Fertilizer profitability for smallholder maize farmers in Tanzania: A spatially-explicit ex ante analysis.

We present an easily calibrated spatial modeling framework for estimating location-specific fertilizer responses, using smallholder maize farming in Tanzania as a case study. By incorporating spatially varying input and output prices, we predict the expected profitability for a location-specific smallholder farmer. A stochastic rainfall component of the model allows us to quantify the uncertainty around expected economic returns. The resulting mapped estimates of expected profitability and uncertainty are good predictors of actual smallholder fertilizer usage in nationally representative household survey data. The integration of agronomic and economic information in our framework makes it a powerful tool for spatially explicit targeting of agricultural technologies and complementary investments, as well as estimating returns to investments at multiple scales.

Introduction

Smallholder farming systems of sub-Saharan Africa are characterized by persistently low productivity levels. While there has beenpan> some growth in recenpan>t years, most of tpan> class="Disease">his has come from area expansion rather than yield gains, and average yield gaps remain about 80% [1]. Increasing mineral fertilizer application is generally accepted as a fundamental component of strategies to address this productivity gap [2]. But levels of fertilizer usage, and application levels by those who do use fertilizer, generally remain low across the region [3].

Why are fertilizer usage levels so low? A rich empirical literature has developed in recent years, which emphasizes three key conpan>straints:—agronpan>omic responpan>ses to fertilizer are oftenpan> much lower in farmers’ fields thanpan> onpan> researcher-manpan>aged trials, anpan>d such responpan>ses are substanpan>tially variable over geograppan> class="Disease">hic space [4-8]. Low and variable agronomic returns translate into low and variable economic returns once considering the local farm-gate crop and fertilizer prices. A number of empirical studies document such fertilizer profitability patterns for maize farmers in SSA [9-15]. (See [16] for a recent review of over 20 studies estimating the profitability of applying inorganic fertilizer on maize in various African locations.) Fourth, the stochastic nature of agricultural production in the absence of insurance markets means that small farmers face high variability of expected returns [17]. Given risk averseness, such uncertain returns may represent powerful disincentives to invest even where the expected returns are relatively high [17-19].

But while profitability and risk are longstanding components of agricultural economists’ evaluations of this question, there has been a dearth of planning and targeting frameworks for fertilizer that integrate biophysical responses with information about profitability, crop management and riskiness of returns(although there have been a number of very important investments in spatially explicit soils information—e.g. the Tanzanian Soil Information System TanSIS—which could inform such integrative frameworks). This is problematic because without such frameworks governments and private sector actors may struggle to identify optimal areas to focus market development activities—i.e., areas where farmers will likely face the most substantial gains to fertilizer investments—or to coordinate complementary investments—e.g., promoting fertilizer alongside crop insurance or other risk-reducing financial instruments. Furthermore, the fact that locally optimal fertilizer recommendations for any particular crop may vary considerably across locations argues for planning frameworks that allow for spatial variation in agronomic responses [20].

The goal of this paper is to present a spatially explicit framework for evaluating the likely economic and agronomic returns to fertilizer investments by smallholder farmers (and the uncertainty around those returns). We use data from smallholder maize farmers in Tanzania to parameterize an empirical model, and then implement that model within a spatially explicit environment that takes account of the spatial distributions of soil and rainfall characteristics, farmers and farmland, and input and output prices. Tanzania is a useful case study because it is emblematic in many ways of the broader adoption issues in the region. Recent nationally representative data indicate that only 15% of smallholder farmers use fertilizer, at an average rate of <70 kg/ha (authors’ calculations from the 2008/09, 2010/11 and 2012/13 waves of the Tanzanian LSMS-ISA surveys). Considerable efforts have been made by the Tanzanian government to stimulate demand and facilitate access to fertilizers, including the National Agricultural Input Voucher Scheme (NAIVS), which provided fertilizer at subsidized rates between 2008/9 and 2013/14. One of the goals of NAIVS was to facilitate a relatively low-risk learning opportunity around fertilizer for farmers, which was expected to translate to eventual increases in market demand [21]. Understanding and planning for such demand will depend in part on better tools for estimating the economic returns to fertilizer at market prices.

We show that there is substantial variation in local yield responses and that after incorporating local price ratios for maize anpan>d pan> class="Chemical">nitrogen fertilizer, even larger variability in economic returns over space. We show that such spatial variability in returns is a useful predictor of actual farmer fertilizer usage. Furthermore, the role of stochastic rainfall is similarly highly variable across the country, varying in ways that differ from the distribution of expected profitability. Furthermore, we show that the returns to locally-optimized fertilizer recommendations (as opposed to national-level blanket recommendations) appear to be substantial and may represent important ways of raising aggregate economic returns to fertilizer investments at the farming system level.

We provide the data and code necessary to replicate our results and to implement similar frameworks in other settings (i.e., other countries, crops or inputs). We argue that greater usage of such approaches to evaluating the potential economic returns to fertilizer—as well as other production technologies promoted by international R&D institutions—will help to address the disconnect between agricultural technology R4D and farmer decision-making on the ground.

Spatial ex ante analysis framework

Overview

Tn class="Disease">his section outlines a spatial framework that integrates biophysical and socio-economic variables measured over broad spatial scales (Fig 1). A key idea is that if we are able to reasonably predict yield responses to fertilizer as a function of spatially varying predictors, thenpan> we have a basis for building a spatially explicit evaluation framework. Inpan> principle, such a response function could be based on a structural model, such as QUEFTS [22] or could take various parametric or non-parametric approaches to empirical prediction. The only requiremenpan>ts are that (a) the agronomic response predictions are reasonably good, and (b) we have a sufficienpan>t set of geospatial model covariates to serve as out of sample predictors witn class="Disease">hin similar geographies.

Fig 1

Framework overview.

In the current era, we have increasing amounts of georeferenced agronomic response data to work with, even in traditionally data-sparse environments and a similarly broad set of modeling approaches. In this anpan>alysis, we take anpan> empirical approach, defining a Ranpan>dom Forest model onpan> a georeferenpan>ced dataset of small farmer pan> class="Species">maize yields and associated agronomic management data, as well as soils, terrain, rainfall and other biophysical parameters taken from geospatial datasets in the public domain. We describe these in more detail in the next section. While our modeling focus is on yield responses to nitrogen, in principle, any other agronomic response that has a coherent spatial expression could be modeled in this way, including any agronomic responses conditioned by soils, terrain, rainfall, temperature, etc.

A second key idea is the incorporation of spatially varying input and output prices. Smallholder farmers in SSA operate within large anpan>d heterogenpan>eous market access conpan>texts, with farm-gate prices varying conpan>siderably from locationpan> to locationpan> (e.g., [23-25]). Recognpan>itionpan> of tpan> class="Disease">his is important to any efforts to meaningfully evaluate technology attractiveness from the farmer’s perspective. Despite the absence of local market price data, we show that modeling approaches for predicting local prices in spatially coherent ways are feasible.

A third key conpan>ceptual feature of our approach is based onpan> accounpan>ting for the stochasticity of responpan>ses. Smallholder farmers are famously risk-averse, anpan>d abunpan>danpan>t empirical evidenpan>ce suggests that risk is anpan> importanpan>t elemenpan>t of smallholder decisionpan> making [26-28]. Inpan> our implemenpan>tationpan>, we acpan> class="Disease">hieve this through the inclusion of seasonal rainfall parameters. However, other sources of spatially varying uncertainty could also be incorporated, such as price volatility, which is known to vary with remoteness [29]. Model output can then be defined as a function of the stochastic parameters.

Linking all these elements, we have a framework for evaluating (a) an expected site-specific agronomic response—in this case: pan> class="Species">maize yield responses to nitrogen fertilizer, (b) the expected profitability of such input use, under local input and output prices and other assumptions, and (c) the uncertainty around these expected returns at any given location. Given the availability of databases on the distribution of rural populations, cropland and production, we can aggregate up model output to evaluate the likely aggregate benefits. Such guidance is critical for policymakers and development partners who must allocate scarce resources to meeting strategic rural development goals.

