take-up.

#### b. When uncertainty is low, a higher take-up price increases tree survival conditional on take-up.

At low levels of uncertainty, the difference between the two lines in panels C and D of figures 3 and 4 (the screening effect of price) shows that follow-through rates are higher among those who face a high take-up price compared to those who face a low take-up price (proposition 1).

#### c. The screening effect of the take-up price falls substantially with high levels of uncertainty.

This result can be seen from tracking the difference between the two lines in panels C and D from low to high levels of uncertainty. For the level of uncertainty identified from our data ($σF1=195$), the gain in tree survival from charging more at take-up is modest—fewer than five trees—and it continues falling as uncertainty increases. The reduction in the screening effect at high levels of uncertainty is analogous to proposition 3 in our conceptual model. Importantly, our simulations suggest that even in the presence of static heterogeneity, uncertainty remains an important driver of whether a screening effect exists. The magnitude is such that halving the standard deviation of the shock relative to the value we estimate would result in 15% higher follow-through (figure 3, panel D).30

#### d. The effect of a high subsidy on take-up may dominate its effects on screening.

This result is most clearly seen by comparing unconditional tree survival (panels A and B of figure 4) with tree survival conditional on take-up, which excludes the take-up effect (panels C and D). The boost associated with the selection effect observed at low levels of uncertainty in panels C and D is more than offset by the take-up effect: many more farmers take-up when subsidies are high (see panels A and B in figure 3). The two counteracting effects lead to similar average tree survival across subsidy levels, unconditional on take-up (panels A and B). Hence, for technologies whose benefits kick in with total follow-through (whether or not follow-through is spread among few or many adopters), subsidies may increase the benefits of adoption. Note, however, that uncertainty also lowers the take-up advantage of high subsidies, as take-up increases with uncertainty for all subsidy levels.

#### e. When uncertainty is high, a reward conditional on follow-through is more effective at inducing tree survival than a subsidy.

This result can be appreciated when comparing the effect of moving from a lower $R$ to a higher $R$ as compared to moving from a low $A$ to a high $A$. Even with the optimal (in our setting) combination of a low take-up subsidy and high-threshold reward, uncertainty can bring down the number of farmers that reach the 35-tree threshold.

### C. Discussion and Interpretation

Farmers frequently refer to shocks as a primary determinant of agricultural outcomes. The first version of our model allows for idiosyncratic but not common shocks. This restriction is relaxed in our second version of the model, where we allow for a specific type of common shock: an unexpected homogeneous mean shift on the distribution of private profit after take-up. The data indicate that the mean shift, which could be interpreted as an unexpected common transitory shock or as homogeneous learning (see below), is consistent with a common increase in costs after take-up. The estimated mean shift is small in magnitude relative to the variance (see table 3). We interpret this estimate as evidence that this type of common shock is present but of limited importance.

The variation in our data does not allow us to identify other types of common shocks: namely, shocks whose distribution is known at take-up or are correlated across subsets of farmers (as opposed to all). Instead, we consider two additional sources of information about the importance of common and idiosyncratic shocks: household self-reports from our surveys and the existing literature on agricultural productivity in rural sub-Saharan Africa. First, two frequently discussed common shocks are weather and prices. To the extent that these types of common shocks are incorporated into the take-up decision, our estimates for the variance of idiosyncratic shocks will be biased upward even in the mean shift model. That said, our baseline data suggest that idiosyncratic shocks are an important concern for farmers. When asked about the hardships faced by their households, respondents describe idiosyncratic shocks: two-thirds list health problems as their greatest hardship, nearly half report losing cattle or livestock to death or theft during the past year (a substantial income shock), and 10% report the death or marriage of a working-age member (a shock to the opportunity cost of labor). Second, a growing literature documents large, negative effects of household illness on labor supply and agricultural productivity in the region of study (Fink & Masiye, 2012) and on consumption more broadly. These findings are consistent with a larger literature that highlights a disproportionate share of income risk from idiosyncratic factors in rural developing country settings (summarized in Dercon, 2002).

