metadata: authors: 0: author: Yacoubou Djima,Ismael Claude Ignanda
1: author: Tiberti,Marco
2: author: Kilic,Talip
count: World
docna: 0: docna: Yielding Insights : Machine Learning-Driven
            Imputations to Filling Agricultural Data Gaps
docty: Policy Research Working Paper
abstracts: cdata!: This paper addresses the challenge of
            missing crop yield data in large-scale agricultural surveys,
            where crop-cutting, the most accurate method for yield
            measurement, is often limited due to cost constraints.
            Multiple imputation techniques, supported by machine
            learning models are used to predict missing yield data. This
            method is validated using survey data from Mali, which
            includes both crop-cut and self-reported yield information.
            The analysis covers several crops, providing insights into
            the importance of different predictors, including
            farmer-reported yields and geo-spatial variables, and the
            conditions under which the approach is valid. The findings
            show that machine learning-based imputations can provide
            accurate yield estimates, especially for crops with low
            intercropping rates and higher commercialization. However,
            survey-to-survey imputations are less accurate than
            within-survey imputations, suggesting limitations in
            extrapolating data across different survey rounds. The study
            contributes valuable insights into improving cost-efficiency
            in agricultural surveys and the potential of imputation methods.
display_title: Yielding Insights : Machine
            Learning-Driven Imputations to Filling Agricultural Data Gaps
listing_relative_url: /research/2024/11/34417194/yielding-insights-machine-learning-driven-imputations-filling-agricultural-data-gaps
topicv3: Agriculture and Food Security m1326205 435,Geographic Information Systems m1326400 663,Rural Development m1504505 2667
publishtoextweb_dt: 2024-11-04T00:00:00Z
dois: 10.1596/1813-9450-10964
origu: Off of Sr VP Dev Econ/Chief Econ (DECVP)
no_of_pages: 52
author_keys: 0: author_key: 1200143
1: author_key: 1302596
2: author_key: 886702
model_extractions: Policy Research Working Paper 10964

# Yielding Insights

Machine Learning-Driven Imputations to Filling Agricultural Data Gaps _Ismaël Yacoubou Djima Marco Tiberti Talip Kilic_ Development Economics Development Data Group November 2024
Policy Research Working Paper 10964

# **Abstract**

This paper addresses the challenge of missing crop yield data in large-scale agricultural surveys, where crop-cutting, the most accurate method for yield measurement, is often limited due to cost constraints. Multiple imputation techniques, supported by machine learning models are used to predict missing yield data. This method is validated using survey data from Mali, which includes both crop-cut and self-reported yield information. The analysis covers several crops, providing insights into the importance of different predictors, including farmer-reported yields and geo-spatial variables, and the conditions under which the approach is valid. The findings show that machine learning-based imputations can provide accurate yield estimates, especially for crops with low intercropping rates and higher commercialization. However, survey-to-survey imputations are less accurate than within-survey imputations, suggesting limitations in extrapolating data across different survey rounds. The study contributes valuable insights into improving cost-efficiency in agricultural surveys and the potential of imputation methods.

This paper is a product of the Development Data Group, Development Economics. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The authors may be contacted at iyacouboudjima@worldbank.org; mtiberti@orldbank.org; and tkilic@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
Yielding Insights: Machine Learning-Driven Imputations to Filling Agricultural Data Gaps<sup>∗</sup> Isma ̈el Yacoubou Djima<sup>†</sup> Marco Tiberti<sup>_†_</sup> Talip Kilic<sup>_†_</sup>

**JEL Codes:** C53; C55; C83; Q12.

**Key words:** Smallholder farming, Agricultural Crop Yields Measurements, Machine learning, Missing Data, Multiple Imputation, Household Surveys

> ∗The authors would like to thank (i) Ksenia Abanokova, the participants of The Ninth International Conference on Agricultural Statistics (ICAS IX) for their comments, (ii) the Statistics Unit of the Ministry of Agriculture in Mali (CPS/SDR) for the successful implementation of the agricultural surveys that this study leverages, (iii) Giulia Ponzini who co-lead the technical support to CPS/SDR for the implementation and the data curation of the surveys data used for this study. We are grateful for the funding from the Mali Mission of the United States Agency for International Development (USAID) for the implementation of the LSMS–Integrated Surveys on Agriculture (LSMS-ISA)-supported surveys in Mali. This paper was produced with the financial support from the World Bank LSMS Program (worldbank.org/lsms) and the 50x2030 Initiative to Close the Agricultural Data Gap (50x2030.org), a multi-partner program that seeks to bridge the global agricultural data gap by transforming data systems in 50 countries in Africa, Asia, the Middle East and Latin America by 2030.

> †Living Standards Measurement Study (LSMS), Development Data Group, World Bank.
# **1 Introduction**

Microdata from agricultural surveys is an essential ingredient for empirical analysis of the economic life of smallholder farmers. Particularly in Africa, farm surveys remain the backbone of agricultural statistics (Carletto et al., 2015). However, collecting accurate data in lowincome countries through agricultural surveys is challenging due to various factors, such as the complexity and seasonality of agricultural operations, illiteracy among respondents, and unfamiliarity with standard units of measurement. Overcoming these challenges requires the implementation of complex and costly survey operations. Therefore, the cost-effectiveness and design efficiency of farm surveys, as well as the use of statistical methods to overcome the analysis challenges of their data, remain active areas of methodological research to which this paper intends to contribute.

The analysis focuses on crop yields at the plot level. Generally, plot-level crop yield statistics obtained from agricultural surveys are calculated using either farmers’ reported harvest weight or enumerators’ measured crop-cut harvest weight. Research has shown that self-reported crop yields are prone to non-classical measurement errors and tend to be higher than objectively measured yields obtained through crop cutting (Abay et al., 2019, Desiere and Jolliffe, 2018, Gourlay et al., 2019, Yacoubou Djima and Kilic, 2024). Although enumerator-measured crop-cutting is widely considered the most precise method for quantifying agricultural output (Fermont and Benson, 2011), its implementation is more costly and time-intensive. As a result, this information is often available only for a subset of the survey, leading analysts to rely on statistical methods and imputation techniques to fill these data gaps.

With the recent advances and their off-the-shelves availability, machine learning (ML) algorithms have become go-to tools of analysts to perform prediction exercises so including them as part of an imputation exercise is a natural next step. Economics research has seen the increasing use of ML techniques in recent years, with proven effectiveness. According to Athey (2018), evaluation of ML’s early contributions to economics, ML techniques have been particularly successful when applied to prediction-based problems, such as the one addressed in our study. In addition, utilizing ML in agricultural economics research is a logical approach to model critical variables, such as crop yield, which involves a complex combination of factors, including soil quality, weather, input timing, and management choices, which have non-linearities and interactions (Storm et al., 2019). Previous research attempting to estimate crop-yields in the context of smallholder farmers using ML techniques often attempt this exercise combining manually-labeled optical imagery, and ground data collection, including as part of household and farm surveys. Azzari et al. (2021) provide examples of these studies and recommendations on how large-scale household surveys should be conducted to generate the data needed to train models for satellite-based crop type mapping in smallholder farming systems. Our study relies essentially on survey data integrated with geospatial variables to make crop yield predictions at a granular level. Yacoubou Djima and Kilic (2024) attempt to apply ML techniques for the prediction of yields, leveraging survey data from Mali, to validate an alternative approach to estimate the relationship between crop yields and inputs. The authors conduct a within-survey imputation exercise that derives predicted, otherwise unobserved, objective crop yields that stem from a machine learning model that is estimated with a random sub-sample of plots for 2
which crop cutting and self-reported yields are both available. This approach allows the authors to replicate the relationship between yields and input obtained with crop-cut yields using the predicted yield showcasing the validity of this imputation framework. However, their exercise is conducted with one crop (sorghum) and only considers one agricultural season limiting the external validity of the framework they develop.

Against this background, our analysis attempts to address these limitations. We take advantage of the availability of two consecutive rounds of the nationally representative agriculture survey of Mali collected as part of the Living Standards Measurement Study - Integrated Surveys on Agriculture (LSMS-ISA)<sup>1</sup> project to validate their approach when used in a surveyto-survey imputation framework. Moreover we extend the imputation exercise to more crops: in addition to sorghum, we work with millet, maize, rice, groundnut and cowpea allowing us to generalize the conditions on which the approach is valid. For reasons of computational ease and tractability, we focus on the estimation of the mean value of yields. We go beyond within-survey imputations exercises to look at survey-to-survey imputations. We also explore which set of covariates are more potent for the imputations exercises. Finally we also explore the effect of training sample sizes and strategies. By varying the size of the training sample, we investigate whether reducing the sample size can still yield reliable imputation results, with the aim of balancing cost efficiency and the accuracy of imputation methods.

Our main findings are threefold: (i) farmers’ reported yields are good predictors of crop-cut yields but the results point to a greater predictive power of integrated geo-spatial variables; (ii) on average the imputation exercises work better for crops that have low intercropping rate, and are more commercialized, which can be related to the accuracy in standard units of the farmerreported yields; (iii) in most of the cases, the imputation approach provides accurate results in the within-survey imputation framework and collecting crop-cut measurements on a sub-sample of plots can offer a cost-effective approach while still achieving reliable ML predictions of CC yields, but less so in the survey-to-survey framework especially when statistics are computed at a desegregated level. These results point to important cost savings in survey operations, but also highlight the stringent survey data requirements in terms of quality.

The paper is organized as follows. Section 2 describes data situations in which crop-cut yields are missing and how the data at our disposal allows us to investigate imputation frameworks that are suited to handle the situations. Section 3 describes the survey data. Section 4 presents the empirical approach. Section 5 discusses the results and section 6 concludes.