To carry out the analysis in tn class="Disease">his paper, we used R 4.0.2 [30]. Ranpan>dom forest models were constructed using the "ranpan>domForest" R package. Least-cost distanpan>ces to estimate market access were calculated using the "gdistanpan>ce" package.

Modeling yield response to fertilizer

To model maize yield responses to nitrogen, we used the Tanzania Agronomy Panel Survey (APS) on 553 households in 25 districts of Tanzania collected during the main maize harvest periods of 2016 and 2017 [31]. Because of lack of measurements in the field, only 601 yield estimates from 455 households were available for modeling. The districts in our study were selected based on representativeness of favorable maize production defined as (1) areas with suitable research and extension partners that would allow the scaling of fertilizer decision support tools, (2) areas with extensive coverage of maize producing areas as classified by the Africa Soil Information Service—AfSIS, and (3) areas with relatively high human population densities (i.e., >25/km2) with good access to urban markets (within 4 hrs of travel time). Georeferenced maize yields were measured using crop cuts (see [32]), and are accompanied by detailed data on plot characteristics, agronomic management (including fertilizer applications), and other household, farm and farm manager characteristics. The crop cut protocol involved collecting a grain sample, which was dried to 15% moisture before weighing. An aggregate N application rate for the plot was calculated on the basis of all the fertilizer applications reported by the farmer for that field—i.e., recorded across multiple fertilizer types and application rates, and normalized by the size of the field.

To estimate maize yield responses to nitrogen fertilizer, we employed a Random Forest model, a machine learning approach for diagnostics and prediction [33, 34]. In addition to nitrogen and crop management household variables from the survey data, spatial estimates of elevation, slope, soil organic carbon and pH, and total seasonal rainfall were included as predictors. Altitude and slope were obtained from the CGIAR-SRTM 90m digital elevation model Version 4.1 [35]. Soil property maps for organic carbon and pH at a 250m resolution soil came from the soil prediction surfaces from the AfSIS project [36]. We calculated seasonal (December to May) rainfall for each household from monthly predictions at 4 km2 resolution from the TAMSAT v3.0 database [37].

The averages of the household variables found in the survey data were used to simulate the yields countrywide (Table 1). The model was validated using bootstrap sampling and partial dependency plots were reviewed for theoretical coherence.

Table 1

Mean and standard deviation (SD) of the Tanzania Agronomy Panel Survey (APS) data.

Variable	Mean	Standard Deviation
Maize yield (kg/ha)	2604.0	1832.8
Fertilizer use (yes = 1)	0.357	0.479
N application rate among fertilizer users (kg/ha)	35.2	98.0
P application rate among fertilizer users (kg/ha)	11.5	45.4
Intercrop (yes = 1)	0.573	0.4950
Crop rotation (yes = 1)	0.062	0.2407
Use of manure (yes = 1)	0.203	0.4028
Use of crop residue (yes = 1)	0.090	0.2864
Number of weedings	1.827	0.5542
Use of improved seeds (yes = 1)	0.148	0.3557
Field in fallow in the last 3 years (yes = 1)	0.040	0.1961
Erosion control structure (yes = 1)	0.245	0.4304
Terraced field (yes = 1)	0.035	0.1839
Area in hectares of focal plot (log)	-0.507	0.9556
Age of head of household	47.702	13.7150
Household size (Number of persons)	5.692	3.1144
Years of education of head of household	7.067	3.5461
Households	455
Observations	601

Values pooled across years. The table shows the average and standard deviation of values in the farm survey data, which were used to estimate yield responses.

Values pooled across years. The table shows the average and standard deviation of values in the farm survey data, wn class="Disease">hich were used to estimate yield responses.

Spatial prices estimation

Local farm-gate prices for maize in unpan>sampled locationpan>s were estimated with a model that captures informationpan> onpan> geograppan> class="Disease">hic location, as well as pixel-level meteorological and other environmental conditions, and market access characteristics, an approach similar to that described by [38]. Wholesale market prices for maize were obtained from the 4th wave of the Tanzania LSMS National Panel Survey 2014–2015 [39]. Original prices in TZS/kg were transformed to USD/kg using an exchange rate TZS 1598 to the US Dollar. We used this exchange rate throughout the analysis. The 601 spatially located observed prices were used to fit a random forest model using predictor variables capturing aspects of market access (travel time to market and distance to port), potential demand (population density and cropland) and precipitation averages, as well as longitude and latitude. Table A in S1 Text describes the complete list of variables used in the maize market price model.

From the estimated local market prices, we predict farm-gate maize prices by assuming a "last mile" tranpan>sport cost rate of 0.01 USD/kg/hr. Specifically, a farm-gate price is estimated for every grid locationpan> as the pan> class="Disease">highest of all possible farm-gate prices obtainable from different market locations, after accounting for the market-specific transportation costs between the market and the farm location (i.e., the embedded assumption is that a farmer will sell her production to the market which gives the highest price, after accounting for the costs required to transport output to that market).

For nitrogen applicationpan>, we start with a represenpan>tative market price of 0.95 USD per kg of Ng, wpan> class="Disease">hich we derive from the average price of urea (generally the cheapest source of N) reported from AfricaFertilizer.org for Tanzania over the last five years. The price for nitrogen was inferred from the urea price, on the basis of the 46% N content of urea. We estimated farm-gate nitrogen prices by fitting a logistic transportation cost model under which delivered fertilizer prices treble at 5 hours of travel time from a local market (Fig A in S1 Text).

A key predictor of local input and output prices was the estimated travel time to large towns. These estimates were produced by creating a conductance surface by assigning travel speeds to each pixel based on the national road network and land cover and calculating the quickest travel time to each market using least-cost-path algorithms. The road network in Tanzania was obtained from Open Street Maps anpan>d travel speeds were assignpan>ed depenpan>ding onpan> their classificationpan> (primary, seconpan>dary or tertiary pan> class="Disease">highways). We assigned travel speeds to the pixels outside the road network by using the Globcover 2009 Version 2.3 Land Cover Classification [40] and assuming different travel speeds in each land cover class. With the travel speed covering Tanzania, market access was estimated by calculating the least accumulated time from each pixel to a town with a population of more than 50,000 inhabitants. Market town locations were taken from the GRUMP database [41].

Fertilizer scenarios

We evaluate fertilizer profitability over four different application rate scenarios: no nitrogen usage (ZERO), a commonpan>ly recommenpan>ded N applicationpan> rate of 55 kg/ha (BK, [42]) anpan>d two potenpan>tial fertilizer recommenpan>dationpan>s optimized to obtain the pan> class="Disease">highest maize yields (OPyield) or the highest net revenue (OPnetrev) obtainable at any particular location. Optimization scenarios use the average seasonal rainfall data over the 1980–2019 period as the basis for the calculation.

Results

Market and farm-gate prices of maize and fertilizer

Maize market prices in the LSMS dataset had a meanpan> of 0.37 USD/kg anpan>d ranpan>ged from 0.07 to 0.94 USD/kg. The ranpan>dom forest model performed well, explaining 92% of tpan> class="Disease">his variation of the training data with an RMSE = 0.17. Predicted prices ranged from 0.14 USD/kg in the Southern Highlands and areas near Shinyanga to a maximum of 2 USD/kg in some western regions (Fig 2A). After accounting for transport costs from local markets, 60% of the territory had predicted farm-gate between 0.2 and 0.4 USD/kg (Fig 2B). Prices reach to a maximum of 0.69 USD/kg in Zanzibar. Areas with large maize production, such as the Southern Highlands and areas near Arusha, had predicted farm-gate prices near 0.3 USD/kg. 12% of Tanzania is predicted to have no positive farm-gate maize price.

Fig 2

Predicted maize prices in Tanzania.

(A) Market prices. (B) Farm-gate prices.

