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\begin{document}

\title{The Role of Active Soil Carbon in Influencing the Profitability of
Fertilizer Use: Empirical Evidence from Smallholder Maize Plots in
Tanzania}



\author[1]{Jordan Chamberlin}%
\author[2]{TS Jayne}%
\author[2]{S Snapp}%
\affil[1]{CIMMYT Kenya}%
\affil[2]{Michigan State University}%


\vspace{-1em}



  
  \date{May 08, 2024}


\begingroup
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\selectlanguage{english}
\begin{abstract}
We use recent plot-level panel data from Tanzanian smallholder farmers
to investigate maize yield responses to inorganic fertilizer under
variable production conditions. We find that that the marginal product
of nitrogen is strongly conditioned by soil organic carbon and rainfall
levels. These results highlight important sources of variation in the
returns to fertilizer investments across plots and smallholder farmers
in the region. When farmgate prices for maize and fertilizer are
incorporated into calculations of economic returns, we find that the
profitability of fertilizer use is strongly dependent upon farmgate
price ratio assumptions: under our most optimistic agronomic response
estimates, while 71\% of our sample has an AVCR greater than 1.5 at a
maize-nitrogen price ratio of 0.15, that share drops to 30\% at a price
ratio of 0.12 and 2\% at a price ratio of 0.09. Our findings provide
insights into the low levels of commercial fertilizer use in Tanzania
and elsewhere in the region, and suggest that raising active carbon
stocks in smallholder systems should be a strategic priority for
sustainable development.%
\end{abstract}%



\sloppy


\section*{Motivation}

{\label{motivation}}

Staple crop yields in sub-Saharan Africa (SSA) remain very low by
international standards, with yield gaps on the order of 80\% (van
Ittersum et al. 2017). Inorganic fertilizer is widely agreed to be the
technology with the greatest potential to raise yields in SSA's
smallholder systems (Vanlauwe et al., 2014; Holden 2018). Nitrogen is
the main constraining nutrient for cereal crop performance across most
environments, both in terms of yield level and yield stability (Vanlauwe
et al., 2011). Indeed, nitrogen has been identified as one of the grand
challenges of the 21\textsuperscript{st}~Century given its pivotal role
in food production, and nowhere is this more important than in
sub-Saharan Africa where a strong negative relationship has been
observed between soil nitrogen balances and population density (Drechsel
et al., 2001). Yet the relatively low uptake of nitrogen fertilizers by
SSA smallholders indicates important constraints, which are not yet
fully understood.

The large spatial heterogeneity in fertilizer usage in SSA (Sheahan \&
Barrett 2017) suggests that both market factors (e.g. farmgate
crop/fertilizer price ratios) as well as environmental factors (such as
soil and rainfall) may play an important role. Yield response -- i.e.
the marginal or average physical product of fertilizer -- is often low
and highly variable for smallholder staples producers, resulting in low
levels of profitability of fertilizer use when farm-gate crop and
fertilizer prices are applied (Xu et al., 2009; Marenya \& Barrett,
2009; Sheahan et al., 2013; Jayne \& Rachid, 2013; Liverpool-Tasie et
al., 2017; Burke et al., 2017; Koussoube \& Nauges, 2017).11See Jayne et
al. (2018) for a recent review of over 20 studies estimating the
profitability of applying inorganic fertilizer on maize in various
African locations. Relatedly, fertilizer is not profitable for many
farmers even where the \emph{average} benefits are positive and
relatively large, given differences in management ability and other
factors that vary across plots and households (Suri, 2011). Fertilizer
responses in many areas may be limited by depleted soil organic matter
(Marenya \& Barrett, 2009, Dreschel et al., 2001), soil acidity (Burke
et al., 2017), and other factors. Risk-averse farmers are especially
likely to forgo expected gains in the face of uncertainty around the
performance or profitability of a given technology (Emerick et al.,
2016; Magruder, 2018). Disentangling the patterns of fertilizer
responses may help us to better understand how to design area-,
household-, and plot-specific interventions to overcome constraints to
the profitable use of fertilizer in African smallholder production
systems.