Our theoretical and empirical models are similar from an ex ante perspective if the information that arrives between take-up and follow-through is a persistent (learning) or a transient shock to opportunity cost, provided that both types of new information are independent across farmers. To the extent that learning shocks are common across all farmers and unexpected, the mean shift model could account for learning. Interpreted this way, the positive mean shift estimate is consistent with farmers' systematically underestimating the costs of follow-through at the time of take-up. Its small magnitude would then imply little systematic updating across all farmers. Learning shocks that are independent across farmers and whose distribution is known by the farmers ex ante would show up in the variance of $F1$. Thus, the model cannot distinguish between persistent and transitory shocks to the opportunity costs of cultivating trees.

The potential for learning about the value of the technology during the study is limited given that tree survival benefits are not realized until after the study ends. Thus, any learning will be related to the opportunity costs of cultivating the trees. Appendix table A.7.9 shows no differential likelihood of paying to take-up and keeping no trees alive by baseline measures of farmer knowledge about the trees. We take this as evidence that learning about tree cultivation is unlikely to be the primary driver of our results.

## VII. Conclusion

This paper shows that uncertainty can play an important role in the adoption of technologies that require costly investments over time and have a substantial impact on the performance of incentives designed to increase adoption. We provide a broad framework for adoption decisions that allows for both time-varying heterogeneity and multiple dimensions of time-invariant heterogeneity across potential adopters. This framework applies to many adoption decisions in agriculture, development, environment, and health. In our conceptual model, we show that uncertainty in the opportunity cost of adoption can increase take-up rates at the cost of reducing average follow-through rates. A high level of uncertainty at the time of take-up provides an additional explanation to what has been discussed in the technology adoption literature for why charging higher prices may be ineffective at selecting for adopters likely to follow through.

Our study is an example of how experimental variation can be used to identify dynamic structural models. The use of experimental variation in treatments at two different points in time offers an alternative to a panel data structure, since statistically independent samples are exposed to different treatment combinations. To our knowledge, this is the first paper to introduce experimental variation in order to satisfy the exclusion restrictions needed for sequential identification. One caveat of our basic identification strategy is that it relies on shocks being independent across farmers. Therefore, a variant of our model allows for a uniform common shock to farmers, provided that it is completely unanticipated (i.e., the subjective probability assigned by farmers is 0).

The combination of the experimental data with a structural model allows us to look beyond our study setting and simulate adoption outcomes under different levels of uncertainty. The simulations point to the potential for incentives placed directly on follow-through, conditional on take-up (the threshold reward in our experiment), to perform better than take-up subsidies in the presence of uncertainty. We stop short of drawing strong policy conclusions from these results because our study was not designed to test optimal policy design to maximize follow-through or social welfare.31 Instead, we use the paper to make progress on identifying the role of new information in adoption dynamics, which has implications for future work to investigate optimal contract design in the presence of uncertainty at the follow-through stage.

From a policy standpoint, uncertainty has the effect of lowering adoption outcomes per dollar of subsidy invested, while increasing the expected private profits to the adopter because the downside risk of take-up is bounded at 0. To the extent that subsidies rely on public funds, an increase in uncertainty represents an ex ante transfer from the public to the private domain, driven entirely by the adopter's ability to reoptimize follow-through once new information becomes available. While stronger contracts that force adopters to follow through once they take up a subsidized technology would address the problem of high take-up coupled with low follow-through, they would do so at a clear cost to the adopter. Future research to explore more innovative solutions to encouraging both take-up and follow-through in the presence of uncertainty offers a promising direction for both environmental and development policies. For example, cheaper monitoring solutions that facilitate rewards for follow-through outcomes can have positive effects on both take-up and follow-through, as shown in our setting.