Because of the sparse number of large market towns, our model predicts that approximately 77% of the territory has a n class="Chemical">nitrogen price of above 2.5 USD/kg anpan>d only 12% of the area with prices lower thanpan> 1.5 USD/kg (Fig B in S1 Text). Only northernpan> anpan>d easternpan> regions, with a pan> class="Disease">higher density of cities and roads, present large areas with lower fertilizer prices.

Yield response model

The yield response model fitted with the random forest model explained 24% of the variance found in the yields reported in the APS household survey (Fig 3A). The applied pan> class="Chemical">nitrogen rate was the variable with the highest importance followed by rainfall, altitude and soil organic carbon (Fig A in S1 Text). Crop management variables such as improved seed, manure use, intercropping were useful predictors in the model.

Fig 3

Yield response random forest model selected results.

(A) Observed vs predicted yield and fitness measures of the yield model. Partial dependence plots of (B) seasonal rainfall, (C) nitrogen and (D) organic carbon from the yield random forest model.

(A) Observed vs predicted yield and n class="Disease">fitness measures of the yield model. Partial depenpan>denpan>ce plots of (B) seasonal rainfall, (C) pan> class="Chemical">nitrogen and (D) organic carbon from the yield random forest model.

Partial dependency plots for the random forest model showed a positive response of yield to rainfall, nitrogen and soil organic carbon (Fig 3B–3D). Increasing seasonal rainfall between the 500 mm and 1250 mm positively affects yields, as we would expect. (Negative effects of increasing precipitation were predicted between 0 mm to 500 mm, although very few sample points fall in this rainfall range; these results may reflect unobserved irrigation practices.) Yield increases rapidly when increasing the amount of nitrogen with diminishing returns after an application of 300 kg/ha.

Simulation results

Given spatial price variability, higher yields are not necessarily associated with higher net revenues (Fig C in S1 Text). In our scenarios, a blanket recommendation will result, on average, 27% more production and a -4% increase in returns compared to a baseline scenario across the country. Optimizing fertilizer to maximize yields results in an increase of 57% of yields and a 10% reduction in profitability. Optimizing for returns results in a significant increase in yields, 47% more than without the use of nitrogen, but an average increase of 16% of returns across the maize distribution.

However, these yield and profitability changes are highly depenpan>denpan>t onpan> the regionpan> of the counpan>try. Yields chanpan>ges vary with soil conpan>ditionpan>s, wpan> class="Disease">hile profitability is more dependent on the proximity to large market towns. According to our model, the maximum yields are obtained with an application of 175 kg/ha of N for over 90% of the maize distribution and can increase the production over 60% in areas such as the southern highlands and Dodoma and Singida, but decrease the profitability because of the low farm-gate prices. Maximizing for yields is predicted to most profitable in areas such as Dar es Salaam, Musoma, Mwanza and Kigoma, where the farm-gate maize price is high enough to allow higher investments in nitrogen.

Optimizing for higher yields by using the pan> class="Disease">highest possible N dose can also result in prohibitive costs of fertilizers that are not recovered with the sale of the higher production, resulting in negative net revenues. Based on our fertilizer price model, areas such as Rungwa and the inland regions of the southeast are predicted to perform better with no fertilizer. Only a substantial decrease in fertilizer prices, most likely as a result of higher accessibility, can improve the profitability of nitrogen applications in these areas.

Maximum profitability is a result of only moderate increases in yields, especially in northwestern regions. High nitrogen rates that maximize net revenue are mostly correlated with high accessibility areas (Fig 4). Only crop areas near cities have recommendations above 125 kg/ha and only 6% of the maize distribution may benefit from applications above 100 kg/ha. Recommendations between 50 and 100 kg/ha are estimated to be appropriate for 75% of the territory. In the simulation results, areas near large market towns were those which most benefitted economically from the use of nitrogen (Table 2). Regions such as Dar es Salaam, Kigoma and Mara, with Mwanza, Kagera and Kigoma, with large rural populations and high maize farm-gate prices, are predicted to have the highest returns to nitrogen fertilizer investments.

Fig 4

Optimized amounts of nitrogen fertilizer rate to maximize net revenue.

Table 2

Summary table of aggregate gains in net revenue.

Region	Rural population (million)	Maize area (km2)	Average gains when changing nitrogen scenarios (USD/ha)
			ZERO to OPnetrev	BK to OPnetrev
Arusha	1.7	723.9	23.5	118.2
Dar es Salaam	0.3	13.1	463.9	297.9
Dodoma	2.6	933.8	68.6	106.2
Geita	1.8	1085	279.9	147.8
Iringa	1.1	1444.2	107.8	90.6
Kagera	3.3	702.3	225.1	99
Katavi	0.7	583.9	219.2	101.4
Kigoma	2.2	1296.8	369.8	158.5
Kilimanjaro	1.8	627.4	31.7	79.1
Lindi	1.1	482.7	108	86.6
Manyara	2.1	1348.8	20	88
Mara	2.2	491.5	374.6	199.7
Mbeya	3.0	2463.5	165	107.3
Morogoro	2.2	1248.5	78.9	79
Mtwara	1.5	688.5	241.4	126.8
Mwanza	2.9	689.9	271.5	178.2
Njombe	0.9	860.8	154.8	48.6
Pwani	1.2	633	150.8	120.5
Rukwa	1.2	841.6	335.2	139.6
Ruvuma	1.6	959.9	88.9	60.8
Shinyanga	2.2	942.3	178.1	134.7
Simiyu	2.3	1234.2	80.1	103.6
Singida	1.7	728.3	28.9	76.8
Tabora	3.0	1639.5	136.7	107.2
Tanga	2.3	1492	112.7	87.4

The distribution of the potential profitability distribution in each location was calculated accounting for pixel level rainfall variability. Results are shown in Fig 5B (with rainfall variability expressed as coefficient of variation in panel A for reference). Over 44% of the crop distribution has a coefficient of variation higher thanpan> 5% whenpan> using anpan> optimized pan> class="Chemical">nitrogen rate and accounting for seasonal rainfall variability. The lower predicted production in the northern and northeastern regions results in higher uncertainty in the distribution of returns. The Southern Highlands has lower pixel rainfall variability and, combined with the higher yield results, relatively high expected returns with low variability.

Fig 5

Rainfall and net revenue variation.

(A) Seasonal (December-May) rainfall coefficient of variation. (B). Net revenue coefficient of variation resulting from the OPnetrev scenario.

Validation

As a way of validating whether or not predicted profitability has any practical value, we used the log of predicted net revenue from our baseline scenario, as well as the standard deviation of net revenue as a measure of uncertainty, in a model of fertilizer usage by smallholder farmers in Tanzania, using three panel waves of the Tanzania LSMS National Panel Survey (2008/9, 2010/11, and 2012/13). For ease of interpretation, we use a linear probability model. To address time-invariant unobserved heterogeneity which might otherwise bias our results, we modeled the unpan>observed time invarianpan>t heterogenpan>eity as a funpan>ctionpan> of the time-averages of (time-varying) observed characteristics (i.e. the Munpan>dlak-Chamberlain device [43, 44]). Thus, time-averages are added to the model, but not interpreted. Results, shownpan> in Table 3, indicate that the log of expected profitability is a stronpan>g positive correlate of fertilizer usage, anpan>d the stanpan>dard deviationpan> of expected profitability is a stronpan>gly negative correlate of fertilizer usage. The latter result is conpan>sistenpan>t with stylized empirical finding Africanpan> smallholders are less likely to make fertilizer investmenpan>ts if the returns have pan> class="Disease">higher levels of uncertainty. The fact that these predicted profitability indicators are significant correlates even after controlling for region and travel time from each household location to the nearest market town suggests that there is information content in our model predictions beyond simply proxying for market remoteness.

Table 3

Validation: Out of sample prediction of fertilizer usage.