This study identifies key soil-related drivers of maize yield and maize
yield response to nitrogen fertilizers for Tanzanian smallholders. Our
particular emphasis is on organic carbon, a particularly important
component of soil fertility (Lal 2006; Nord \& Snapp 2020). We use
two-wave panel data on farmer-managed plots in 25 maize-producing
districts in Tanzania. In addition to the standard farmer-, farm- and
community-level characteristics typically included in such analyses, our
dataset features well-measured yields (through yield sub-plot crop cuts
at harvest time), plot-level soil chemical analysis, and detailed
plot-level agronomic management information. We find that estimated
maize yield response to N is similar to other empirical studies from the
region based on farmer-managed fields and that they are strongly
conditioned by both rainfall and soil organic carbon stocks. Our
production function estimates indicate that the marginal product of
nitrogen increases by 25\% when moving from the 25\textsuperscript{th}to
the 75\textsuperscript{th} percentile of available carbon in our sample.
Furthermore, the variability around these expected returns are high.
After factoring in local input and output prices, profitability
assessments indicate relatively low returns to fertilizer investments:
less than half of the sample have AVCR\textgreater{}2 under our most
favorable estimation results and very conservative estimates of farmgate
price ratios. Our results also highlight differences in conclusions
about the profitability of fertilizer use on farmers' own fields and
management conditions vs. studies relying on farm trials and
demonstration plots (e.g., Jama et al., 2017), which tend to benefit
from researcher management protocols that many smallholder farmers may
not be able to replicate (Snapp et al., 2014). Our results highlight the
importance of considering the factors that condition fertilizer response
(and profitability) from the farmer's standpoint when designing
agricultural intensification programs and investment strategies. Our
analysis concludes that agricultural intensification strategies based on
raising the intensity of fertilizer use are unlikely to lead to
widespread adoption if the variation in agronomic and economic returns
is not accounted for and if the sources of low active soil carbon are
not also addressed.

The rest of this paper is organized as follows. After describing our
setting, data and empirical estimation strategy, we present estimation
results for agronomic and economic returns to fertilizer investments, in
turn. We discuss these results and their implications for sustainable
intensification strategies, concluding with key messages for
policymakers and recommendations for further research.

\section*{Empirical framework}

{\label{empirical-framework}}

\subsection*{Context}

{\label{context}}

Tanzania is one of the largest countries in Eastern and Central Africa,
and an important source of the region's maize production. However, most
of this production comes from smallholders who have relatively low
levels of productivity, and few of which use modern inputs such as
fertilizer. As such, raising maize yields has been an important
investment and policy target for the country and its partners in recent
years. Tanzania is representative in many ways of the maize-based
farming systems found elsewhere in the region, in terms of its
agroecologies and range of biophysical endowments, the predominant
production characteristics of its smallholder farmers, and the
relatively low levels of market infrastructure development. At the same
time, the heterogeneity of production characteristics found within
Tanzania's maize growing areas bodes well for its value as a test case
for evaluating variability of agronomic responses across key
geographical characteristics (Nord \& Snapp 2020).

\subsection*{Data}

{\label{data}}

Farm household survey data were collected in Tanzania in 2016 and 2017
on 624 households, located in 25 districts (Figure 1). These districts
are located in both the Southern Highlands and Northern zone,
representing the most important maize growing areas in the country.
Within each district, a stratified sampling frame was used that
maximized soil type variability so as be able to make broad inferences
about crop response, and to identify survey localities (Walsh \& V\selectlanguage{ngerman}ågen
2006; Shepherd et al., 2015). Within each locality, a listing of all
maize producing households was generated with the assistance of the
local headman. From this listing, 24 households in each locality were
randomly selected. Data were collected on household demographics, farm
and non-farm economic portfolios, land holdings and productive assets,
and other characteristics. Within each farm household, basic information
was collected for each plot managed by the household (e.g. land use
status, production decisions). In addition, very detailed agronomic
management information was collected for household's most important
maize plot (henceforth the farm's ``focal plot''). This plot was
identified by the farmer as the plot which generated the most maize
production, and which received the most managerial effort.

Nitrogen and other macronutrient supplies were calculated from the
various fertilizer blends farmers reported using. To account for
implausible values, we replaced application rates exceeding 700 kg
ha\textsuperscript{-1} of N with that value, which was tantamount to
winsorizing at the 99\textsuperscript{th} percentile of N application
rates for fertilizer users, and which follows the protocols used by
Liverpool-Tasie et al. (2017) and Sheahan and Barrett (2017).

Maize yields on focal plots were measured using crop cuts from three 5x5
meter quadrants, calculated at 12.5\% grain moisture content. Soil
characteristics from these plots were measured from samples taken at
quadrant locations at 0-10 and 10-20 cm depths. Soil organic carbon is
largely conditioned by topography and soil parent material; however,
once a field is converted to agriculture, active soil organic matter
fractions largely determine soil productivity, and this is markedly
influenced farmer practices (Zingore et al., 2008). Developments in
laboratory assays to monitor `active' soil organic matter fractions have
highlighted the value of permanganate oxidizable carbon as an early
indicator of management influence on soil organic carbon (Culman et al.,
2012). Total soil organic carbon also provides insights regarding
sustainable soil management, although at a slow timestep (five to ten
years). For this work, permanganate oxidizable carbon (POXC) was
determined on a ground (1mm sieve) sub-sample, oxidized with 0.02 M
KMnO4, and subsequently absorbance was read at a wavelength of 550nm
(ibid.). To address potential measurement error, and under the
assumption that the soil properties of interest here (particularly soil
active carbon) are relatively stable, we use the average measure across
the two years for each plot in our regression work.

Rainfall was measured as the sum of dekadal values recorded for the main
growing season, using the CHIRPS dataset (Funk et al., 2017). Rainfall
variability was measured as the coefficient of variation on the dekadal
observations within a season.