## Notes

1

If the follow-through decision has an intensive margin, individuals who take up with a subsidy may follow through with lower or higher intensity compared to those who take up at full price depending on whether the privately optimal follow-through intensity is positively or negatively correlated with the total profit from the technology (Ashraf, Berry, & Shapiro, 2010; Cohen & Dupas, 2010; Suri, 2011; Berry, Fischer, & Guiteras, forthcoming). In other words, the screening effect of take-up prices on follow-through may be either positive or negative.

2

Screening for follow-through using the take-up price is not always desirable. Positive externalities from follow-through or an absence of uncertainty mean that screening for individuals with high follow-through rates may be efficient. Yet allocational efficiency requires that individuals learn about their private benefits from the technology.

3

Several papers have studied how learning about the technology affects subsequent purchase (take-up) decisions and show that subsidies for take-up also affect the likelihood of future take-up (Carter, Laajaj, & Yang, 2014; Dupas, 2014; Fischer et al., 2014).

4

Uncertainty is not the only explanation for these divergent findings. Liquidity constraints, for example, can mean that subsidies increase take-up by adopters with a high valuation and therefore a high propensity to follow through (Tarozzi et al., 2014).

5

Many agricultural technologies fit our framework due to the sequential nature of investment necessitated by cropping cycles. Other technologies fit our framework less well, like those with an initial take-up decision that can be postponed (e.g., some types of machinery), a single investment decision (e.g., land leveling), or new information that arrives after all investments have been made (e.g., fertilizers that must be applied before planting).

6

The lack of self-selection in our setting stands in contrast with Jack (2013), who provides evidence that farmers self-select based on future costs into a tree planting incentive contract in Malawi. She studies a different context and contract design and finds selection effects over time that are consistent with a multiyear extension of our conceptual framework.

7

Our model allows for correlated heterogeneity in both the privately optimal number of trees and the net cost of follow-through, akin to correlated random coefficient (CRC) models (Heckman, Schmierer, & Urzua, 2010).

8

We assume linear utility (risk neutrality) because it allows for closed-form solutions that aid the intuition. We have simulated the model under risk aversion and find that this does not qualitatively change our results (see appendix A.2).

9

The results from our conceptual model are robust to different distributional assumptions. More specifically, results from propositions 1 to 3 also hold under any distribution of shocks, $F1$, with only the restrictions of symmetry and unimodality. Proposition 4 is a direct consequence from investment under uncertainty theory and holds under any distributional assumption with similar regularity restrictions (Dixit & Pindyck, 1993).

10

Corollary 3.1 in appendix A.1 suggests an additional empirical test: the sign of the interaction effect of $R$ and $A$ on follow-through is informative about whether uncertainty is large enough to dissipate the screening effect of take-up prices. We provide suggestive evidence in appendix table A.7.5 that this result holds in our empirical context.

11

In our empirical application, we cannot completely disentangle these two interpretations (see section VIC).

12

Our empirical model imposes a simplified version of the timing. We assume there are only two decision periods (take-up and follow-through) as opposed to many. This simplification corresponds to the empirical setting if the bulk of the information arrives shortly after take-up or if shocks are are highly correlated.

13

Appendix figure A.7.1 shows the implementation time line.

14

Eligibility required that land must have been unforested for twenty years, must be owned by the farmer, and must not be under flood irrigation.

15

The threshold reward was also easy to enforce, consistent with other related contracts offered by Dunavant, and easy to explain to the farmers. The threshold was chosen based on Faidherbia survival rates in other programs in eastern Zambia.

16

At the time of the study, the exchange rate was just under ZMK 5,000 $=$ US\$1. In piloting, the distribution of payments extended to ZMK 200,000 but was scaled back prior to implementation. Six cards with values above ZMK 150,000 were inadvertently included in the main study. For the analysis, we top-code payments at ZMK 150,000.

17

Selection into treatment is also a threat to the experiment's internal validity. By design, this is unlikely: group-level participation subsidy treatments were revealed only after individuals arrived for training, and individual-level reward treatments were assigned in one-on-one interactions with the study enumerators.