Dep var: fertilizer user (=1)	(1)	(2)
log(net revenue)	0.0952***	0.110***
	(2.84e-06)	(1.76e-07)
std.dev.(net revenue)		-0.000691***
		(0.00101)
area cultivated	0.000498	0.000466
	(0.771)	(0.787)
age of head	-0.000105	-0.000168
	(0.770)	(0.639)
female head (=1)	-0.00568	-0.00662
	(0.668)	(0.617)
education of head	0.00985***	0.00960***
	(8.46e-09)	(1.76e-08)
# members	0.000830	0.00100
	(0.777)	(0.732)
log value of productive assets	0.00621***	0.00635***
	(0.00681)	(0.00576)
log travel time to market town	-0.0372***	-0.0382***
	(1.82e-05)	(1.04e-05)
mean annual rainfall 1997–2014	0.000113**	7.99e-05
	(0.0349)	(0.143)
Region FE?	yes	yes
Year FE?	yes	yes
Mundlak-Chamberlain device?	yes	yes
Observations	5,819	5,819
R-squared	0.236	0.238

Dependent variable is a dummy indicator taking a value of 1 if the household is a user of inorganic fertilizer. Data are from the 2009, 2010 and 2013 waves of the Tanzania LSMS-ISA data, restricted to landholding households in the rural areas. Standard errors are robust to clustering at the enumeration area level. Model (2) includes the standard deviation of the expected profitability.

Robustness check

Our estimated agronomic use efficiencies (AE) are low compared with reported values from researcher managed studies [32, 45]. We attribute this to the observationpan>al nature of our data: as others have noted, calculated pan> class="Chemical">nitrogen use efficiencies for maize are much higher on researcher-managed plots than on plots managed exclusively by smallholders [45-47]. Our estimated use efficiencies (mean of 7.2 kg grain per additional kg of N) are comparable to those found by [21] using LSMS-ISA data for Tanzania (7-8kg). Nonetheless, as a robustness check, we re-estimate the predicted spatial distributions of fertilizer profitability under assumptions of 125% and 150% increases in our predicted agronomic use efficiency (bringing the mean value from 7.2 to 9.2 and 11 kg/kg, respectively. The resulting changes to the cumulative distribution of profitability (Fig 6) are relatively modest: when moving from our estimated agronomic efficiency distribution (mean = 7.2 kg/kg) to a distribution with a mean of 9.2 kg/kg (i.e., 125% of the AE predicted by our model), we have an increase of 3% of pixels for which fertilizer net revenue exceeds 100 USD/ha (i.e., from 90% to 93%). When we assume an agronomic efficiency distribution with a mean of 11 kg/kg (i.e., 150% of our predicted AE), we have an increase of 4% of pixels for which fertilizer net revenue exceeds 100 USD/ha (i.e., from 90% to 94%).

Fig 6

Cumulative distribution of net revenue differences of the BK scenario from the ZERO scenario under different agronomic use efficiencies (AUE) assumptions.

Discussion and conclusions

This paper has illustrated a simple yet useful method of predicting yield responpan>ses to fertilizer over heterogenpan>eous productionpan> lanpan>dscapes, with a view toward guiding strategic investmenpan>ts anpan>d policy intervenpan>tionpan>s. Inpan> our case study of smallholder Tanpan>zanpan>ianpan> pan> class="Species">maize farmers, our results indicate highly variable fertilizer responses over geographic space, in line with other empirical studies in the region (e.g., [4-7]). While fertilizer use is profitable, on average, it is not profitable everywhere. Farmers in very remote areas would not gain financially, given local input-output price ratios, even where agronomic returns are high. This result underscores the importance of acknowledging spatial differences in economic remoteness, and the implications for technology profitability, in designing agronomic interventions. This is particularly important for primarily agrarian economies with large shares of the rural population in remote areas, conditions that characterize many of the countries in sub-Saharan Africa.

Our analysis has direct implications for the debate on closing yield gaps. Closing yield gpan> class="Disease">aps may not be economically feasible in areas which are remote from markets. However, using a framework such as the one we propose may help to identify where to prioritize investments in closing yield gaps, i.e., where returns on investment are largest.

Our results also highlight the importance of acknowledging uncertainty in modeling the returns to investments from a farmer’s perspective. In our modeling framework, both agronomic and economic returns to fertilizer investments are strongly conditioned by location-specific rainfall patterns. Given the uncertainty around rainfall outcomes in any particular year, there is a corresponding amount of uncertainty in investment returns from the farmer’s perspective. The variability of estimated returns from our model is a good predictor of actual fertilizer usage in a nationally representative sample of Tanzanian smallholders: higher levels of uncertainty around investment returns are strongly negatively associated with the likelihood of fertilizer usage. This finding underscores the role that risk plays risk in smallholder decision-making and signals that technology promotion efforts, which fail to address economic risk, are fundamentally flawed. In addition, and, conversely, agronomic practices that improve agronomic use efficiencies through technology promotion can reduce these financial risks.

Only when farmer decision-making is more fully integrated into planning frameworks will the required changes in production technology begin to take place at the scale necessary to deliver expected changes in smallholder-dominated food systems. The ex ante framework articulated in this paper is onpan>e way in wpan> class="Disease">hich economic returns and the variability of those returns may be better linked with agronomic modeling and incorporated into strategic planning and targeting frameworks. We envision such frameworks becoming increasingly important ways to address the challenge of increasing sustainable intensification efforts in the region.

(DOCX)

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30 Jun 2020

PONE-D-20-10700

Fertilizer profitability for smallholder n class="Species">maize farmers in Tanpan>zanpan>ia: A spatially-explicit ex anpan>te anpan>alysis

PLOS ONE

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1. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Partly

Reviewer #2: Yes

**********

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Reviewer #1: Yes

Reviewer #2: Yes

**********

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Reviewer #1: Yes

Reviewer #2: Yes

**********

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Reviewer #2: Yes

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Reviewer #1: Dear authors,

It was a pleasure to read the well written manuscript. The issues around fertilizer profitability and risk are important for both smallholders and governments with regional implications for food security.

The approach is n class="Disease">highly interesting, accounpan>ting for location in prices anpan>d crop yield responses combined with temporal variability due to rainfall. I do have some concernpan>s about the approach used with respect to the grain yield response to N applications anpan>d increasing rainfall.

1. The key component is the yield response to N-application determining the net return of investment in fertilizers. I would appreciate if authors canpan> conpan>sistenpan>tly use N applicationpan> rather thanpan> fertilizer as that may refer to types of fertilizer with very differenpan>t N conpan>cenpan>trationpan>s. For example, the nationpan>al voucher scheme uses 2 vouchers: onpan>e for 50 kg pan> class="Chemical">DAP or 50 kg of rock phosphate and one for 50 kg Urea or for ammonium sulphate. This equates to 100 kg fertilizer, but to only 15*0.18 + 50*0.46 = 32 kg N for DAP + Urea but also to 0 + 50*0.21 = 10.5 kg N when rock phosphate is combined with ammonium sulphate. The latter with be very rare. I would not expect that these amounts are applied on exactly one ha, which seems to be suggested by the authors (line 188), with reference to a World bank report that does not detail recommendations. Typically, recommendations are 50 kg of DAP + 50 kg of CAN per acre for e.g. OneAcreFund clients, amounting to 55 kg N/ha.

2. A pure empirical approach to estimate yield responses to fertilizer is somewhat problematic. The data given in Figure 3c suggest that a 125 kg N / ha application increases yields by about 900 kg/ha, reflecting an agronomic efficiency (AE) of 900/125 = 7.2 kg grain / kg N applied. This is a very low value, much below values founpan>d for agronpan>omic experimenpan>ts (25-50 kg/kg, depenpan>ding onpan> PK fertilizationpan>, Ichami et al 2020)) onpan>-farm trials that typically are arounpan>d 10-11 kg/kg across a ranpan>ge of enpan>vironpan>menpan>ts (Rurinda et al., 2020). Tpan> class="Disease">his suggest that other growth limitations played an important role, e.g. water deficiency and pests and diseases that reduced growth. Some additional context about these seasons would be much appreciated as that helps to interpret the outcomes.