# **2 Data situations**

Contexts where yields data based on crop-cuts are unavailable at large scale are very common and it has led researchers to develop statistical methods to overcome such scarcity. Table 1 provides an overview of data situations as it pertains to crop-cut yield and the potential

> 1The Living Standards Measurement Study - Integrated Surveys on Agriculture (LSMS-ISA) is a unique system of longitudinal surveys designed to improve the understanding of household and individual welfare, livelihoods and smallholder agriculture in Africa. Partners countries include: Burkina Faso, Ethiopia, Malawi, Mali, Niger, Nigeria, Tanzania, and Uganda. For more information see: https://www.worldbank.org/en/programs/lsms/initiatives/lsms-ISA.

3
imputation solutions to fill the gap for this measure. We group these situations into two broad categories. In the first category, where the data is ”partially missing”, the household survey collects plot level information and agriculture practices, and crop-cuts on a subsample usually selected randomly. A within-survey imputation framework is applied in this case. In the second category, the household survey has plot level information on agriculture practices and self-reported crop production and no harvest data based on crop-cutting. In this case an across survey imputation framework is applied. We provide more details for each of these cases in the reminder of this section.

# **2.1 Partially missing: Within-survey imputation**

The situation of partially missing crop-cut data is a common scenario in most farm surveys.<sup>2</sup> In such cases, crop yield measurements are obtained in two ways: through relatively inexpensive, but less accurate, self-reported harvest data, and through more fieldwork-intensive, expensive, but more objective measures acquired via crop-cutting on a subsample. This survey design is adopted for cost-efficiency and has the advantage of providing multiple measures of crop yields for a small proportion of plots in a single survey.

In the case of LSMS-ISA surveys, several country programs<sup>3</sup> have integrated crop-cutting into their survey operations. The proportion of the sample with crop-cuts (CC) varies across programs. Generally, a list of plot-crop combinations is made at the Enumeration Area (EA) level. If the number of these combinations exceeds a minimum threshold, a random sample of plots is selected for crop-cut implementation.<sup>4</sup> This survey design is conducive to within-survey (within agricultural season) imputation. A key reason for this is that plot-level information and agricultural practices are collected for all plots in the survey, providing a common basis for the covariates used in statistical modeling. In this context, an important question arises: What proportion of crop-cuts is necessary to obtain valid crop yield statistics? This paper addresses this question by varying the proportion of the sample used to train the model.

# **2.2 Completely missing: Across surveys imputation**

In general, the scenarios we consider for completely missing crop-cut data involve living standard surveys with integrated agricultural modules where crop-cut data were not collected, yet there exists a farm survey within the statistical system that does collect plot-level agricultural practice data. To illustrate, consider Mali or Ethiopia, which conduct repeated cross-sectional crop cutting annually. One might question whether it is feasible to conduct crop cutting less frequently—perhaps every other year or every three years—and rely on data imputation to bridge the gaps while reducing costs. This approach is particularly pertinent for these countries, given

> 2Among countries in West Africa conducting annual farm surveys, Burkina Faso with the Enquˆete Permanente Agricole (EPA) conducts crop-cuts on all plots of the households sampled.

> 3Mali, Ethiopia, Uganda, and Malawi are among the countries with a survey design that includes crop-cut collection on a subsample.

> 4Details of the crop-cut sampling protocol can be found in the survey documentation manual on The World Bank Microdata Catalog: https://microdata.worldbank.org/

4
their recent experiences with conflict. Imputation techniques could be invaluable in fragile and conflict-affected regions, offering a way to circumvent the challenges and practical difficulties of extensive crop-cutting surveys. These techniques provide a more efficient and cost-effective method for estimating crop yields, enabling timely and reliable data analysis. Moreover, they can address data collection disruptions caused by conflict or political instability. By imputing missing values, we can maintain the continuity of data series, leading to more complete and consistent datasets for analysis. This is crucial for assessing agricultural trends and evaluating interventions in situations where direct data collection is challenging.

Another practical application of survey-to-survey imputation of crop yields is seen in the WAEMU harmonized survey program. Here, national statistics offices in West Africa collect plot-level agricultural information while conducting parallel farm surveys with crop-cut operations either in the same or the previous year. An across-survey imputation model could effectively fill these crop-cut data gaps.

In this study, we focus on evaluating the validity of the imputation procedure by forecasting (and backcasting) mean crop-cut yields in the 2018 (2017) dataset using the 2017 (2018) cropcut sample as the training sample.

# **3 Data**

We have access to data from two nationally representative surveys of rural areas in Mali, conducted during two successive agricultural campaigns. The Enquˆete Agricole de Conjoncture Int ́egr ́ee aux Conditions de Vie des M ́enages 2017 (EACI-2017), administered in the 2017-2018 season, covered 8,398 households, while the Enquˆete Agricole de Conjoncture 2018 (EAC2018), carried out in the 2018/2019 season, involved 8,225 households. These datasets were collected by the Statistics Unit of the Ministry of Agriculture, in collaboration with the LSMSISA team of the World Bank. This collaboration resulted in repeated cross-sectional surveys of households (in the same Enumeration Areas, or EAs) that gathered comprehensive data on household characteristics and living conditions. The surveys, with a focus on agriculture, provided detailed and precise plot-level information. For each edition of the survey, households were visited twice: the same households interviewed on the first visit were re-interviewed on the second visit, and the visits were planned to match the timing of the post-planting (between August and October) and post-harvest (November and February) periods of the 2017/18 and 2018/19 agricultural rainy seasons. Semi-resident enumerators conducted these visits, with an additional visit between the two for crop-cut harvesting. In both survey waves, crop cuts were carried out for all crops grown during the main agricultural season. A third of the plots per crop were randomly selected for crop cutting from a list of all plots, which was stratified by the crops cultivated by the sampled households within an enumeration area.

## **3.1 Summary statistics and sample counts**

In this analysis, we concentrate on six crops that appear in 80% of all observations and for which non-standard unit conversion factors are used: millet, sorghum, rice, maize, cowpea, and groundnut. Table 2 presents the sample details for these crops across each survey wave.

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In total, we have approximately 31,032 observations: 21,657 from the 2017 wave and about 9,375 from the 2018 wave.<sup>5</sup> For each crop, we have slightly less than a third of observations with both crop-cut and self-reported production information. This is in line with the cropcutting protocol of the survey, which stipulates that crop-cuts are conducted randomly on a third of all plot-crop combinations in an Enumeration Area (EA). For a more comprehensive view, detailed tables with summary statistics of yields by crop, cropping method (either pure or intercropping), and whether the plot underwent a crop-cut are included in the appendix, specifically in Tables B.1 and B.2.

To validate the imputation framework, our analysis will focus on the subset of the sample where both Crop Cutting (CC) and Self-Reported (SR) yield data are available. It is crucial to ascertain whether the plots selected for crop cutting are representative of the broader sample. This aspect is examined in Table 3 and Table 4, which present summary statistics for SR yields<sup>6</sup> and plot areas for each crop in the 2017 and 2018 campaigns, respectively.

The results reveal that the mean differences between plots with CC and those without are not statistically significant, with the exception of rice in 2017. Regarding plot area, the non-crop cut sample has larger plots of sorghum and maize in 2017, and larger millet plots in 2018. Despite these disparities, the overall evidence suggests that the randomization process was effectively implemented, and the characteristics of the crop cut plots do not systematically differ from the non-crop cut plots. This finding is particularly relevant for the within-survey imputation exercise, where understanding the nature of data missingness is crucial. The results support the application of the Missing At Random (MAR) framework, indicating that the model is likely trained on a representative sample. Finally, the presence of zeros in the dataset may raise some discussion about the choice of the imputation methods and the analysis results. In our dataset the zeros yields are real zeros as they denote plots that did not produce any outputs. In addition, the share of zeros is quite low. Overall, 5% of the observations have 0 yields. By crop, the share of observations with 0 yields ranges from 2% for millet to 13% for maize. For these reasons we can reasonably argue that our estimates are not biased by the presence of zeros in the dataset.

# **3.2 Measurement errors in SR yields**

In this paper, we capitalize on the unique opportunity provided by having data on harvest from the same plots measured using two distinct methods: crop cuts and self-reported production. Previous studies, such as those by Abay et al. (2019), Desiere and Jolliffe (2018), Gourlay et al. (2019), Yacoubou Djima and Kilic (2024) have explored similar datasets in Ethiopia, Uganda, and Mali, particularly for maize and sorghum, to investigate measurement errors in yield reports. Our descriptive analysis corroborates these findings. We observe that selfreported yields demonstrate the same pattern of correlated measurement errors with plot area, as documented in the literature for all crops examined. Figures 1 and 2 graphically illustrate

> 5For the 2018 wave, we limited our analysis to plots of households that did not cultivate the same crop on multiple plots because self-reported harvest data was collected at the crop level.

> 6 SR yields were adjusted: yields exceeding six times the national norms provided by the Ministry of Agriculture were normalized to the mean yields at the Enumeration Area (EA) level, or to district or regional levels if needed.

6
this phenomenon. They show the difference in yields (SR-CC) across quintiles of plot area (measured via GPS) for the entire sample. These figures highlight a consistent correlation between the SR-CC difference and the quantity of cultivated area, as noted in the literature: farmers’ overestimation is more pronounced on smaller plots and decreases, or even reverses, on larger plots.

