Expectations, Shocks, and Climate Adaptation: Evidence from a Rainfall Beliefs Experiment in Eastern Uganda

This study provides smallholder farmers in eastern Uganda with localized historical rainfall information immediately before the main planting season. Farmers in treated villages receive a laminated one-page card specific to their village, containing two elements.

The first is a rainfall calendar showing dekad-level (10-day period) rainfall classifications across the past five growing seasons (2021–2025). Rainfall in each period is classified as none or little, medium, or significant, relative to a 25-year historical baseline (2001–2025) derived from satellite rainfall data (CHIRPS). The calendar uses a simple water-droplet icon system (one, two, or three droplets) to make the information accessible to participants with limited formal education.

The second is a harvest outcome overview showing satellite-derived vegetation conditions (EVI2 from Sentinel-2) for each of the past five seasons, paired with a visual image of the corresponding rainfall condition and a written description of harvest outcomes in both absolute and relative terms.
The information cards are village-specific, generated from satellite data at the parish level, and produced before fieldwork begins. Enumerators present the card after the participant has completed a memory recall exercise and pre-season expectations elicitation. Enumerators answer clarifying questions but provide no interpretation, advice, or recommendations. The visual language of the card is consistent with the token-based belief elicitation tasks used in the survey.

The study also includes a third arm in which a subset of villages receives the information card before any expectation elicitation, to identify anchoring effects separately from belief updating.

The experiment randomizes village-level access to localized historical rainfall and vegetation information immediately before the main agricultural season (March 2026) in Bulambuli District, eastern Uganda. Sixty villages are assigned to three arms using matched-pair rerandomization (Bruhn & McKenzie, 2009; Imai, King & Nall, 2009), stratified by subcounty × elevation tercile, with pairs matched on standardized elevation and peak EVI within strata. Final assignment: A = 24 villages (control), B = 26 villages (information treatment), C = 10 villages (anchoring robustness arm). Randomization seed: 966, achieved after 844 rerandomization draws starting from seed 123. Maximum standardized difference A-B: 0.085.

Survey structure by arm:

Group A receives the full survey with no information treatment: demographic and farming module, memory recall for five past seasons (2021–2025) via token-based elicitation across nine rainfall images and ten onset intervals, pre-season expectations elicitation (Round 1), intermediate questions (extreme events, decision-making, social networks, adaptation plans), and a second expectations elicitation (Round 2).

Group B receives the same sequence as Group A, with the information treatment card inserted between the intermediate questions and Round 2 elicitation. This identifies within-person belief updating: the difference between Round 1 and Round 2 beliefs is attributable to the information treatment, controlling for any time trend using Group A as counterfactual.

Group C receives the memory recall module and intermediate questions first, then the information card, then their first and only expectations elicitation. Group C's first-stated beliefs are post-information and serve as: (i) an out-of-sample validation target for the memory-to-expectation kernel estimated on Groups A and B; (ii) an anchoring test comparing Group C's post-information priors to Group A's uninformed priors.

Information treatment content:

The treatment card is village-specific, generated from subcounty-level satellite data before fieldwork begins. It contains two components:

A rainfall calendar showing dekad-level (10-day) rainfall classification across seasons 2021–2025 using CHIRPS daily rainfall data aggregated at subcounty centroids with a 2km buffer. Rainfall is classified into three categories (none/little, medium, significant) using tercile thresholds frozen from the 2001–2025 WMO baseline. Onset detection uses a 21-day rolling cumulative threshold of 25mm confirmed by 10mm in the following 7 days, with April 30 as fallback. The calendar covers the fixed window February 10 – September 30, displayed as 10-day dekad periods per month.
A harvest outcome picture overview showing Sentinel-2 EVI2 (10m resolution) for each of the five display years. Peak EVI is extracted within the May 1 – September 15 window after applying an agricultural mask (baseline EVI2 < 0.20, peak EVI2 > 0.55, amplitude >= 0.25, 3×3 majority filter). Each year is paired with one of nine photorealistic rainfall condition images (the same image set used in the token elicitation tasks) selected via a pre-specified assignment matrix combining EVI band classification (six bands from < 0.35 to >= 0.65) and stage-weighted water direction score (establishment 25%, flowering 40%, pre-harvest 35%). Harvest outcomes are described in both absolute terms (crop failure through excellent harvest) and relative terms (compared to the five-year mean and standard deviation).