3. The response to N strongly depends on applications of P and K. In most areas of Tanzania, k will not be very problematic. However, the response to N is strongly affected by availability of P in the soil and use of P fertilizers. Surprisingly, P application is not included as a co-variate, although it strongly affects the price of fertilizers used. What prices were used for the calculations, was tn class="Disease">his including P?

4. Authors included rainfall data from 2 years in their model, and variation in rainfall is spatial. These spatial correlations cannot be transferred to temporal variations. Farmers adapt their manpan>agemenpan>t to anpan> expected yield anpan>d variability: in areas with conpan>sistenpan>tly good seasonpan>s input levels will be pan> class="Disease">higher and management geared towards high yields; in areas with a higher risk of droughts, lower inputs will be used resulting in lower maximum yields even when rainfall is abundant. Translating rainfall variability across years to net revenue based on a “spatial” model wihout a proper temporal component is in my view flawed as it assumes that farmers are ignorant for this temporal variability. They obviously are not and have a range of management adaptations to droughts and risks. This should be properly discussed.

Points for clarification

Authors mention that crop cuts were taken. Are grain yields referring to dry matter yields or “ fresh” yields? Is tn class="Disease">his for grain or for grain + cobs? How was fertilizer use measured on the plots measured? Farmer reported inputs are very unpan>certain too. Please provide required details. The ranpan>ge of N applications seems near impossible: intenpan>tional applications of more thanpan> 150 kg/ha are very rare in SSA.

Line 37: remove “once considering the local farm-gate crop and fertilizer prices”.

Line 52: risk-reducing rather than risk-smootn class="Disease">hing. Smootpan> class="Disease">hing is a data operation and not a financial instrument.

Liners 66-80: tn class="Disease">his part is odd: is more a summary thanpan> anpan> intro for the approach anpan>d what canpan> be expected in the manpan>uscript.

Line 110: refrase sentence. Sometn class="Disease">hing like: A tpan> class="Disease">hird key conceptual feature of our approach is based on accounting for the stochasticity of responses.

Table 1. Header: add meaning of SD. Maybe add how household size is measured for clarity. Can you explain why an average value for a boolean variable can be >1? Tn class="Disease">his applies to female heads of households.

Line 168: is tn class="Disease">his per kg of N or per kg of fertilizer, and if so of what type?

Line 188: the reference does not detail recommendations, but explains voucher schemes. See point 1. Typical recommendations are 55 kg N/ha, including 1 bag of CAN + 1 n class="Chemical">DAP per acre.

Line 199: are values per kg of grain at 12.5%moisture?

Line 201: RMSE value seems impossible given the ranges in prices. Please add a unit to the corrected number.

Line 217: give full abbreviation of TZn class="Disease">APS whenpan> first used please.

Line 235: explain what is 1% referring to after “an average increase of 1% across...”

Line 239, 242 and 245: please be consistent: aren’t authors just optimizing for yields? Maximum yields would just require n class="Disease">highest possible dose...

Line 265: authors mean coefficient of variation >5% rather than profitability (not shown in Figure 5).

Line 276-277: puzzling sentence. Did authors add the averages of regressors that vary across years or did authors replace those variables by the average values? Time invariant unobserved heterogeneity is boiling down to spatial variability or consistent differences in management practices....maybe just mention that? How does tn class="Disease">his affect rainfall anpan>d assopan> class="Disease">ciated interactions?

Line 280-282: refrase tn class="Disease">his sentence please.

Line 314-316: or emphasises that technology promotion needs to be embedded in good agronomic practises. From the results, technological risks (i.e. low AEs) are dominating and translating into financial risks, but these should be dampened by good practises wn class="Disease">hich is very feasible.

References:

Ichami, S.M., Shepherd, K.D., Sila, A.M., Stoorvogel, J.J., Hoffland, E., 2019. Fertilizer response and n class="Chemical">nitrogen use efficienpan>cy in Africanpan> smallholder pan> class="Species">maize farms. Nutr Cycl Agroecosyst 113.

Rurinda, J., Zingore, S., Jibrin, J.M., Balemi, T., Masuki, K., Andersson, J.A., Pampolino, M.F., Mohammed, I., Mutegi, J., Kamara, A.Y., Vanlauwe, B., Craufurd, P.Q., 2020. Science-based decision support for formulating crop fertilizer recommendations in sub-Saharan Africa. Agric. Sys. 180, 102790.

Reviewer #2: This paper presents a methodological framework for addressing the question of how to target interventions to enhance the benefits of using inorganic fertilizer under high spatial heterogeneity and rainfall variability faced by smallholder farmers. The framework addresses this question by estimating the response of yields and profitability to inorganic fertilizer application using location-specific data in the case of maize in Tanzania by combining different sources of data from household surveys to spatial data. The authors use methods that I have never seen applied to issues of agronomic responses before, such as the Random Forest model. In fact, I had to find out exactly what this model entailed, so by reviewing this paper I have learned something completely new to me. In my opinion, this is a very interesting and innovative paper. It is well-written and useful. I have however a few comments.

The authors mention three constraints for low fertilize usage: gap in agronomic response, low and variable economic returns, and risk averseness. However, a constraint that is not explicitly addressed is the lack of physical availability. Even if a farmer wants to buy fertilizer, nobody may sell it in the area. Obviously, this meanpan>s a very pan> class="Disease">high price due to transportation costs, but also search costs. So fertilizer is expensive and difficult to find and procure. In fact, one of the reasons for outside interventions is to increase the physical availability of fertilizer. So, the constraints the authors mention are demand constraints, but there they fail to mention supply constraints.

In lines 46-48, the authors state that there has been a dearth of planning and targeting frameworks such as the one they propose in the paper. Tn class="Disease">his is a very importanpan>t point, but it may be useful to discuss whether there have beenpan> other types of frameworks to address the issue of targeting intervenpan>tions to increase access to fertilizer.

Also, it may be useful as part of the background to talk about programs to procure fertilizers to farmers. No mention of those explicitly. Particularly in the context of Tanzania.

Lines 13- 131. Fertilizer response was modeled with ~ 14.5 farms per district. Is tn class="Disease">his enpan>ough to capture the variability presenpan>t in Tanpan>zanpan>ia?

Sine I assume that many of the readers of tn class="Disease">his paper may be like myself, i.e. not familiar with Ranpan>dom Forest model, I suggest, if possible, that the authors refer to a paper that provides a non-technpan>ical explanpan>ation of the model. They do cite the paper by Breimanpan> L., but it is quite technpan>ical. I had to search the Inpan>ternpan>et to find information on the model. Providing a non-technpan>ical referenpan>ce to the model will be very useful for a reader not familiar with the model.

Table 1 shows that there were 601 pooled observations in the farm survey, based on 362 farms for two years. Since there where 362 households, tn class="Disease">his indicates that there were 123 missing cases (362*2= 724-601). They do not menpan>tion that anpan>d the reasons for missing data.

In the same table, for the variable female head of household (yes=1) it states a value of 7.067. Tn class="Disease">his value does not make senpan>se. I imagine it refers to 7%. So for consistenpan>cy should be expressed as 0.07

Lines 152-154, could you give a short summary of the approach used. Not everybody has the time to read the original paper. I extracted tn class="Disease">his from the paper they cite:

“We show that in many countries tn class="Disease">his variation canpan> be predicted for unpan>sampled locations by fitting models of prices as a funpan>ction of longitude, latitude, anpan>d additional predictor variables that capture aspects of market access, demanpan>d anpan>d enpan>vironmenpan>tal conditions.”

Lines 156-160 summarizes the method to estimating farm-gate n class="Species">maize prices. Refers to Table A in SI text, lots of variables used. What was the number of observations of prices used?

Lines 278-280 and Table 3 be more explicit about what (1) and (2) mean, I assume that in (1) std dev is not considered and in (2) it is. Please clarify.