18

Of the farmers eligible for monitoring, we were unable to locate nine of them and thus assume zero tree survival in the analysis.

19

Appendix table A.7.6 shows the relationship between outcomes and observables.

20

A correlation (positive or negative) between the optimal scale and the level of profit can emerge from the joint distribution of the primitive parameters that govern a profit function (e.g., marginal costs, fixed costs, marginal benefits). See, for example, Suri (2011).

21

A similar source of variation has been used to identify the distribution of health shocks in the insurance literature: the performance reward varies the distribution of net benefits from follow-through much in the way that varying the terms of an insurance contract has a state-contingent effect on the distribution of payoffs (Einav et al., 2013).

22

In stochastic dynamic structural models, the discount factor is not separately identified from the scale parameter of future period shocks. We used survey data on time preferences to inform our choice of 0.6, which is in line with observed interest rates in our setting and in other rural developing country settings (Conning & Udry, 2007).

23

This assumption is innocuous to the extent that the changes in income produced by our program are small relative to total income. The highest reward from our program is roughly 3.5% of average annual income.

24

It can be shown that there exists some $f¯$ s.t. $ψ(F0i;ri)$ is strictly monotonically decreasing on $(-∞,f¯)$.

25

Assumption c is necessary for maximum likelihood estimation.

26

In our survey, two-thirds of respondents list health problems as their household's greatest hardship, and almost 50% of households report losing cattle or livestock to death or theft during the past year. See section VIC for further discussion of shocks in our setting.

27

Unfortunately, we cannot calculate the share of the variance attributed to common shocks using model estimates since we are not explicitly modeling random common shocks with a known distribution at the time of take-up.

28

$F1$ is assumed to be orthogonal to $F0$ and $T$. Thus, the correlation between $F$ and $T$ stems solely from the correlation between $F0$ (the known component of $F$) and $T$.

29

This treatment of the mean shift parameter is consistent with a common-shock interpretation. Results using our baseline model estimates are qualitatively similar.

30

Lower tree survival in the low-subsidy group (with strong self-selection) relative to the full-subsidy group (without self-selection) is driven by a reduction in follow-through conditional on take-up for the highly self-selected group (see proposition 2). Without self-selection (i.e., if take-up is fully subsidized), it appears that follow-through increases slightly with the variance of shocks whenever the reward is low (solid line in C of figure 3). We call this effect the corner solution effect, as it takes place when the sign of the condition for cultivating more than no trees is to the left of the mean of $F$ (i.e., for very low $R$). This effect emerges when we relax the assumption of binary shocks and assume a distribution of shocks that is continuous and symmetric around the mean and is dominated by the self-selection effect.

31

A number of other features of our setting make us cautious about using our results to discuss optimal policy. For example, we cannot estimate marginal costs separately from marginal benefits, limiting our exploration of alternative contract structures. The assumption of risk neutrality would be less appropriate if we were to compare contracts that impose different levels of risk. Finally, the optimal contract depends on whether the new information that arrives after take-up is a transient shock to opportunity cost or a more permanent shock that affects subsequent take-up decisions. We are unable to fully distinguish between these interpretations.

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## Author notes

We are grateful for helpful comments from audiences at numerous seminars and conferences. We thank the IGC, CDKN and Musika for financial support and the Center for Scientific Computing at the CNSI and MRL at UC Santa Barbara (NSF MRSEC DMR-1121053 and NSF CNS-0960316) for use of its computing cluster. Jonathan Green, Farinoz Daneshpay, Mwela Namonje, Monica Banda, and Innovations for Poverty Action supported the fieldwork. The project was made possible by the collaboration and support of Shared Value Africa and Dunavant Cotton, Ltd. The views expressed in this paper are our own and do not necessarily reflect those of the Federal Reserve Bank of Philadelphia or the Federal Reserve System.

A supplemental appendix is available online at http://www.mitpressjournals.org/doi/suppl/10.1162/rest_a_00823.