Belief elicitation:

Token-based probabilistic elicitation following Delavande, Gine & McKenzie (2011). Respondents allocate 10 physical tokens across: (i) nine photorealistic images depicting rainfall conditions from extreme drought (image 1) to severe flooding (image 9) with optimal balanced rainfall at image 5; (ii) ten calendar intervals of approximately 5 days spanning the planting window. The full distribution is recorded, yielding mean, variance, entropy, and divergence measures at the individual level. Each elicitation is followed by a 1–5 confidence scale and binary extreme weather expectation questions.

2026-03-09

2026-03-23

The primary outcome is end-of-season vegetative performance at respondent farm coordinates, measured by the EVI2 composite (Enhanced Vegetation Index 2) derived from Sentinel-2 L2A satellite imagery at 10m resolution. The outcome is standardized as a within-village z-score using the 2021–2025 distribution. The primary estimand is the intention-to-treat effect of village-level information provision (Group B vs. Group A) on this standardized outcome.

Three pre-declared outcome families are tested with Romano-Wolf stepdown correction:

Family 1 — Agronomic Performance: EVI2 (primary), NDVI (secondary), Sentinel-1 SAR VH-VV ratio in dB (cloud-robust secondary). Decision rule: the treatment is deemed economically meaningful if at least one optical outcome shows an effect of -0.15 SD or larger with Romano-Wolf adjusted q ≤ 0.10, and the SAR outcome shows a concordant sign with unadjusted p ≤ 0.10.

Family 2 — Belief Precision: Negative log probability score, ranked probability score, and Shannon entropy of post-information beliefs. These capture whether the information treatment improves forecast accuracy and reduces belief uncertainty.

Family 3 — Belief-Relative Shock: The surprise measure S_i = 1 - F_i(k_i^R), where F_i is the farmer's pre-season cumulative belief distribution and k_i^R is the realized rainfall category. This tests whether expectation-relative deviations predict agronomic outcomes better than conventional rainfall anomalies from historical means.

Secondary outcomes include planting timeliness (indicator for planting within the optimal onset window), the greenness integral from onset to onset + 90 days, and the onset-to-peak timeliness index.

EVI2 (primary agronomic outcome): Computed from Sentinel-2 L2A surface reflectance as EVI2 = 2.5 * (NIR - Red) / (NIR + 2.4*Red + 1). Pixels are cloud- and shadow-masked using the SCL quality layer (classes 0,1,2,3,7,8,9,10,11 excluded). An agricultural mask is applied retaining only pixels with baseline EVI2 < 0.20, peak EVI2 > 0.55, seasonal amplitude >= 0.25, and peak occurring within May 1 – September 15, with a 3×3 majority filter. The outcome snapshot is the spatial mean of valid masked pixels within a 100m radius of reported farm coordinates, using the latest valid observation in the final week before reported harvest date. If no valid optical observation exists within 30 days before harvest, the SAR proxy is used and the optical outcome is flagged as missing. The raw EVI2 value is then standardized to a within-village z-score using the mean and standard deviation of the 2021–2025 EVI2 distribution for that village.

NDVI (secondary agronomic outcome): Computed from the same Sentinel-2 scenes as (NIR - Red) / (NIR + Red), using the same agricultural mask and spatial aggregation as EVI2. Standardized identically.

SAR outcome: Sentinel-1 GRD VH-VV ratio in dB, spatially aggregated to farm coordinates using the same 100m buffer, using the latest valid acquisition within the final two weeks before harvest. Serves as cloud-robust secondary and primary inference fallback when optical coverage is insufficient.

Belief precision outcomes: Shannon entropy of the post-information token distribution is computed as H_i = -sum_k p_{i,k} * log(p_{i,k}), where p_{i,k} is the share of tokens allocated to category k. The negative log probability score is computed as LS_i = -log(p_{i,k_i^R}), where k_i^R is the realized rainfall category. The ranked probability score is RPS_i = sum_k [F_i(k) - 1(k >= k_i^R)]^2, where F_i(k) is the cumulative token distribution. All three are computed on the same ordered 9-category support as the token elicitation task.

Belief-relative shock: S_i = 1 - F_i(k_i^R), where F_i is the farmer's pre-season cumulative belief distribution over the nine ordered rainfall categories and k_i^R is the realized rainfall category for the village in the 2026 season, determined from CHIRPS daily data using the pre-specified onset-aligned classification. S_i = 0 when the realized category falls at or above the median of the farmer's prior; S_i approaches 1 when the realized outcome falls in the extreme tail of the prior. The conventional rainfall anomaly Z_i is constructed on the same onset-aligned 9-category support using the 2001–2025 tercile-based climatology, for direct comparison in the horse-race regression.