I tn class="Disease">hink that the authors could make the paper more interesting if they include in the discussion section their views on the implications of their findings for the debate on closing yield gpan> class="Disease">aps. This is an important issue in the literature, and I see that their results are very relevant. They show that in fact maximizing yield is not profitable and that what is profitable will translate into maintaining a relatively large yield gap. Worth discussing.

In general, I tn class="Disease">hink tn class="Disease">his is an very good paper that deserves to be published.

**********

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Reviewer #1: No

Reviewer #2: No

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13 Aug 2020

Reviewer #1:

Dear authors,

It was a pleasure to read the well written manuscript. The issues around fertilizer profitability and risk are important for both smallholders and governments with regional implications for food security.

The approach is n class="Disease">highly interesting, accounpan>ting for location in prices anpan>d crop yield responses combined with temporal variability due to rainfall. I do have some concernpan>s about the approach used with respect to the grain yield response to N applications anpan>d increasing rainfall.

We thank the reviewer for tn class="Disease">his positive overall assessmenpan>t of our paper, anpan>d for the specific commenpan>ts anpan>d suggestions, wpan> class="Disease">hich we found very helpful. We have addressed each of these comments in detail below.

1. The key component is the yield response to N-application determining the net return of investment in fertilizers. I would appreciate if authors canpan> conpan>sistenpan>tly use N applicationpan> rather thanpan> fertilizer as that may refer to types of fertilizer with very differenpan>t N conpan>cenpan>trationpan>s. For example, the nationpan>al voucher scheme uses 2 vouchers: onpan>e for 50 kg pan> class="Chemical">DAP or 50 kg of rock phosphate and one for 50 kg Urea or for ammonium sulphate. This equates to 100 kg fertilizer, but to only 15*0.18 + 50*0.46 = 32 kg N for DAP + Urea but also to 0 + 50*0.21 = 10.5 kg N when rock phosphate is combined with ammonium sulphate. The latter with be very rare. I would not expect that these amounts are applied on exactly one ha, which seems to be suggested by the authors (line 188), with reference to a World bank report that does not detail recommendations. Typically, recommendations are 50 kg of DAP + 50 kg of CAN per acre for e.g. OneAcreFund clients, amounting to 55 kg N/ha.

We appren class="Disease">ciate the need for clarity that the reviewer notes. We have revised the manpan>uscript to consistenpan>tly refer to N application rather thanpan> fertilizer, wherever tn class="Disease">his makes contextual sense.

We also revised our blanket recommendation assumption to a rate of 55 kg/ha, is in line with the reviewer’s suggestion, which indeed corresponpan>ds to the One Acre Funpan>d recommenpan>dationpan>. We now note tpan> class="Disease">his on page 11 of the revised manuscript. We changed the reference from the World Bank report to the work by Kanyeka et al, which includes the recommendation amount used. The N content of CAN depends on the brand, but if we use 27%, then the OAF recommendation is: ((.18*50)+(.27*50))/0.404686 = 55.6 kg/ha

2. A pure empirical approach to estimate yield responses to fertilizer is somewhat problematic. The data given in Figure 3c suggest that a 125 kg N / ha application increases yields by about 900 kg/ha, reflecting an agronomic efficiency (AE) of 900/125 = 7.2 kg grain / kg N applied. This is a very low value, much below values founpan>d for agronpan>omic experimenpan>ts (25-50 kg/kg, depenpan>ding onpan> PK fertilizationpan>, Ichami et al 2020)) onpan>-farm trials that typically are arounpan>d 10-11 kg/kg across a ranpan>ge of enpan>vironpan>menpan>ts (Rurinda et al., 2020). Tpan> class="Disease">his suggest that other growth limitations played an important role, e.g. water deficiency and pests and diseases that reduced growth. Some additional context about these seasons would be much appreciated as that helps to interpret the outcomes.

This is a fair point, anpan>d deserves further elaborationpan>. Trials onpan> farmer’s fields, wpan> class="Disease">hile more representative of actual smallholder farm responses than researcher-managed agronomic experiments, are still often managed with management protocols (and very small plot sizes) that result in yields which are higher on average than those found in observational data, i.e. farm survey data. As an example, Mather et al. (2016) found for Tanzania using LSMS-ISA data (7-8kg). Rurinda et al 2020 uses nutrient omission trials data, which are on farmer’s fields, but follow optimal management protocols. As such, we would expect them to be a bit higher.

However, in the current version of the paper, we have included two additional assumptions: where estimated AE values are increased to 125% and 150% of the empirically estimated rates, bringing the average AE up to 9.2 and 11, respectively. Tn class="Disease">his senpan>sitivity analysis is described on page 18 of the revised manuscript.

3. The response to N strongly depends on applications of P and K. In most areas of Tanzania, k will not be very problematic. However, the response to N is strongly affected by availability of P in the soil and use of P fertilizers. Surprisingly, P application is not included as a co-variate, although it strongly affects the price of fertilizers used. What prices were used for the calculations, was tn class="Disease">his including P?

In order to keep the analysis simple, we focus on N, accounting for the cheapest source of N in our pricing. We use spatially distributed market prices for urea as reported in the LSMS data to predict the spatial distributionpan> of pan> class="Chemical">nitrogen. P is excluded from this price calculation for reasons of simplicity (although it is included in the yield response random forest model). As such, our pricing and profitability estimates can be taken as lower bounds.

4. Authors included rainfall data from 2 years in their model, and variation in rainfall is spatial. These spatial correlations cannot be transferred to temporal variations. Farmers adapt their manpan>agemenpan>t to anpan> expected yield anpan>d variability: in areas with conpan>sistenpan>tly good seasonpan>s input levels will be pan> class="Disease">higher and management geared towards high yields; in areas with a higher risk of droughts, lower inputs will be used resulting in lower maximum yields even when rainfall is abundant. Translating rainfall variability across years to net revenue based on a “spatial” model wihout a proper temporal component is in my view flawed as it assumes that farmers are ignorant for this temporal variability. They obviously are not and have a range of management adaptations to droughts and risks. This should be properly discussed.

To clarify, we use a pixel specific measure of rainfall variability in our simulation. Thus, the temporal variability we account for in our estimation of uncertainty of returns is location-specific. We have specified this in the text onpan> page 11 of the revised manpan>uscript, wpan> class="Disease">hich now reads as follows: “Accounting for rainfall variability will gives us an insight into the distribution of the profitability in each location. To account for seasonal rainfall variability, we run each scenario using 21 years of spatial time-series estimates of seasonal rainfall for 21 years of rainfall data between 1980 1987 andto 2019 from the TAMSAT v3.0 dataset [36]. We calculate the pixel level distribution of the expected yield and net revenue results on the basis of the resulting model output from each seasonal rainfall estimate (holding other spatial covariates at their observed temporally-invariant levels).”

Points for clarification

Authors mention that crop cuts were taken. Are grain yields referring to dry matter yields or “ fresh” yields? Is tn class="Disease">his for grain or for grain + cobs? How was fertilizer use measured on the plots measured? Farmer reported inputs are very unpan>certain too. Please provide required details. The ranpan>ge of N applications seems near impossible: intenpan>tional applications of more thanpan> 150 kg/ha are very rare in SSA.

The crop cut protocol involved collecting a grain sample, wn class="Disease">hich was dried to 15% moisture before weigpan> class="Disease">hing. This is the same protocol used by Rurinda et al. 2020. - We have clarified this in the revised manuscript on page 7.

An aggregate N application rate was calculated on the basis of all the fertilizer applications reported by the farmer for that field – i.e. recorded across multiple fertilizer types and application rates, and normalized by the size of the field. The n class="Disease">higher enpan>d of the application rate genpan>erally corresponds to very small plots. We have clarified tn class="Disease">his in the text on page 7.

Line 37: remove “once considering the local farm-gate crop and fertilizer prices”.