The average overestimation of SR yields in comparison to CC yields in Mali is likely influenced by the fact that the average plot area in Mali is larger than in the studies previously mentioned. This larger average plot size means that the underestimation trend observed in other studies begins earlier in the distribution for Mali. Generally, SR yields are overestimated compared to CC yields in the first plot area quintile. However, in each of the subsequent quintiles, SR yields tend to be underestimated. The distinct trend observed for cowpea may be attributed to the fact that cowpeas are typically planted on smaller plots. Despite this, the general trend of decreasing overestimation across land quintiles is still evident, though it is not a linear decrease.

Additionally, the high confidence interval reported for cowpea yields may be attributed to the prevalence of intercropping in its cultivation.<sup>7</sup> Accurately self-reporting harvest quantities in intercropped plots can be particularly challenging. As for groundnut, we observe consistent underestimation across all plots. This finding could be linked to the findings by (Bardasi et al., 2011), which suggests that women’s labor tends to be underestimated by men. A plausible explanation for the underestimation observed in our study is that groundnuts are predominantly cultivated by women, while the majority of respondents for the 2017 and 2018 surveys were men, who usually tend to underreport the product harvested by women. According to EACI-17 and EAC-18 data, groundnut plots, which are managed by women at a higher rate than average (18% compared to the overall average of 7%), also have a high rate of proxy respondents. Specifically, 42% of the information about these plots is not provided directly by the manager.

# **4 Empirical approach**

## **4.1 Validation approach**

We have structured our empirical framework to identify the limitations of imputation accuracy and to offer recommendations for capturing the essential data set. This includes the necessary variables, the most effective machine learning (ML) modeling approach, and the minimum sample size for robust statistical analyses of crop yields when crop-cut data is either completely or partially missing.

To determine the required set of variables and the most effective ML modeling approach, we train our model on 75% of the plots with crop-cut data, then make predictions on the remaining 25%. This process is carried out separately in the EACI 2017 and EAC 2018 datasets.

To explore the limitations imposed by survey sampling when using crop-cut data to train an imputation model, we experiment with the ML approach, and with varying sample sizes of

> 7Among the six crops analyzed, cowpea has the highest rate of intercropping, with 27% of the plots cultivated with cowpea being intercropped.

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the training dataset. We use proportions of 10, 20, 33, 25, 50, 67, and 75 percent of the crop-cut measures, with the rest of the sample serving as the test set in each scenario. These simulations are performed using the EACI 2017 dataset, which has the largest sample of crop-cut plots.

To assess the robustness of statistical analyses using imputed crop yields, our approach involves several key steps. First, for the within-survey imputation procedure, we train the ML model on one-third of the plots that have crop-cut data and test the model on the remaining two-thirds. This allows us to evaluate the effectiveness of the model in accurately imputing yields within the same survey. Secondly, for the survey-to-survey imputation procedure, we train the machine learning model on the entire crop-cut sample from EACI 2017 and then test its performance on the crop-cut sample from EACI 2018. This step further our understanding of how well the model can generalize and impute data across different survey years. Lastly, we invert the training and test samples to experiment with backcasting. In this process, we train the model on the EACI 2018 crop-cut sample and test it on the EACI 2017 sample. This reverse application provides insights into the model’s capability to predict past yields based on more recent data, further testing the limits of the imputation model’s robustness.

# **4.2 Imputation framework**

## **_Using machine learning (ML) for the imputation model_**

In recent years, ML techniques have increasingly been incorporated into economics research, demonstrating significant utility in various applications. As noted by Athey (2018), ML methods have shown remarkable success in predictive problems, much like the one we address in our study. Introducing ML into agricultural economics enables the modeling of key variables, such as crop yields, which are influenced by a complex array of factors including soil quality, weather conditions, timing of inputs, and other management choices, often characterized by non-linearities and interactions.

Moreover, ML algorithms are specifically designed to prevent overfitting to the training dataset. This is achieved through techniques like regularization and the empirical selection of tuning parameters. While overfitting is generally not a primary concern in missing data imputation for within-survey applications, this feature of ML algorithms becomes particularly advantageous in survey-to-survey imputation scenarios. Here, the ability of ML to generalize across different datasets without overfitting is a significant benefit, enhancing the reliability and applicability of the imputation results.

One complication in our setting is that the set of covariates we use has a hierarchical structure: we conduct imputation at the plot level, as each crop, even when intercropped, is modeled separately. However, we include covariates at both the household and EA levels. A potential issue with using ML algorithms in a non-i.i.d. setting is that test performance may be overly optimistic. This occurs when selecting covariates that identify household characteristics or EAs that are good at predicting yields without capturing the idiosyncratic details of plots that may affect yield values. This, in turn, would decrease the predictive performance of the ML model at the plot level. To mitigate this issue, we have interacted geospatially extracted characteristics with plot characteristics that make sense, for example, the date of planting and the amount of rainfall per dekad. This is not done systematically for all variables to keep 8
the set of covariates manageable from a computational standpoint. Additionally, we split the training data to ensure that algorithms are trained and cross-validated across small clusters when possible. This reduces instances where plots from the same EAs are all clustered in the same training samples.<sup>8</sup> Ngufor et al. (2019) suggests a two-step procedure, which we intend to apply as a robustness check to investigate the improvements it brings in terms of performance.

# **_Outcomes variables_**

We employ ML methods to impute both yield levels and log yields.<sup>9</sup> In this process, we calibrate the model using Crop Cutting (CC) as the outcome variable. CC is regarded as the ’gold standard’ method for measuring yields at the plot level.

# **_Covariates_**

Our covariates set is made of about 162 variables<sup>10</sup> in the following categories: (1) Self-reported yields<sup>11</sup> ; (2) Plot characteristics, excluding the quantity of key plot inputs.<sup>12</sup> This category includes land tenure, soil type, fertility measures, distance from the household, etc.; (3) Climate and rainfall variables, derived from GPS coordinates of the plots; (4) Farmer agricultural practices (such as sowing dates, type of labor) interacted with rainfall measures, along with agricultural and welfare implementation indices; (5) Household characteristics, including composition, demographics of the household head, and welfare measures; (6) Fieldwork variables, encompassing respondent characteristics, dates of visits, and observations of any damage to the crop cut noted by enumerators, survey design variables such as household weights.<sup>13</sup>

# **_Evaluation metrics_**

To assess the performance of the machine learning models, we utilize the coefficient of determination ( _R_<sup>2</sup> ) from the regression of Crop Cutting (CC) yields against the ML-predicted yields.

8Increasing the number of cross-validation samples is also a way to reduce the decrease in performance, but when we experimented with a higher number of cross-validation samples, the increase in terms of performance was marginal while the computational cost was high.

> 9The logarithm of crop yield is often the preferred variable for regression analyses in empirical research, such as exploring the inverse relationship (IR) between farm size and productivity. Since there is no significant difference between predictions for levels and logs, we have included the results for log predictions in the appendix.

> 10The full list of covariates can be found in the appendix C.

> 11We include self-reported yields in levels for predicting yields and in logarithmic form for predicting log yields.

> 12As analysts often regress yields obtained using ML on the quantity of inputs, we exclude these variables from the ML covariates to ensure that the regression coefficients are not simply a mechanical result of the ML prediction model. We also tested models that included inputs as covariates and found no significant in the results.

13The inclusion of the weights in the model followed Rubin (1987), who implicitly assumed that the imputer should have access to the variables used to construct any weights and should always include them in the imputation model. However, as pointed out by Quartagno et al. (2019), previous works have shown that following this approach results in an upwardly biased estimate of the variance, although the simulations in these works have shown that this issue is of little practical importance. As a robustness check, we verify whether the inclusion of survey weights has an impact on predictive performance.

9
While the _R_<sup>2</sup> does not precisely represent prediction accuracy, it offers an intuitive measure of relative performance, i.e. the proportion of variance in the observed yields that is explained by the predicted yields. The ultimate validity of our proposed imputation framework hinges on the accuracy of the crop yield statistics derived from modeling. Therefore, we examine the difference between the means of the CC yields and those computed using the ML model not only in the test set, but also across the entire sample, both nationally and at disaggregated levels. To put things in perspective, we compare the mean yields obtained through ML with those obtained from self-reported (SR) yields. We also assess whether the ML estimate falls within one standard error or the 95% confidence interval of the observed mean CC estimate, further evaluating the reliability of our imputation approach. We also considered other metrics such as root mean square errors to ensure that it does not impact the conclusion that we make. Our preferred metric remains the adjusted _R_<sup>2</sup> because it allows us to compare across crops without the average size of yields per crop biasing the conclusions we make.

# **_Multiple imputation_**

The ML modeling is used in a multiple imputation framework (MI). As such, we generate several imputations, which are different since the cross-validation samples can be drawn differently and thus provide slightly different predictions for each observation. We then follow the MI statistical approach when computing means and standard errors to take into account the variability that comes from the modeling (combining within imputation and between imputation variances). MI, first proposed by Rubin (1987), is a Monte Carlo technique that replaces missing values for a given variable with m _>_ 1 simulated alternatives. MI typically consists of three steps: (i) m imputations (i.e. m complete datasets) are generated based on an imputation model that encompasses a vector of observable covariates that predict the missingness in a given variable, (ii) statistical analysis is performed separately with each of the m complete datasets, and (iii) the results obtained from m complete data analyses are combined into a single set of multiply-imputed parameter estimates and standard errors. The conditions under which valid inferences could be obtained from missing data has been laid out by (Rubin, 1987). Our procedure assumes that data are missing at random (MAR), that is that missing data could be predicted based on observable attributes underlying missingness. While the MAR assumption is not empirically testable, the limits of its tenability could be assessed in our study since the process of missingness is due to the survey design (see discussion in the Data section 3 and precisely Tables 3 and 4). In building the imputation model, the literature advises to include as explanatory variables: (i) the variables appearing in the analysis model that features the multiply imputed variable(s), (ii) the variables that are known to have influenced the occurrence of missing data, and other variables for which the distributions differ between the response and non-response groups, (iii) the variables that explain a considerable amount of variance of the multiply-imputed variable(s) and that help to reduce the uncertainty of the imputations, and (iv) the variables with information on the features of the complex survey design, including stratum and cluster identifiers, and sampling weights. In assessing the validity of our imputed crop-yield, we account for the survey design by weighting our estimations and using designadjusted standard errors corrected for clustering at the enumeration areas. Since we use a multiple imputation approach, we compute means and standard errors following (Little and 10
Rubin, 1987) to account for within and between imputation uncertainty. By adhering to these statistical practices, we aim to provide a robust and accurate evaluation of the imputed cropyield data, ensuring that our findings are reflective of the underlying survey data and the complexities of the imputation process.