Memory divergence (D_i): Euclidean distance between recalled and satellite-derived rainfall distributions, computed as D_i = (1/5) * sum_{t=2021}^{2025} sum_{k=1}^{9} (p_{i,t,k} - r_{v,t,k})^2, where p_{i,t,k} is the farmer's recalled token share for category k in year t and r_{v,t,k} is the satellite-derived objective probability for village v in year t. Jensen-Shannon divergence is a pre-registered robustness check.

Planting timeliness: Binary indicator equal to 1 if the respondent's reported planting date falls within the window [onset - 7 days, onset + 14 days], where onset is the village-level CHIRPS-detected onset date for the 2026 season using the pre-specified detection rule.

The survey collects a rich set of secondary variables that will be used both as controls in primary specifications and as outcomes in exploratory analyses examining the determinants of memory formation, belief accuracy, expectation updating, and adaptive behavior. These include:

Demographic and household characteristics: age, gender, household size, years of farming experience, education level, land area cultivated, primary and secondary crops grown, asset ownership.

Information environment: access to weather forecasts from extension services, radio, or mobile phone; frequency of receiving agricultural advice; social network size and composition; whether the respondent discusses weather expectations with neighbors or family before planting.

Memory quality and salience: individual memory divergence (D_i) for each of the five recalled seasons; self-reported memorable weather events (drought, flood, late onset, early cessation); reported crop losses in past seasons; consistency between recalled distributions and reported memorable events.

Belief characteristics: pre-information belief mean, variance, entropy, and skewness over the nine rainfall categories; onset timing belief mean and spread; pre-information confidence rating (1–5 scale); extreme weather expectation indicators (drought, flood, other).

Belief updating: change in belief mean, variance, entropy, and skewness between Round 1 and Round 2 (Groups A and B); stated adjustment indicator (whether respondent reports wishing to update after seeing information); post-information confidence rating.

Adaptation plans: whether any adaptation is planned for the upcoming season; type of adaptation (crop switching, input adjustment, planting timing, water management, other); estimated cost of planned adaptations; whether information receipt changes stated adaptation plans and estimated cost.
Social and network outcomes: number of people respondent expects to share weather information with; whether respondent intends to show or describe the information card to others; trust in official weather information sources.

Decision-making: primary and secondary decision-makers for farming choices; whether decisions are made individually or jointly; degree of autonomy in input purchases.

The secondary variables listed above will be used in three ways.

First, as baseline controls and heterogeneity dimensions in primary specifications. Farming experience, land area, education, and information access are included as pre-specified covariates in all primary regressions. Memory divergence (D_i) and pre-information belief entropy are pre-specified heterogeneity variables: the information treatment effect on agronomic outcomes is expected to be larger for farmers with higher memory divergence and lower baseline forecast precision.

Second, as outcomes in the structural memory and belief formation analysis. Memory divergence D_i is regressed on recency exposure, extremity exposure, and event salience constructed from the self-reported memorable events and cross-validated against satellite records. The mapping from memory quality to forecast accuracy is estimated separately for pre- and post-information beliefs, allowing us to test whether information substitutes for or complements individual recall quality.

Third, as inputs to exploratory descriptive analyses examining relationships that are not primary hypotheses but are of substantive interest. These include: the relationship between social network size and belief homogeneity within villages; whether households with greater stated decision-making autonomy show larger belief updating responses; whether adaptation cost estimates are correlated with belief precision or memory quality; the gender dimension of information access and expectation formation; and the relationship between stated memorable events and measured divergence from satellite records, which speaks to the cognitive mechanisms underlying memory distortion in this setting.

All exploratory analyses will be clearly labeled as such and will not be subject to the Romano-Wolf correction applied to pre-declared outcome families. They are reported to document the richness of the dataset and to generate hypotheses for future work, not to make causal claims.

This is a village-randomized field experiment with three arms implemented immediately before the main agricultural planting season in three Ugandan Districts (Bugiri, Butaleja and Mayuge), in eastern Uganda, west of Mt. Elgon. Sixty villages are randomly assigned to one of three groups: a control group (Group A, 24 villages), an information treatment group (Group B, 26 villages), and a robustness arm (Group C, 10 villages).

All participating farmers complete a survey covering farming background, memory of past rainfall conditions, expectations about the upcoming season, social networks, and planned agricultural adaptations. Rainfall expectations are elicited using a visual token allocation method in which respondents distribute 10 tokens across nine images depicting rainfall conditions from extreme drought to severe flooding. A separate token task elicits beliefs about the timing of rainfall onset. Both tasks are completed for each of the past five seasons (memory recall) and for the upcoming season (expectations).