Wn class="Disease">hile we are aware that these words may be redunpan>danpan>t, we tpan> class="Disease">hink they serve to clarify and emphasize our transformation of agronomic returns into economic returns, thus increasing clarity of the analysis.

Line 52: risk-reducing rather than risk-smootn class="Disease">hing. Smootpan> class="Disease">hing is a data operation and not a financial instrument.

Changed to “risk-reducing”

Liners 66-80: tn class="Disease">his part is odd: is more a summary thanpan> anpan> intro for the approach anpan>d what canpan> be expected in the manpan>uscript.

Yes, tn class="Disease">his indeed is a summary statemenpan>t of the results wpan> class="Disease">hich are explained in more detail in the body of the paper.

Line 110: refrase sentence. Sometn class="Disease">hing like: A tpan> class="Disease">hird key conceptual feature of our approach is based on accounting for the stochasticity of responses.

We have rephrased as suggested on page 3

Table 1. Header: add meaning of SD. Maybe add how household size is measured for clarity. Can you explain why an average value for a boolean variable can be >1? Tn class="Disease">his applies to female heads of households.

We have updated the table title. Household size definition added. “Female heads of households”was incorrect, changed to “Years of education of head of household:

Line 168: is tn class="Disease">his per kg of N or per kg of fertilizer, and if so of what type?

We have now specified that it is kg of N on page 10.

Line 188: the reference does not detail recommendations, but explains voucher schemes. See point 1. Typical recommendations are 55 kg N/ha, including 1 bag of CAN + 1 n class="Chemical">DAP per acre.

We also reviewed the blanket recommendation and changed it to a rate of 55 kg/ha.

Line 199: are values per kg of grain at 12.5%moisture?

The crop cut protocol involved collecting a grain sample, wn class="Disease">hich was dried to 15% moisture before weigpan> class="Disease">hing. This is the same protocol used by Rurinda et al. 2020. - We have clarified this in the revised manuscript on page 7.

Line 201: RMSE value seems impossible given the ranges in prices. Please add a unit to the corrected number.

Corrected. The error was because RMSE was being calculated using Etn class="Disease">hiopianpan> Birr instead of USD.

Line 217: give full abbreviation of TZn class="Disease">APS whenpan> first used please.

Updated and full abbreviation given in Line 131.

Line 235: explain what is 1% referring to after “an average increase of 1% across...”

Specified in page 13 that it is a % increase of returns.

Line 239, 242 and 245: please be consistent: aren’t authors just optimizing for yields? Maximum yields would just require n class="Disease">highest possible dose...

In Figure 3 we show that the random forest model predicts diminishing returns with pan> class="Disease">high concentrations of N when maintaining every other covariate constant. Our model suggests that the highest possible yields are obtained with an N application of 175 kg/ha. We have clarified this in the revised manuscript on page 13.

Line 265: authors mean coefficient of variation >5% rather than profitability (not shown in Figure 5).

Corrected to coefficient of variation.

Line 276-277: puzzling sentence. Did authors add the averages of regressors that vary across years or did authors replace those variables by the average values? Time invariant unobserved heterogeneity is boiling down to spatial variability or consistent differences in management practices....maybe just mention that? How does tn class="Disease">his affect rainfall anpan>d assopan> class="Disease">ciated interactions?

Yes, the Mundlak-Chamberlain device entails modeling unobserved time invariant heterogeneity as a function of the time-averages of observed characteristics. Thus time-averages are added to the model, but not normally interpreted. This approach (wpan> class="Disease">hich is sometimes referred to the as the Correlated Random Effects estimator) is commonly employed in applied econometric analyses, as well as increasingly in agronomic analyses (e.g. van Dijk et al. 2017, Assefa et al. 2019). Mundlak (1984), Chamberlain (1984) and Wooldridge (2010, 2019) all provide proofs that, if the core assumption is valid, the coefficient estimates converge on those of a fixed effect estimator in a large sample. We have rephrased this for clarity on page 15 of the revised manuscript.

Line 280-282: refrase tn class="Disease">his sentence please.

Rephrased for clarity on page X of the revised manuscript, wn class="Disease">hich now reads as “The latter result is consistenpan>t with stylized empirical finding Africanpan> smallholders are less likely to make fertilizer investmenpan>ts if the returnpan>s have pan> class="Disease">higher levels of uncertainty.”

Line 314-316: or emphasises that technology promotion needs to be embedded in good agronomic practises. From the results, technological risks (i.e. low AEs) are dominating and translating into financial risks, but these should be dampened by good practises wn class="Disease">hich is very feasible.

Rephrased on page 19 of the revised manuscript, which now reads as “This finding underscores the role that risk plays risk in smallholder decision-making, and signals that technology promotion efforts, which fail to address economic risk, are fundamentally flawed. In addition, and, conversely, agronomic practices that improve agronomic use efficiencies through technology promotion can reduce these financial risks”.

References:

References

Assefa, B.T., Chamberlin, J., Reidsma, P., Silva, J.V. and van Ittersum, M.K., 2020. Unravelling the variability and causes of smallholder n class="Species">maize yield gpan> class="Disease">aps in Ethiopia. Food Security, 12(1), pp.83-103. https://doi.org/10.1007/s12571-019-00981-4

Chamberlain, G., 1984. Panel Data. In: In: Grilliches, Z., Intriligator, M.D. (Eds.), Handbook of Econometrics, vol. 2. North-Holland Press, Amsterdam, pp. 1248–1318.

Ichami, S.M., Shepherd, K.D., Sila, A.M., Stoorvogel, J.J., Hoffland, E., 2019. Fertilizer response and n class="Chemical">nitrogen use efficienpan>cy in Africanpan> smallholder pan> class="Species">maize farms. Nutr Cycl Agroecosyst 113.

Mather, D., Minde, I., Waized, B., Ndyetabula, D. & Temu, A. (2016). The profitability of inorganic fertilizer use in smallholder maize productionpan> in Tanpan>zanpan>ia: Implicationpan>s for alternative strategies to improve smallholder pan> class="Species">maize productivity (No. 1093-2016-88057). GISAIA Working Paper #4. No 245891, Food Security Collaborative Working Papers from Michigan State University, Department of Agricultural, Food, and Resource Economics. http://DOI.org/10.22004/ag.econ.245891

Mundlak, Y., 1978. On the pooling of time series and cross section data. Econometrica 46 (1), 69–85.

Rurinda, J., Zingore, S., Jibrin, J.M., Balemi, T., Masuki, K., Andersson, J.A., Pampolino, M.F., Mohammed, I., Mutegi, J., Kamara, A.Y., Vanlauwe, B., Craufurd, P.Q., 2020. Science-based decision support for formulating crop fertilizer recommendations in sub-Saharan Africa. Agric. Sys. 180, 102790.

van Dijk, M., Morley, T., Jongeneel, R., van Ittersum, M., Reidsma, P. and Ruben, R., 2017. Disentangling agronomic and economic yield gn class="Disease">aps: An integrated framework anpan>d application. Agricultural Systems, 154, pp.90-99. https://doi.org/10.1016/j.agsy.2017.03.004

Wooldridge, J.M., 2010. Econometric analysis of cross section and panel data. MIT press.

Wooldridge, J.M., 2019. Correlated random effects models with unbalanced panels. Journal of Econometrics, 211(1), pp.137-150.

Reviewer #2:

This paper presents a methodological framework for addressing the question of how to target interventions to enhance the benefits of using inorganic fertilizer under high spatial heterogeneity and rainfall variability faced by smallholder farmers. The framework addresses this question by estimating the response of yields and profitability to inorganic fertilizer application using location-specific data in the case of maize in Tanzania by combining different sources of data from household surveys to spatial data. The authors use methods that I have never seen applied to issues of agronomic responses before, such as the Random Forest model. In fact, I had to find out exactly what this model entailed, so by reviewing this paper I have learned something completely new to me. In my opinion, this is a very interesting and innovative paper. It is well-written and useful. I have however a few comments.