# **5 Results**

## **5.1 Modeling lessons**

### **5.1.1 Top predictors**

In this section, we look at the most relevant variables as identified in the random forest algorithm prediction<sup>14</sup> for 50 different simulations. Table 5 shows the top 10 most important variables in the prediction for each crop’s yield levels.<sup>15</sup> SR yield variable is an important predictor for crop yield in levels (with the exception of millet), but not as important as for logs predictions (it is the most important predictor of yield in logs only for cowpea). Geospatial variables are consistently among the top predictors for both levels and logs yields. It is reassuring for the machine learning approach to observe that the combinations of farmer practices and different rainfall variables are among the most important predictors for most of the modeled crops (both for logs and levels yield predictions). Indeed, in a context of smallholder farmers like the one in Mali where most of the crop production relies on rainfall, one would expect that yield would be significantly impacted by the complex interaction of timing of the seeding timing and the amount of rain that fall. This underlies the usefulness of collecting detailed agricultural practices information, as well as being able to link the georeferenced data collected with geo-spatial, when conducting a crop yield prediction exercise.

The relevance of SR yield for improving the quality of yield predictions highlights the importance of collecting farmer-reported information on crop production. Therefore, particular attention should be devoted to enhancing the quality of SR yields, for example by reducing the length of the recall period as noted in (Wollburg et al., 2021), and improving the completeness and quality of conversion factors for non-standard measurement units.

To further assess the degree to which the most important variable matter compared to the second one for example, we look at the average value of the importance metric produced by the random forest algorithm for the 50 different simulations we conducted. Figure 3 and Figure 4 exhibit these values for rice yield predictions in levels. Household weights and SR yields appear as one of the top three key variables in the predictions: household weights represent the most important variable for rice yield predictions in levels while SR yields variable is scored as the third most important for rice yield predictions in levels. The plot slope and average annual total rainfall are the second most important variables for levels and logs, respectively. One

> 14For our predictions for log or levels, we rely on the ensemble prediction. But to take a deeper look at the set of covariates, we rely on the covariate importance measure of the Random Forest algorithm, which is the most efficient algorithm for yield predictions for most of the crops when imputing levels, as shown in Table A.1 and it has the lowest error outside the ensemble for the log predictions.

> 15We show the equivalent table for predicting logs in Table B.3.

11
striking observation from Figure 3 is how much more important SR yields are in comparison to the rest of the covariates when it comes to log predictions. We assess the relative importance of covariates in the accuracy of the prediction in the following subsection.

# **5.1.2 Relative importance of SR yields and GPS extracted variables**

We run the ensemble of methods described in Appendix A for 25 different cross-validation splits to predict CC yields, testing for the inclusion of SR yields and geospatial variables extracted using the EA GPS coordinates<sup>16</sup> among the set of predictors. This approach allows us to evaluate the impact and relevance of these specific variables in the context of our machine learning models and the overall accuracy of the yield predictions.

Table 6<sup>17</sup> shows the impact of including SR yields and/or GPS extracted variables on the quality of the predictions, measured in terms of _R_<sup>2</sup> for the whole set of crops and individually for each crop. The reference model set up does not include SR or geospatial variables in the set of covariates.

First, including SR yield or GPS extracted variables increases unambiguously the accuracy of yield prediction as the difference in _R_<sup>2</sup> is for the most part positive and statistically significant. Second, combining SR and GPS provides on average better accuracy than using one or the other set of covariates. Third, there is some heterogeneity in terms of crops. The SR yield variable is more relevant for sorghum and cowpea imputations, although the overall accuracy of prediction of SR yield without including GPS extracted variables is low. GPS extracted variables, both with and without including SR yields, are particularly important for groundnut, sorghum and millet yield predictions. Finally, cowpea yield prediction benefits particularly from the inclusion of both SR yield and GPS extracted variables. The heterogeneity of the impact of the different combinations of covariates for each crop predictions is difficult to interpret especially since the coefficients are in general not statistically different to each other. As such, the main lesson that we retain here is that combining the subjective measure of yields and the objective covariates is always the most beneficial to improve the accuracy of the predictions. This conclusion is also robust to the use of alternative model performance metrics. This is confirmed in Table B.6 which shows how the inclusion of different covariates impacts the performance as measured by the root mean square of the predictions when we model level yields: we find that for all crops including both SR yields and geospatial variables improve the model performance (reduce the root mean square error) the most. The improvement is marginal although significant when SR is included without geospatial variables, highlighting the fact that geospatial variables are the most potent in improving the predictions. Looking at the base root mean square error across crops, it appears that in average the prediction from cowpea yield in average the best prediction, but that is because the average yield for cowpea is smaller than the other crops and as such small deviations from when squared are amplified.

> 16The GPS extracted variables used the publicly available coordinates which have been scrambled for privacy purposes. As discussed in Michler et al. (2022), the degree to which spatial anonymization introduces mismeasurement is a function of which remote sensing weather product is used in the analysis. Care must be taken in choosing a remote sensing weather product when looking to integrate it with publicly available survey data. As such, the results might vary with other types of weather products.

> 17See Table B.4 for the results for log yields, which do not differ significantly from the levels.

12
We also verified the impact of the inclusion of weights in the covariates by testing it on predictions of millet yields in the 2017 data set. We find that in average, the standard errors of the imputed mean from a model with survey weights was only 0.38% larger than in the case of a model without weights. The bias is also slightly larger as we find than in average, the root mean square error is 0.5% when including weights. As these results seem to be of little practical concern, we believe it will not affect the lessons gleaned from the imputation exercises conducted in this work and we leave changes to the covariates sets that could allow for the inclusion of survey weights<sup>18</sup> for future work.

# **5.1.3 Prediction accuracy by crops**

Figure 5 provides a graphical representation of the distribution of the _R_<sup>2</sup> of the regression of the CC yields on the ML prediction for yields levels predictions,<sup>19</sup> by crop. There appears to be significant heterogeneity in the performance of the ML algorithms across crops: the _R_<sup>2</sup> for cowpea ranges between 0.1 and 0.42 while that of rice ranges between 0.41 and 0.7. The comparison of these crops is a good case and point for what is the most likely candidate explanation for the disparity in ML prediction performance across crops: the rate of intercropping, which refers to the practice of growing multiple crops in the same field simultaneously. In fact plots with cowpea are the highest intercropping rate (0.26) while rice is not on intercropped plots. Moreover the median performance of the ML algorithm is in general increasing with the rate of intercropping if we focus on sorghum, maize and groundnut. The predictions for millet have a higher performance than those of sorghum or maize even though it has a higher intercropping rate, but we can attribute that to the fact that the number of plots of millet is significantly more important. Another factor that likely explains the heterogeneity in ML predictive performance across crops is the degree of commercialization. Rice and groundnut are also cash crops, hence farmers of these crops use units that have more standardized weights. This also explains why SR yields appears at a higher predictive rank for rice and groundnut than millet or maize for example (see Table 5).

# **5.1.4 Training set size**

This section assesses the minimum share of plot observations that can be sub-sampled for crop-cutting measurements while still obtaining a reliable predicted measure of CC yields. The predictive accuracy, measured in terms of _R_<sup>2</sup> (coefficient of determination), of the ML prediction is evaluated for different sizes of the training dataset. The training dataset sizes considered are 10, 25, 33, 50, 67, and 75 percent of the CC measures. This evaluation is performed for each crop individually and for the entire set of crops across 50 different simulations.

The results, depicted in Figure 6, show that the _R_<sup>2</sup> of CC yields on the ML prediction increases as the percentage of the training dataset size grows. However, the marginal gain in accuracy diminishes as the training dataset size increases, particularly for logs imputation.

> 18One way to correct these issues as noted by Quartagno et al. (2019) is to include in the model (i) the weights, (ii) all the domain indicators (i.e., all relevant covariates of the weighted regression), and (iii) their interactions for valid MI inference in general.

> 19See Figure B.1 for results with the log yield predictions.

13
While there is some heterogeneity in results across different crops, overall, conducting crop cutting on half of the plot observations provides reasonably high accuracy for deriving reliable imputed CC yields, both for levels and logs imputations. Beyond one-third (33 percent) of the sample, the gain in accuracy becomes marginal. Therefore, considering the higher costs associated with crop cutting, the decision regarding the sample size depends on the desired level of _R_<sup>2</sup> accuracy needed for the specific application, as well as on the main crops of interest. These implications suggest that collecting crop-cut measurements on a sub-sample of plots, particularly around 50 percent of the total sample, can offer a cost-effective approach while still achieving reliable ML predictions of CC yields. This information can guide decision-making regarding the optimal allocation of resources for data collection and the measurement of crop yields.