Farmers in Groups B and C additionally receive a laminated information card specific to their village, showing historical rainfall patterns and satellite-derived vegetation outcomes for the past five growing seasons. Group B receives the card between two rounds of expectation elicitation, allowing measurement of within-person belief updating. Group C receives the card before any expectation elicitation, providing a robustness check on how objective historical information anchors first-stated beliefs.

Randomization is conducted at the village level using matched-pair rerandomization, stratified by subcounty and elevation, with pairs matched on elevation and satellite-derived vegetation indices.

Agricultural outcomes are measured at the end of the 2026 growing season using Sentinel-2 satellite imagery at respondent farm coordinates. The primary outcome is end-of-season vegetative performance (EVI2), standardized within village.

Research Questions

The study addresses three related questions. First, how accurately do smallholder farmers recall past rainfall, and what systematic biases characterize memory distortion — recency overweighting, extremity bias, and salience effects from memorable events? Second, does providing localized objective rainfall histories improve forecast accuracy and shift agricultural behavior toward better-adapted choices? Third, are belief-relative shocks, deviations between subjective expectations and realized rainfall, better predictors of agricultural production losses than conventional weather anomalies based on historical means?
Identification Strategy

The experiment uses three sources of variation for identification. The B vs. A contrast identifies the causal effect of information provision on belief updating and end-of-season agronomic outcomes, using village-level randomization with individual-level data. The within-person contrast between Round 1 and Round 2 beliefs in Group B identifies the magnitude and direction of belief updating in response to the specific information signal received, using Group A's Round 1 to Round 2 change as the counterfactual for time trends and regression to the mean. The C vs. A contrast identifies anchoring — the effect of objective historical data on the starting point of belief formation before any subjective recall is elicited — using Group A's uninformed Round 1 beliefs as the baseline.

Survey Instrument

The survey is implemented via KoBoToolbox (CAPI) on tablets. It is organized into the following modules, with routing by treatment arm:
Memory module (all arms): for each of the five past agricultural seasons (2021–2025), respondents allocate 10 tokens across nine rainfall images to express their recalled probability distribution, report onset timing beliefs across ten calendar intervals, rate their confidence on a 1–5 scale, and answer binary questions about whether they remember extreme conditions in that season.
Pre-information expectations module (Arms A and B only): respondents complete the same token allocation tasks for the upcoming 2026 season, yielding Round 1 belief distributions over rainfall amount and onset timing, along with confidence ratings and extreme weather expectations.

Intermediate module (all arms): questions on extreme weather events experienced in past seasons, factors expected to affect rainfall this season, social networks and information sharing, current adaptation plans, types of adaptation, and estimated adaptation costs.
Information treatment (Arms B and C only): enumerator presents the village-specific laminated information card. Respondent is given time to examine the card; enumerator answers clarifying questions only, providing no interpretation or advice.

Post-information expectations module (Arms A and B): Round 2 token allocation over rainfall amount and onset timing, confidence rating, extreme weather expectations, updated adaptation plans and costs. For Group A this round serves as a test-retest reliability check; for Group B it is the post-treatment elicitation. Question labels are neutral and do not reference the information treatment.

First and only expectations module (Arm C): identical in content to the post-information module above, with neutral labels that do not indicate this is a first measurement, to avoid demand effects.

Estimating Equations

The primary intention-to-treat specification is:

Y_iv = tau_Y * Info_v + X'_iv * gamma + lambda_s + u_iv

where Y_iv is the standardized end-of-season EVI2 at farm i in village v, Info_v is a binary treatment indicator equal to 1 for Groups B and C, X_iv is a vector of pre-specified baseline covariates (farming experience, land area, education, information access, pre-information belief entropy, memory divergence), lambda_s are randomization stratum fixed effects, and u_iv is the error term clustered at the village level. Wild cluster bootstrap p-values with Rademacher weights are the primary inference statistic. Conley spatial HAC and randomization-inference p-values are reported as robustness checks.

Belief updating is estimated at the category level as:

Delta_p_{i,k} = phi_0 + phi_1 * (r_{v,k} - p^pre_{i,k}) + mu_i + eps_{i,k}

where Delta_p_{i,k} is the change in token share for category k between Round 1 and Round 2, r_{v,k} is the objective historical frequency for that category from the information card, and p^pre_{i,k} is the Round 1 belief. phi_1 is the elasticity of updating to the information signal. A mixture model additionally estimates the weight placed on the external signal relative to the memory-based prior.