We thank the reviewer for the positive overall assessment of our paper, and for the specific comments and suggestions, wn class="Disease">hich we founpan>d very helpful. We have addressed each of these commenpan>ts in detail below.

The authors mention three constraints for low fertilize usage: gap in agronomic response, low and variable economic returns, and risk averseness. However, a constraint that is not explicitly addressed is the lack of physical availability. Even if a farmer wants to buy fertilizer, nobody may sell it in the area. Obviously, this meanpan>s a very pan> class="Disease">high price due to transportation costs, but also search costs. So fertilizer is expensive and difficult to find and procure. In fact, one of the reasons for outside interventions is to increase the physical availability of fertilizer. So, the constraints the authors mention are demand constraints, but there they fail to mention supply constraints.

Tn class="Disease">his is a good point, wpan> class="Disease">hich we acknowledge in the revised manuscript in Line 36: “First, poor farmers’ physical access to fertilizer as a result of the heterogeneous coverage of key public goods and services”

In lines 46-48, the authors state that there has been a dearth of planning and targeting frameworks such as the one they propose in the paper. Tn class="Disease">his is a very importanpan>t point, but it may be useful to discuss whether there have beenpan> other types of frameworks to address the issue of targeting intervenpan>tions to increase access to fertilizer.

We are not aware of other similar frameworks, although we do now acknowledge that spatial tools for targeting fertilizer recommendations do exist, e.g. the Tanzanian Soil Information System (TanSIS), in a footnote on page 3.

Also, it may be useful as part of the background to talk about programs to procure fertilizers to farmers. No mention of those explicitly. Particularly in the context of Tanzania.

We now make reference to the NAIVS program and the Government of Tanzania’s strategic objectives to raise fertilizer usage on page 4.

Lines 13- 131. Fertilizer response was modeled with ~ 14.5 farms per district. Is tn class="Disease">his enpan>ough to capture the variability presenpan>t in Tanpan>zanpan>ia?

We certainly agree with the reviewer that more data would be better. However, our sample size of 601 observations is comparable to other empirical studies (e.g. Baudron et al, 2019; Komarek et al. 2017; van Loon et al. 2019). Wn class="Disease">hile we believe that our sample is genpan>erally represenpan>tative of the most importanpan>t pan> class="Species">maize producing areas in the country, we make no formal claims of statistical representativeness. We improved the description of the sampling framework in lines 138-144.

Sine I assume that many of the readers of tn class="Disease">his paper may be like myself, i.e. not familiar with Ranpan>dom Forest model, I suggest, if possible, that the authors refer to a paper that provides a non-technpan>ical explanpan>ation of the model. They do cite the paper by Breimanpan> L., but it is quite technpan>ical. I had to search the Inpan>ternpan>et to find information on the model. Providing a non-technpan>ical referenpan>ce to the model will be very useful for a reader not familiar with the model.

Added reference to Liaw and Wiener 2002.

Table 1 shows that there were 601 pooled observations in the farm survey, based on 362 farms for two years. Since there where 362 households, tn class="Disease">his indicates that there were 123 missing cases (362*2= 724-601). They do not menpan>tion that anpan>d the reasons for missing data.

Added in page 7: Because of lack of measurements in the field, only 601 yield estimates from 455 households were available for modeling.

In the same table, for the variable female head of household (yes=1) it states a value of 7.067. Tn class="Disease">his value does not make senpan>se. I imagine it refers to 7%. So for consistenpan>cy should be expressed as 0.07

Corrected: Years of education of head of household

Lines 152-154, could you give a short summary of the approach used. Not everybody has the time to read the original paper. I extracted tn class="Disease">his from the paper they cite:

“We show that in many countries tn class="Disease">his variation canpan> be predicted for unpan>sampled locations by fitting models of prices as a funpan>ction of longitude, latitude, anpan>d additional predictor variables that capture aspects of market access, demanpan>d anpan>d enpan>vironmenpan>tal conditions.”

We have rephrased tn class="Disease">his for clarity on page 9 of the revised manpan>uscript.

Lines 156-160 summarizes the method to estimating farm-gate n class="Species">maize prices. Refers to Table A in SI text, lots of variables used. What was the number of observations of prices used?

601 observations were used. Tn class="Disease">his was specified in page 9.

Lines 278-280 and Table 3 be more explicit about what (1) and (2) mean, I assume that in (1) std dev is not considered and in (2) it is. Please clarify.

Revised note under the table for clarification.

I tn class="Disease">hink that the authors could make the paper more interesting if they include in the discussion section their views on the implications of their findings for the debate on closing yield gpan> class="Disease">aps. This is an important issue in the literature, and I see that their results are very relevant. They show that in fact maximizing yield is not profitable and that what is profitable will translate into maintaining a relatively large yield gap. Worth discussing.

This is a good suggestionpan>. We have revised the manpan>uscript, wpan> class="Disease">hich now includes the following text on page 18: “Our analysis has direct implications for the debate on closing yield gaps. Closing yield gaps may not be economically feasible in areas which are remote from markets. However, using a framework such as the one we propose may help to identify where to prioritize investments in closing yield gaps, i.e. where returns on investment are largest.”

In general, I tn class="Disease">hink tn class="Disease">his is an very good paper that deserves to be published.

We thank you for these comments, wn class="Disease">hich have helped us to improve our manpan>uscript anpan>d make a stronger contribution.

References

Baudron, F., Zaman-Allah, M.A., Chaipa, I., Chari, N. and Cn class="Disease">hinwada, P., 2019. Understanpan>ding the factors influenpan>cing pan> class="Species">fall armyworm (Spodoptera frugiperda JE Smith) damage in African smallholder maize fields and quantifying its impact on yield. A case study in Eastern Zimbabwe. Crop Protection, 120, pp.141-150.

Komarek, A.M., Drogue, S., Chenoune, R., Hawkins, J., Msangi, S., Belhouchette, H. and Flichman, G., 2017. Agricultural household effects of fertilizer price changes for smallholder farmers in central Malawi. Agricultural Systems, 154, pp.168-178.

van Loon, M.P., Adjei-Nsiah, S., Descheemaeker, K., Akotsen-Mensah, C., van Dijk, M., Morley, T., van Ittersum, M.K. and Reidsma, P., 2019. Can yield variability be explained? Integrated assessment of n class="Species">maize yield gpan> class="Disease">aps across smallholders in Ghana. Field Crops Research, 236, pp.132-144.

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1 Sep 2020

Fertilizer profitability for smallholder n class="Species">maize farmers in Tanpan>zanpan>ia: A spatially-explicit ex anpan>te anpan>alysis

PONE-D-20-10700R1

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Reviewer #2: All comments have been addressed

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PLOS On class="Chemical">NE does not copyedit accepted manpan>uscripts, so the lanpan>guage in submitted articles must be clear, correct, anpan>d unpan>ambiguous. Any typograppan> class="Disease">hical or grammatical errors should be corrected at revision, so please note any specific errors here.

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Reviewer #2: I am satisfied with the way the authors addressed my comments. Tn class="Disease">his is a very good anpan>d innovative paper

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Reviewer #2: Yes: Mauricio R. Bellon

11 Sep 2020

PONE-D-20-10700R1

Fertilizer profitability for smallholder n class="Species">maize farmers in Tanpan>zanpan>ia: A spatially-explicit ex anpan>te anpan>alysis

Dear Dr. Palmas:

I'm pleased to inform you that your manuscript has been deemed suitable for publication in PLOS ONE. Congratulations! Your manuscript is now with our production department.

If your institution or institutions have a press office, please let them know about your upcoming paper now to help maximize its impact. If they'll be preparing press materials, please inform our press team witn class="Disease">hin the next 48 hours. Your manpan>uscript will remain unpan>der strict press embargo unpan>til 2 pm Eastern Time onpan> the date of publicationpan>. For more informationpan> please conpan>tact onpan>epress@plos.org.

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