# **5.2 Imputation results**

## **5.2.1 within-survey imputation**

In this section we assess the performance of the within-survey imputation procedure by examining the difference of the ML imputed mean with the CC mean. We look at the differences in a test set representing 2/3 of the sample for each crops and we then examine the differences at the national and regional level. In summary, the results of the within imputation show that our within-survey imputation procedure reliably impute means in the test sample: as Table 7 shows, the differences are not statistically significant in the test set. Moreover to ensure that the results are not a result of a random draw of the test set, we repeated the operation for 100 different samples. These results are illustrated on Figure 8 which shows that the distributions of means of the CC and ML overlap. In at least 86% of the times for sorghum and over 94% of the times for the other crops, the ML mean is within the 95% confidence interval of the CC mean in the test set. The good performance of the ML prediction of the mean can be assessed computing the means at the national level (see Table 8) for all crops with 1/3 of the crop-cut sample used as training sample. Computing regional yields at this level is more challenging but this is mostly due to the small sample size<sup>20</sup> at this level. In fact when we perform the exercise with 1/2 of the sample, the accuracy of the ML imputation at the regional level increases (see Table B.5) and more results are statistically not distinguishable from the CC means. Moreover, the imputed mean is almost always closer to the CC mean than the SR means. In many cases the difference between ML and CC mean yields is statistically significant even if negligible in terms of magnitude. This is due to the fact that ML means have, by construction, very small standard errors compared to SR means, as shown in Figure 7.

> 20Given that we only have one year difference between the two survey editions, it may be possible to pool data together and consider it as one sample and conduct a within-survey imputation exercise, for crops with low sample size. We leave this for future research considering that this work aimed to consider cases that fit real data situations.

14
## **5.2.2 survey-to-survey imputation**

The procedure is also tested in a survey-to-survey imputations. CC yields from the 2018 survey sample are used as a test set, with the model trained with the 2017 survey sample. Table 9 summarizes the results of the survey-to-survey imputation exercise, with 100 percent of the 2017 sample used as training sample. We find that except for millet, rice, and groundnut the difference between the mean obtained with the ML model is statistically different from that of the CC means even at the national level. However, even when the difference between the mean of the ML yields and the mean of the CC yields is statistically different, it remains smaller than the difference of the SR in most cases. The statistical difference that we detect may be due to the fact that despite computing the standard errors following the MI procedure, we are getting standard errors that do not account enough for the variability across imputations. This is also visible in Figure 10 which shows the means computed for 100 simulations. Looking at the regional level estimates, we find that in general these differences are even more pronounced.

The relatively low accuracy of the survey-to-survey imputation may be somehow surprising in this framework, given that the 2017 and 2018 surveys are very similar in terms of geographical coverage, representativeness and survey instruments. Nevertheless, there are some important differences in the questionnaires between the two surveys that can explain the relatively low accuracy of the 2017 sample for imputing the 2018 yields (for example, the seeding date, which interacted with rainfall is a top predictor of yields, was not collected in 2018). (Gourlay et al., 2019) find more promising year-to-year yield predictions using CC yields in Uganda. However, their results rely on a panel of households interviewed in two consecutive years, and predictions are even more accurate when plots from the same parcel are sampled. Interestingly, in this framework predicting the logs results in lower accuracy than predicting the levels, and the difference in _R_<sup>2</sup> level and log yields is positive and significant for all crops. Overall, it seems that the survey-to-survey imputation provides a very low accuracy level for food staple crops, while it is higher for market-oriented crops, in particular for rice and maize (although lower than the within-survey imputation).

# **6 Conclusion**

We assess the validity of imputation of an objective measure of crop yields in farm surveys in situations in which they are partially missing for efficiency design and when they are completely missing in a survey round. Partial and complete missingness of crop-cut yields might be due to resource constraints and logistical limitations in case certain areas are inaccessible or the presence of enumerators must be reduced in terms of time because of security issues.

The data requirements for the validation process reveal several important findings. First, self-reported (SR) yields are considered significant predictors of crop-cut yields. However, the results indicate that integrated geo-spatial variables make a greater contribution to the accuracy of machine learning (ML) predictions. This suggests that factors such as geographical information, climate data, or other spatial variables play a crucial role in accurately predicting crop yields. Furthermore, the accuracy of ML predictions varies across different crops, indicating heterogeneity. This points to the need for reliable non-standard units when dealing with 15
crops that are not commercially traded and more accurate yield measurement for intercropped plots. Additionally, the measurement of intercropped crop yields is found to be important in improving the accuracy of ML predictions. Finally, our results suggest that collecting crop-cut measurements on a sub-sample of plots, particularly around 33 percent of the total sample, can offer a cost-effective approach while still achieving reliable ML predictions of CC yields. This information can guide decision-making regarding the optimal allocation of resources for data collection and the measurement of crop yields.

In terms of validation, ML yields are found to be valid in the within-survey imputation framework, even when using a subsample of the crop-cut data. This implies that ML predictions can effectively replace missing values within the same survey. However, in the survey-to-survey imputation framework, ML yields are less reliable, although they still generally outperform SR yields in terms of accuracy. This suggests that ML predictions might not be as robust when extrapolating or imputing values across different survey rounds. Moreover, in both the withinsurvey imputation and survey-to-survey imputation frameworks, the disaggregated (regional) statistics results are not robust. This indicates that obtaining reliable regional-level statistics from the ML predictions might pose challenges and further investigation or refinement of the methodology may be necessary. Further investigation is also needed to improve the predictions of the tails of the distribution of crop yields, as targeting farmers located in these sections of the distribution is of particular importance for agricultural policy.

16
# **References**

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- Gourlay, S., Kilic, T., and Lobell, D. B. (2019). A new spin on an old debate: Errors in farmerreported production and their implications for inverse scale - productivity relationship in uganda. _Journal of Development Economics_ , 141:102376.

- Little, R. and Rubin, D. (1987). _Statistical Analysis With Missing Data_ . Wiley Series in Probability and Statistics. Wiley.

- Michler, J. D., Josephson, A., Kilic, T., and Murray, S. (2022). Privacy protection, measurement error, and the integration of remote sensing and socioeconomic survey data. _Journal of Development Economics_ , 158:102927.

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- Quartagno, M., Carpenter, J. R., and Goldstein, H. (2019). Multiple Imputation with Survey Weights: A Multilevel Approach. _Journal of Survey Statistics and Methodology_ , 8(5):965– 989.

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- Wollburg, P., Tiberti, M., and Zezza, A. (2021). Recall length and measurement error in agricultural surveys. _Food Policy_ , 100:102003.

- Yacoubou Djima, I. and Kilic, T. (2024). Attenuating measurement errors in agricultural productivity analysis by combining objective and self-reported survey data. _Journal of Development Economics_ , 168:103249.

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# **Tables**

**Table 1:** Data situations

|Type|Extent of missin<br>crop-cut data|g<br>Typical survey situation|Imputation model|
|---|---|---|---|
|A|Partially<br>missing|(i) LSMS-ISA with SR on<br>all plots, CC on subsample<br>within the same survey|Within survey<br>imputations|
|||(ii) LSMS-ISA with SR on<br>all plots CC on subsample<br>CC with plot boundaries|Satelitte<br>crop yield maps|
|B|Completely<br>missing|LSMS-ISA with SR on<br>all plots|Survey to Survey<br>with SR yields|

**Table 2:** Number of observations by crop for each wave

|||2017|2018|
|---|---|---|---|
|Millet|1607|5199 (76%)|1615 (24%)|
|Sorghum|1155|3591 (63%)|2128 (37%)|
|Rice|4130|2990 (72%)|1140 (28%)|
|Maize|5777|3668 (63%)|2109 (37%)|
|Cowpea|1370|918 (67%)|452 (33%)|
|Groundnut|6401|4530 (71%)|1871 (29%)|

19
**Table 3:** Weighted summary statistics of covariates by sample type for 2017 campaign.

|||Mean|Sd|Min|Median|Max|N|
|---|---|---|---|---|---|---|---|
|**Self-reported Yi**|**elds (kg/ha)**|||||||
||_X−cc_|864.85|1072.22|0.00|552.19|7111.11|3592|
|**Millet**|_Xcc_|830.30|1001.05|0.00|550.00|7142.86|1607|
||_X−cc −Xcc_|34_._549||||||
||_X−cc_|654.49|960.22|0.00|394.76|8235.29|2436|
|**Sorghum**|_Xcc_|719.22|1050.64|0.00|430.15|8125.00|1155|
||_X−cc −Xcc_|_−_64_._738||||||
||_X−cc_|2208.12|2926.16|0.00|1291.97|20851.06|2291|
|**Rice**|_Xcc_|1434.14|1941.22|0.00|791.65|17500.00|699|
||_X−cc −Xcc_|773_._972<sup>_∗∗∗_</sup>||||||
||_X−cc_|1175.39|1594.14|0.00|760.43|20930.23|2506|
|**Maize**|_Xcc_|1214.71|1686.57|0.00|769.23|20242.42|1162|
||_X−cc −Xcc_|_−_39_._322||||||
||_X−cc_|428.54|555.76|0.00|238.10|2994.01|576|
|**Cowpea**|_Xcc_<br>_X−cc −Xcc_|472.67<br>_−_44_._128|552.33|0.00|312.39|2727.27|342|
||_X−cc_|967.94|962.66|0.00|666.67|5386.00|3230|
|**Groundnut**|_Xcc_|975.78|970.35|0.00|686.46|5312.50|1300|
||_X−cc −Xcc_|_−_7_._843||||||
|**Plot area (ha)**||||||||
||_X−cc_|2.43|2.51|0.02|1.59|28.86|3592|
|**Millet**|_Xcc_|2.35|2.64|0.01|1.55|30.02|1607|
||_X−cc −Xcc_|0_._079||||||
||_X−cc_|2.62|2.48|0.02|1.94|17.83|2436|
|**Sorghum**|_Xcc_|2.40|2.31|0.03|1.82|17.51|1155|
||_X−cc −Xcc_|0_._216<sup>_∗_</sup>||||||
||_X−cc_|1.00|1.35|0.01|0.58|35.00|2291|
|**Rice**|_Xcc_|0.95|1.05|0.00|0.59|9.86|699|
||_X−cc −Xcc_|0_._044||||||
||_X−cc_|2.08|2.12|0.01|1.43|16.16|2506|
|**Maize**|_Xcc_|1.88|1.89|0.01|1.29|14.04|1162|
||_X−cc −Xcc_|0_._205<sup>_∗∗∗_</sup>||||||
||_X−cc_|1.35|1.82|0.01|0.60|13.90|576|
|**Cowpea**|_Xcc_|1.30|2.05|0.01|0.63|14.28|342|
||_X−cc −Xcc_|0_._049||||||
||_X−cc_|0.97|1.59|0.01|0.46|15.99|3230|
|**Groundnut**|_Xcc_|0.90|1.36|0.02|0.46|13.35|1300|
||_X−cc −Xcc_|0_._071||||||