The belief-relative shock horse race regresses agronomic outcomes jointly on the subjective surprise measure S_i = 1 - F_i(k_i^R) and the conventional rainfall anomaly Z_i constructed on the same onset-aligned 9-category support, comparing explanatory power via R-squared decomposition and out-of-sample prediction.

Inference

All primary specifications use: village-clustered wild bootstrap p-values (Rademacher weights, 9,999 draws) as the primary inference statistic; Romano-Wolf stepdown q-values within pre-declared outcome families; Conley spatial HAC standard errors using village centroids as robustness; and randomization-inference p-values for treatment indicator coefficients. The three pre-declared outcome families (agronomic performance, belief precision, belief-relative shock) are tested jointly with Romano-Wolf correction. All exploratory analyses are clearly labeled and not subject to multiple testing correction.

Timeline

Pre-season survey and information treatment: March 2026. End-of-season satellite outcome measurement: approximately August–September 2026 following harvest. Analysis and paper draft: late 2026.

Randomization was conducted in the office by computer prior to the start of fieldwork, using a pre-registered R script (02_randomize_villages.R) with a fixed random seed. The procedure implements matched-pair rerandomization following Bruhn & McKenzie (2009) and Imai, King & Nall (2009).

Villages were first stratified into strata defined by subcounty × elevation tercile. Within each stratum, villages were matched into pairs using Mahalanobis distance on standardized elevation and satellite-derived peak vegetation index (EVI). Within each matched pair, one village was randomly assigned to Group A (control) and one to Group B (treatment) by computer coin flip. Ten pairs were randomly designated as donor pairs for Group C; within each donor pair one village was randomly assigned to Group C and the remaining village was randomly assigned to Group A or Group B by coin flip.

The assignment was rerandomized if the balance criterion was not met — requiring all pairwise standardized differences for the A-B comparison to be below 0.10 and all comparisons involving Group C to be below 0.25. Starting from seed 123, balance was achieved at seed 966 after 844 draws. The full randomization log recording all 844 failed draws, the final assignment, and the balance table is attached to this pre-registration as a permanent audit trail.

No field personnel or participants were involved in the randomization process. Treatment assignments were communicated to enumerators only through the pre-organized folder structure of village-specific materials, which makes arm membership explicit without disclosing the study hypotheses.

The unit of randomization is the village. All farmers surveyed within a village receive the same treatment assignment. There is only one level of randomization in this study; no individual-level or household-level randomization is applied within villages.

Villages are nested within parishes, parishes within subcounties, and subcounties within Bulambuli District. Randomization is conducted at the village level but stratified at the subcounty × elevation tercile level to ensure balance across administrative and climatic dimensions. The information treatment is delivered at the village level via village-specific laminated cards; individual survey responses are the unit of observation and analysis.

The choice of village-level randomization reflects two design considerations. First, the information treatment is inherently social; farmers in the same village share a common rainfall history and observe each other's planting behavior, making individual-level randomization within villages both operationally infeasible and likely to generate strong spillovers. Second, the primary agronomic outcome (end-of-season EVI2) is measured at farm coordinates via satellite and varies at the individual level within villages, allowing within-village variation in outcomes to be used for precision gains even though treatment is assigned at the village level.

Standard errors are clustered at the village level in all primary specifications, consistent with the unit of randomization.

Yes

60 villages

600 to 800 farmers (10 to 15 per village across 60 villages)

24 villages control (Group A), 26 villages information treatment (Group B), 10 villages anchoring robustness (Group C)

Power calculations assume alpha = 0.05, power = 0.80, outcomes standardized to mean zero and standard deviation one, R-squared from pre-specified covariates and pair matching of 0.35, and an average cluster size of 12 respondents per village (based on 600–800 respondents across 60 villages). Primary contrast — Group B vs. Group A (information treatment effect): At an intracluster correlation (ICC) of rho = 0.03, the MDE is approximately 0.28 standard deviations. At rho = 0.05 the MDE is approximately 0.30 SD; at rho = 0.10 the MDE is approximately 0.35 SD. These are computed using the standard cluster-adjusted formula accounting for 25 treatment and 24 control clusters and the design effect from pair matching. Robustness contrast — Group C vs. Group A (anchoring effect): At rho = 0.05, the MDE is approximately 0.43 SD with 10 treatment and 24 control clusters. Group C is designated as a robustness arm and is underpowered for detecting small anchoring effects; its primary purpose is out-of-sample validation of the memory-to-expectation kernel rather than a powered hypothesis test. The primary B vs. A MDE of 0.28–0.35 SD is within the range of effects documented in comparable information provision experiments in developing country agricultural settings.