_Notes:_ Number of observations may differ by variable (missingness) depending on the level (plot or household).<sup>_†_</sup> denotes a dummy variable. Difference is assessed with t-statistics based on design-adjusted standard errors corrected for clustering at the enumeration area. Statistical significance levels: *p _<_ 0.1; **p _<_ 0.05; ***p _<_ 0.01.

20
**Table 4:** Weighted summary statistics of covariates by sample type for 2018 campaign.

|||Mean|Sd|Min|Median|Max|N|
|---|---|---|---|---|---|---|---|
|**Self-reported Yi**|**elds (kg/ha)**|||||||
||_X−cc_|791.81|639.81|0.00|702.76|7052.24|1096|
|**Millet**|_Xcc_|829.18|651.81|0.00|695.98|6002.40|519|
||_X−cc −Xcc _|_−_37_._368||||||
||_X−cc_|933.42|950.33|0.00|725.57|8100.00|1435|
|**Sorghum**|_Xcc_|888.75|896.81|0.00|700.98|8130.08|693|
||_X−cc −Xcc_|44_._664||||||
||_X−cc_|3205.33|3475.40|0.00|2100.00|21000.00|899|
|**Rice**|_Xcc_|2963.22|3459.49|0.00|2035.28|19983.21|241|
||_X−cc −Xcc_|242_._103||||||
||_X−cc_|1845.10|1665.25|0.00|1443.02|18000.00|1465|
|**Maize**|_Xcc_|1890.11|1792.05|0.00|1428.57|18646.90|644|
||_X−cc −Xcc _|_−_45_._007||||||
||_X−cc_|535.53|454.56|0.00|427.38|2711.86|265|
|**Cowpea**|_Xcc_|553.83|484.77|0.00|434.66|2500.00|187|
||_X−cc −Xcc _|_−_18_._296||||||
||_X−cc_|1053.99|918.97|0.00|769.23|5378.57|1317|
|**Groundnut**|_Xcc_|1020.61|806.37|0.00|769.23|4911.59|554|
||_X−cc −Xcc_|33_._379||||||
|**Plot area (ha)**||||||||
||_X−cc_|2.52|2.85|0.05|1.84|44.09|1096|
|**Millet**|_Xcc_|2.16|2.18|0.07|1.50|21.01|519|
||_X−cc −Xcc_|0_._366<sup>_∗∗∗_</sup>||||||
||_X−cc_|1.79|2.26|0.02|1.18|52.05|1435|
|**Sorghum**|_Xcc_|1.75|1.65|0.03|1.31|13.61|693|
||_X−cc −Xcc_|0_._038||||||
||_X−cc_|1.21|1.59|0.01|0.76|30.00|899|
|**Rice**|_Xcc_|1.51|1.91|0.01|0.63|10.00|241|
||_X−cc −Xcc_|_−_0_._299||||||
||_X−cc_|1.53|1.60|0.01|1.07|22.97|1465|
|**Maize**|_Xcc_|1.48|1.59|0.02|1.00|17.80|644|
||_X−cc −Xcc_|0_._051||||||
||_X−cc_|0.74|1.08|0.00|0.48|8.01|265|
|**Cowpea**|_Xcc_|0.84|1.72|0.02|0.40|14.63|187|
||_X−cc −Xcc_|_−_0_._097||||||
||_X−cc_|0.72|0.90|0.00|0.49|14.18|1317|
|**Groundnut**|_Xcc_|0.77|1.08|0.03|0.48|9.48|554|
||_X−cc −Xcc_|_−_0_._046||||||

_Notes:_ Number of observations may differ by variable (missingness) depending on the level (plot or household).<sup>_†_</sup> denotes a dummy variable. Difference is assessed with t-statistics based on design-adjusted standard errors corrected for clustering at the enumeration area. Statistical significance levels: *p _<_ 0.1; **p _<_ 0.05; ***p _<_ 0.01.

21
|**Sorghum**<br>Seeding date x wettest quarter avg<br>Avg total rainfall in wettest quarter<br>Avg annual total rainfall<br>SR Yield<br>Annual Precipitation<br>HH Distance to admin center of District of Residence<br>Seeding date x wettest quarter<br>Seeding date wettest quarter average start<br>Slope<br>HH Distance to Nearest Population Center<br>**Maize**<br>Elevation<br>Seeding date x rain fall planting season<br>Rain fall during planting season<br>Long-term max dekadal NDVI value in primary growing season<br>Annual Mean Temperature<br>Long-term avg NDVI value in primary growing season<br>Avg annual total rainfall<br>HH Distance to admin center of District of Residence<br>Seeding date x wettest quarter avg<br>SR Yield<br>**Groundnut**<br>Annual Precipitation<br>Long-term avg NDVI value in primary growing season<br>SR Yield<br>Seeding date x rain fall planting season<br>Avg annual total rainfall<br>HH Distance to admin center of District of Residence<br>Rain fall during planting season<br>HH Distance to Nearest Population Center<br>Seeding date x wettest quarter avg<br>Household weights|
|---|
|e x wettest quarter avg<br>ainfall in wettest quarter<br> total rainfall<br>e to admin center of District of Residence<br>e to Nearest Population Center<br>cipitation<br>weights<br>e x rain fall planting season<br>e to Nearest Border Crossing<br>max dekadal NDVI value in primary growing season<br>weights<br>e to Nearest Border Crossing<br>max dekadal NDVI value in primary growing season<br><br>avg NDVI value in primary growing season<br>e x rain fall planting season<br>cipitation<br>e to Nearest Population Center<br>e to admin center of District of Residence<br>e to Nearest Border Crossing<br>weights<br>ercentage<br>e 41-70<br>avg NDVI value in primary growing season<br>e 0-5|
|t<br>r<br>l <br>c<br>c<br>e<br> <br>t<br>c<br> <br> <br>c<br> <br>ts<br> <br>t<br>e<br>c<br>c<br>c<br> <br>p<br>g<br> <br>g|
|a<br>l <br>a<br>n<br>n<br>r<br>d <br>a<br>n<br>m<br>d <br>n<br>m<br>l<br>m<br>a<br><br>r<br>n<br>n<br>n<br>d <br>t <br> a<br>m<br> a|
|g d<br>ta<br>nnu<br>sta<br>sta<br>l P<br>hol<br>g d<br>sta<br>er<br>hol<br>eld<br>sta<br>er<br> sa<br>er<br>g d<br>ion<br>l P<br>**ea**<br>eld<br>sta<br>sta<br>sta<br>hol<br>lo<br>les <br>er<br>les|
|**et**<br>n<br>to<br>a<br>i<br>i<br>a<br>e<br>n<br>i<br>-t<br>e<br><br>i<br>i<br>-t<br>ss<br>-t<br>n<br>t<br>a<br>**p**<br>i<br>i<br>i<br><br>i<br>e<br> p<br>a<br>-t<br>a|
|**Mill**<br>Seedi<br>Avg <br>Avg <br>HH D<br>HH D<br>Annu<br>Hous<br>Seedi<br>HH D<br>Long<br>**Rice**<br>Hous<br>Slope<br>SR Y<br>HH D<br>Long<br>Exce<br>Long<br>Seedi<br>Eleva<br>Annu<br>**Cow**<br>SR Y<br>HH D<br>HH D<br>Slope<br>HH D<br>Hous<br>Crop <br>of m<br>Long<br>of m|

22
**Table 6:** Difference in terms of _R_<sup>2</sup> of the levels CC regressed on the ML predictions for different combinations of covariates

|||||Levels||||
|---|---|---|---|---|---|---|---|
||All crops|Millet|Sorghum|Rice|Maize|Cowpea|Groundnut|
|SR in W, GPS not in W|0.052<sup>_∗∗∗_</sup>|0.047<sup>_∗∗∗_</sup>|0.095<sup>_∗∗∗_</sup>|0.033|0.012|0.072<sup>_∗∗∗_</sup>|0.055<sup>_∗∗∗_</sup>|
||(0.014)|(0.014)|(0.018)|(0.032)|(0.016)|(0.024)|(0.012)|
|SR not in W, GPS in W|0.184<sup>_∗∗∗_</sup>|0.221<sup>_∗∗∗_</sup>|0.234<sup>_∗∗∗_</sup>|0.161<sup>_∗∗∗_</sup>|0.106<sup>_∗∗∗_</sup>|0.103<sup>_∗∗∗_</sup>|0.280<sup>_∗∗∗_</sup>|
||(0.014)|(0.014)|(0.018)|(0.032)|(0.016)|(0.024)|(0.012)|
|SR,GPS in W|0.206<sup>_∗∗∗_</sup>|0.223<sup>_∗∗∗_</sup>|0.248<sup>_∗∗∗_</sup>|0.196<sup>_∗∗∗_</sup>|0.112<sup>_∗∗∗_</sup>|0.167<sup>_∗∗∗_</sup>|0.290<sup>_∗∗∗_</sup>|
||(0.014)|(0.014)|(0.018)|(0.032)|(0.016)|(0.024)|(0.012)|
|Constant|0.277<sup>_∗∗∗_</sup>|0.277<sup>_∗∗∗_</sup>|0.132<sup>_∗∗∗_</sup>|0.342<sup>_∗∗∗_</sup>|0.427<sup>_∗∗∗_</sup>|0.177<sup>_∗∗∗_</sup>|0.309<sup>_∗∗∗_</sup>|
||(0.010)|(0.010)|(0.013)|(0.023)|(0.011)|(0.017)|(0.008)|
|Obs|600|100|100|100|100|100|100|
|Adj. R<sup>2</sup>|0.350|0.797|0.716|0.334|0.448|0.330|0.905|

_Notes:_ The reference group is covariate without SR and GPS extracted. The constant shows the mean average _R_<sup>2</sup> for the reference group Significance levels: *p _<_ 0.1; **p _<_ 0.05; ***p _<_ 0.01

**Table 7:** CC mean yields and differences with ML and SR yields in the test set by crops and by survey year.

||Millet|Sorghum|Rice|Maize|Cowpea|Groundnut|
|---|---|---|---|---|---|---|
|||||2017|||
|CC|936.7|1049.0|2576.1|1685.0|332.5|1841.2|
|ML - CC|-7.1|22.6|-111.6|-0.4|-7.7|185.2|
|SR - CC|-101.0|-284.6<sup>_∗∗∗_</sup>|-1164.8<sup>_∗∗∗_</sup>|-429.6<sup>_∗∗∗_</sup>|203.9<sup>_∗_</sup>|-909.0<sup>_∗∗∗_</sup>|
|N|1072|773|465|775|228|869|
|||||2018|||
|CC|931.0|1182.1|3353.0|1914.1|577.4|1997.2|
|ML - CC|6.1|-61.7<sup>_∗_</sup>|829.2<sup>_∗∗_</sup>|-47.6|-121.0<sup>_∗∗_</sup>|178.0<sup>_∗_</sup>|
|SR - CC|-97.2|-296.6<sup>_∗∗∗_</sup>|-427.4|6.0|-5.8|-928.0<sup>_∗∗∗_</sup>|
|N|346|458|160|428|123|371|

_Notes:_ The training set represent 1/3 of the total sample size. The mean CC yield and differences with ML and SR yields are computed using survey design weights. Statistical significance are assessed using standard errors clustered at the enumeration area level. In the case of the ML, the standard errors used for statistical significance tests account for the between imputations variance computed with 100 simulations. Significance levels: *p _<_ 0.1; **p _<_ 0.05; ***p _<_ 0.01 23
**Table 8:** CC mean yields and differences with ML and SR yields by crops, in the overall sample and by region for 2017.

||Millet|Sorghum|Rice|Maize|Cowpea|Groundnut|
|---|---|---|---|---|---|---|
|||||National|||
|CC<br>ML - CC|934.3<br>2.4|1045.5<br>-6.4|2542.8<br>95.5|1684.7<br>-28.8|320.5<br>-6.8|1866.3<br>108.3|
|SR - CC|-104.0<sup>_∗_</sup>|-326.2<sup>_∗∗∗_</sup>|-1108.7<sup>_∗∗∗_</sup>|-470.0<sup>_∗∗∗_</sup>|152.2|-890.5<sup>_∗∗∗_</sup>|
|N|1607|1155|699|1162|342|1300|
|||||Kayes|||
|CC|548.0|754.7|4114.4|774.9|216.3|2090.8|
|ML - CC|198.8<sup>_∗∗∗_</sup>|155.2<sup>_∗∗∗_</sup>|22.4|336.5<sup>_∗∗∗_</sup>|62.7<sup>_∗_</sup>|47.1|
|SR - CC|619.1|-196.2<sup>_∗∗_</sup>|-3098.6<sup>_∗_</sup>|128.1|113.8|-753.3<sup>_∗∗∗_</sup>|
|N|64|327|26|284|47|594|
|||||Koulikoro|||
|CC|1024.3|1057.1|1523.0|1650.5|288.6|1398.4|
|ML - CC|-44.6<sup>_∗_</sup>|-4.9|267.4<sup>_∗_</sup>|24.2|-5.8|510.0<sup>_∗∗_</sup>|
|SR - CC|-400.2<sup>_∗∗∗_</sup>|-483.5<sup>_∗∗∗_</sup>|-330.5|-712.5<sup>_∗∗∗_</sup>|342.3<sup>_∗_</sup>|-696.8<sup>_∗∗_</sup>|
|N|276|305|110|247|58|235|
|||||Sikasso|||
|CC|832.8|1079.5|2299.3|2141.8|330.6|1518.6|
|ML - CC|-97.8<sup>_∗∗∗_</sup>|33.4|98.8|-222.3<sup>_∗∗∗_</sup>|-7.6|255.4<sup>_∗∗∗_</sup>|
|SR - CC|-121.2|-184.1|-1473.5<sup>_∗∗∗_</sup>|-548.2<sup>_∗∗∗_</sup>|278.3<sup>_∗∗∗_</sup>|-640.7<sup>_∗∗∗_</sup>|
|N|166|222|156|534|79|239|
|||||Segou|||
|CC|1132.3|1438.9|5786.8|2196.4|433.6|2566.8|
|ML - CC|-103.3<sup>_∗∗∗_</sup>|-212.5<sup>_∗∗∗_</sup>|-526.6|-256.6<sup>_∗∗_</sup>|-67.8<sup>_∗∗∗_</sup>|-559.9<sup>_∗∗∗_</sup>|
|SR - CC|-142.5|-527.4<sup>_∗∗∗_</sup>|-4268.2<sup>_∗∗_</sup>|-1144.7<sup>_∗∗∗_</sup>|14.0|-1837.8<sup>_∗∗∗_</sup>|
|N|485|243|40|93|68|168|
|||||Mopti|||
|CC|862.0|839.3|1760.5|768.3|315.9|1711.1|
|ML - CC|71.2<sup>_∗∗∗_</sup>|-25.5|585.1<sup>_∗_</sup>|-0.0|2.9|108.7|
|SR - CC|-54.2|-37.0|-376.4|-108.7|-11.4|-1142.2<sup>_∗∗∗_</sup>|
|N|594|54|154|4|88|63|

_Notes:_ The training set represent 1/3 of the total sample size. The mean CC yield and differences with ML and SR yields are computed using survey design weights. Statistical significance are assessed using standard errors clustered at the enumeration area level. In the case of the ML, the standard errors used for statistical significance tests account for the between imputations variance computed with 10 simulations. Significance levels: *p _<_ 0.1; **p _<_ 0.05; ***p _<_ 0.01 24
**Table 9:** Survey to survey imputation results: CC mean yields and differences with ML and SR yields by crops, in the overall sample and by region for 2018..

||Millet|Sorghum|Rice|Maize|Cowpea|Groundnut|
|---|---|---|---|---|---|---|
|||||National|||
|CC<br>ML - CC|928.2<br>-54.7|1167.1<br>-151.7<sup>_∗∗∗_</sup>|3661.7<br>-297.3|1898.4<br>-229.1<sup>_∗∗∗_</sup>|534.6<br>-122.4<sup>_∗∗_</sup>|2033.8<br>103.3|
|SR - CC|-99.0|-278.4<sup>_∗∗∗_</sup>|-698.4|-8.2|19.3|-1013.2<sup>_∗∗∗_</sup>|
|N|519|693|241|644|187|554|
|||||Kayes|||
|CC|949.1|1129.8|8293.7|1201.2|580.8|2603.2|
|ML - CC|-282.0<sup>_∗_</sup>|-282.4<sup>_∗∗∗_</sup>|-2823.2|-245.7<sup>_∗∗∗_</sup>|-218.5<sup>_∗∗_</sup>|-436.6<sup>_∗∗∗_</sup>|
|SR - CC|-18.6|-301.6<sup>_∗∗∗_</sup>|-5520.2<sup>_∗∗_</sup>|320.0|175.4|-1384.6<sup>_∗∗∗_</sup>|
|N|40|257|9|206|31|179|
|||||Koulikoro|||
|CC|1035.8|1214.7|2360.7|1931.8|746.4|1717.9|
|ML - CC|-110.9|-154.6<sup>_∗∗_</sup>|905.8|-215.2|-249.6<sup>_∗∗_</sup>|204.4|
|SR - CC|-358.5<sup>_∗∗∗_</sup>|-260.0<sup>_∗_</sup>|-713.7|-42.2|-145.4|-862.3<sup>_∗∗∗_</sup>|
|N|154|163|37|158|44|138|
|||||Sikasso|||
|CC|1018.4|1246.2|2881.2|2383.5|473.5|1667.7|
|ML - CC|-133.8<sup>_∗_</sup>|-222.0<sup>_∗_</sup>|-330.9|-212.7<sup>_∗∗_</sup>|-110.2|188.0|
|SR - CC|-16.9|-338.0<sup>_∗∗∗_</sup>|-1152.0<sup>_∗_</sup>|-95.8|-47.8|-351.1|
|N|107|109|53|225|41|94|
|||||Segou|||
|CC|1106.4|1308.4|7329.0|2203.7|381.0|2116.1|
|ML - CC|-52.8|-7.9|-2665.6<sup>_∗∗_</sup>|-353.6<sup>_∗∗_</sup>|56.6|493.1<sup>_∗∗∗_</sup>|
|SR - CC|-285.8<sup>_∗∗∗_</sup>|-506.9<sup>_∗∗∗_</sup>|-4928.6<sup>_∗∗∗_</sup>|-686.6<sup>_∗∗∗_</sup>|145.7<sup>_∗_</sup>|-1330.5<sup>_∗∗∗_</sup>|
|N|110|123|23|53|42|122|
|||||Mopti|||
|CC|639.7|780.8|2923.3|786.7|460.1|1469.8|
|ML - CC|195.1<sup>_∗_</sup>|77.4|-235.0|289.2|-90.6|93.9|
|SR - CC|227.7<sup>_∗_</sup>|317.8|955.7|459.4|70.8|-525.3<sup>_∗_</sup>|
|N|70|21|40|2|19|21|

_Notes:_ The training set is the EACI 2017. The mean CC yield and differences with ML and SR yields are computed using survey design weights. Statistical significance are assessed using standard errors clustered at the enumeration area level. In the case of the ML, the standard errors used for statistical significance tests account for the between imputations variance computed with 100 simulations. Significance levels: *p _<_ 0.1; **p _<_ 0.05; ***p _<_ 0.01 25
# **Figures**

**Figure 1:** SR over area quintile for 2017 (left) and 2018 (right) wave for Millet (top), Sorghum (middle), rice (bottom)

<!-- Start of picture text --> 1 2 3 4 5 1 2 3 4 5<br>1 2 3 4 5 1 2 3 4 5<br>1 2 3 4 5 1 2 3 4 5<br>800<br>200<br>600<br>400<br>0<br>200<br>(Kg/Ha) 0 (Kg/Ha) −200<br>−200<br>−400 −400<br>−600<br>400<br>200<br>200<br>0<br>0<br>(Kg/Ha) −200 (Kg/Ha)<br>−200<br>−400<br>−400<br>−600<br>−600<br>0<br>1000<br>−500<br>−1000 0<br>(Kg/Ha) (Kg/Ha) −1000<br>−1500<br>−2000<br>−2000<br>−2500 −3000<br><!-- End of picture text --> 26
**Figure 2:** SR over area quintile for 2017 (left) and 2018 (right) wave for Maize (top), Cowpea (middle), Groundnut (bottom)

<!-- Start of picture text --> 1 2 3 4 5 1 2 3 4 5<br>1 2 3 4 5 1 2 3 4 5<br>1 2 3 4 5 1 2 3 4 5<br>500 600<br>400<br>0 200<br>(Kg/Ha) (Kg/Ha) 0<br>−500<br>−200<br>−1000 −400<br>−600<br>6000<br>600<br>5000<br>4000 400<br>3000<br>(Kg/Ha) (Kg/Ha)<br>200<br>2000<br>1000 0<br>0<br>0<br>0<br>−500<br>−1000 −1000<br>(Kg/Ha) (Kg/Ha)<br>−1500<br>−2000<br>−2000<br>−3000 −2500<br><!-- End of picture text --> 27
**Figure 3:** Random forest importance for the top 15 most important variables for ML prediction of levels of Rice. _Notes:_ 3/4 of the crop-cut sample is used. 5 validation cross-fold splits are used.

<!-- Start of picture text --> Population Center<br>rict of Residence<br>g planting season<br>rter average start<br>ean Temperature<br>nual Precipitation<br>Elevation<br>l planting season<br>y growing season<br>Excess salts<br>y growing season<br>Border Crossing<br>SR Yield<br>Slope<br>ousehold weights<br>0e+00 2e+08 4e+08 6e+08 8e+08<br><!-- End of picture text --> 28
**Figure 4:** Random forest importance for the top 15 most important variables for ML prediction of logs of Rice. _Notes:_ 3/4 of the crop-cut sample is used. 5 validation cross-fold splits are used.

<!-- Start of picture text --> rict of Residence<br>Border Crossing<br>g planting season<br>Welfare index<br>y growing season<br>vailability to roots<br>y growing season<br>l planting season<br>Elevation<br>nual Precipitation<br>n wettest quarter<br>ettest quarter avg<br>ousehold weights<br>nnual total rainfall<br>SR Yield<br>0 500 1000 1500<br><!-- End of picture text --> 29
**Figure 5:** _R_<sup>2</sup> of CC regressed again the ML prediction for each crop. _Notes:_ The model predicts yields levels. The training sample is 3/4 of the 2017 sample.

<!-- Start of picture text --> Cowpea Rice Sorghum Maize Groundnut Millet<br>0.7<br>0.6<br>0.5<br>0.4<br>0.3<br>0.2<br>0.1<br><!-- End of picture text --> 30
**Figure 6:** _R_<sup>2</sup> of CC regressed again the ML prediction for each crop and overall. _Notes:_ The black curve shows the overall average. The model includes both SR and GPS extracted vars. By increasing order of sample size: Purple is for cowpea, blue for rice, green for sorghum, sky blue for maize, yellow for groundnut and red for millet.

<!-- Start of picture text --> 0.1 0.2 0.3 0.4 0.5 0.6 0.7<br>Training set percent<br>0.6<br>0.5<br>0.4<br>0.3<br>R squared<br>0.2<br>0.1<br><!-- End of picture text --> 31
**Figure 7:** crop-cut (red), machine-learning (green) and, self-reported (blue) yield means at the national and regional levels in 2017.

<!-- Start of picture text --> Millet Sorghum<br>National National<br>Kayes Kayes<br>Koulikoro Koulikoro<br>Sikasso Sikasso<br>Segou Segou<br>Mopti Mopti<br>0 500 1000 1500 0 500 1000 1500<br>Rice Maize<br>National National<br>Kayes Kayes<br>Koulikoro Koulikoro<br>Sikasso Sikasso<br>Segou Segou<br>Mopti Mopti<br>0 2000 4000 6000 0 500 1000 1500 2000<br>Cowpea Groundnut<br>National National<br>Kayes Kayes<br>Koulikoro Koulikoro<br>Sikasso Sikasso<br>Segou Segou<br>Mopti Mopti<br>0 200 400 600 800 0 1000 2000<br><!-- End of picture text --> 32
**Figure 8:** Distribution of the means of the CC (red) and ML (blue) in the test sample for 100 simulations

<!-- Start of picture text --> Millet<br>900 950 1000<br>Rice<br>2000 2500 3000<br>Cowpea<br>250 300 350 400<br>0.04<br>0.02<br>0.00<br>0.002<br>0.000<br>0.04<br>0.02<br>0.00<br><!-- End of picture text --> <!-- Start of picture text --> Sorghum<br>950 1000 1050 1100 1150 1200<br>0.020<br>0.010<br>0.000<br><!-- End of picture text --> <!-- Start of picture text --> Maize<br>1500 1600 1700 1800 1900<br>0.010<br>0.000<br><!-- End of picture text --> <!-- Start of picture text --> Groundnut<br>1700 1800 1900 2000 2100 2200<br>0.012<br>0.006<br>0.000<br><!-- End of picture text --> 33
**Figure 9:** Survey to survey imputation results: crop-cut (red), machine-learning (green) and, self-reported (blue) yield means at the national and regional levels in 2018.

<!-- Start of picture text --> Millet Sorghum<br>National National<br>Kayes Kayes<br>Koulikoro Koulikoro<br>Sikasso Sikasso<br>Segou Segou<br>Mopti Mopti<br>0 300 600 900 1200 0 500 1000<br>Rice Maize<br>National National<br>Kayes Kayes<br>Koulikoro Koulikoro<br>Sikasso Sikasso<br>Segou Segou<br>Mopti Mopti<br>0 3000 6000 9000 0 500 1000 1500 2000 2500<br>Cowpea Groundnut<br>National National<br>Kayes Kayes<br>Koulikoro Koulikoro<br>Sikasso Sikasso<br>Segou Segou<br>Mopti Mopti<br>0 250 500 750 0 1000 2000<br><!-- End of picture text --> 34
**Figure 10:** Distribution of the means of the ML (blue) in the test sample (2018) for 100 simulations. The red vertical line shows the mean CC and the red horizontal line shows the 95% confidence interval in the 2018 sample

<!-- Start of picture text --> Millet Sorghum<br>850 900 950 1000 1000 1050 1100 1150 1200<br>x x<br>Rice Maize<br>3000 3500 4000 1700 1800 1900 2000<br>x x<br>0.20<br>0.20<br>0.10<br>0.10<br>0.00 0.00<br>0.008 0.12<br>0.08<br>0.004<br>0.04<br>0.000 0.00<br><!-- End of picture text --> <!-- Start of picture text --> Cowpea<br>400 450 500 550 600<br>x<br>0.12<br>0.08<br>0.04<br>0.00<br><!-- End of picture text --> <!-- Start of picture text --> Groundnut<br>1850 1900 1950 2000 2050 2100 2150 2200<br>x<br>0.06<br>0.04<br>0.02<br>0.00<br><!-- End of picture text --> 35