\subsection*{Estimation strategy}

{\label{estimation-strategy}}

The intent of this paper is to understand the agronomic and economic
returns to nitrogen fertilizer applications in smallholder maize
production. In keeping with agronomic and agricultural economic
literature, we frame maize yield (y) as a function of fertilizer
application rates (F), other agronomic management decisions (M), and
other exogenous conditioners (G).

\(y\ =\ f(\mathbf{F},\mathbf{M},\mathbf{G})\) (1)

Because farmers in Tanzania use a variety of fertilizer blends, we
integrate these decisions be decomposing each blend into its
macronutrient content, i.e. nitrogen (N), phosphorous (P) and potassium
(K). Other management factors include improved maize seed, maize-legume
intercropping (common in the southern highlands), organic matter
integration via compost, manure and crop residue retention, plant
spacing, weeding, fallowing, terracing and erosion control structures,
and herbicide and pesticide applications. Other exogenous conditioners
include slope, rainfall, rainfall variability and the presence of
disease or striga (witchweed).

We adopt a flexible polynomial functional form, allowing for quadratic
terms and interactions between variables. In this approach, we follow
similar empirical studies (e.g. Burke et al., 2017, Sheahan et al.,
2013, Xu et al., 2009). This flexibility is important in enabling us to
investigate how yield response to nitrogen is conditioned by other
factors. We may generalize this function as:

\(y_{\text{it}}\ =\ \alpha+\beta_{1}N_{\text{it}}+\beta_{2}N_{\text{it}}^{2}+\beta_{10}\mathbf{X}_{\mathbf{\text{it}}}++\beta_{11}N_{\text{it}}*\mathbf{X}_{\mathbf{\text{it}}}+\ u_{\text{it}}\)(2)

where N is nitrogen, our primary input of interest, \emph{i} indexes
plots, \emph{t} indexes observations over time, and where, for
convenience, we have subsumed \textbf{M} and \textbf{G} in the
vector\textbf{X} . As indicated earlier, \emph{a priori} hypotheses
include the possibility of positive interactions between nitrogen, soil
organic carbon and rainfall, after controlling for other factors.

A key consideration is the possibility that unobserved factors may
possibly bias our estimation results. Concretely, we may decompose the
residual in equation 2 as:

\(u_{\text{it}}\ =\ o_{\text{it}}+\ c_{i}+\ \epsilon_{\text{it}}\)(3)

where \(o\) represents unobserved time-varying factors,
\(c\) represents unobserved time-constant factors, and
\(\epsilon\) is a randomly distributed error term. Time-varying
unobservables may include soil moisture, nutrient status or other
factors which are often missing from empirical studies (or poorly
measured). Time-constant unobservables may include farmer ability or
plot biophysical characteristics which change little from year to year,
but which may affect both fertilizer usage and yield outcomes. Finally,
correlation between model covariates and the stochastic error term may
be an additional source of bias.11Burke\emph{et al} . (2017) provide a
useful, detailed discussion of these issues and corresponding
identification strategies in survey data settings.

In the present study, we argue that our dataset does a better job at
controlling for time-varying plot and plot-management factors than is
typically the case in empirical studies, and therefore
unobseved\(o_{\text{it}}\)is unlikely to be a major issue. Our larger
concern is with time-invariant unobserved farmer and plot-level
heterogeneity which are likely to upwardly bias our results if not
addressed (e.g. under the assumption that more able farmers are more
likely to use fertilizer than less able farmers). To address this, we
estimate models with the Mundlak-Chamberlain device (i.e. the Correlated
Random Effects model (Wooldrige 2010), as well as a Fixed Effects
estimator.

\section*{Results}

{\label{results}}

\subsection*{Descriptive statistics}

{\label{descriptive-statistics}}

Summary statistics on our dataset are reported in Table 1. The average
farm size is 3.3 hectares, and is comprised of 4 plots. Most of our
sample consists of farms in the 1-4 hectare range, which is typical for
smallholder systems in the region. Only 7\% had a single plot, and 14\%
had more than 5 plots. The mean and median focal plot sizes are 0.85 and
0.51 ha, respectively. Thirteen \% of our sample farms are managed by
female household heads.

Yields in our sample are somewhat higher than the national averages
reported elsewhere for Tanzania, with a median value of 2.7 tons/ha.
This reflects the fact that the focal plot is not a random maize plot,
but the most important and generally most productive plot available to
the farmer. Furthermore, because our sample districts were selected on
the basis of being important maize producing districts, maize yields in
our sample likely reflect more favorable production conditions than a
nationally representative sample. This sample orientation
notwithstanding, only about a third of sample uses fertilizer on these
plots.11Sheahan \& Barret (2017) estimate that 17\% of Tanzanian farm
households use fertilizer, drawn from the nationally representative 2011
wave of the LSMS-ISA data. Mather et al. (2016), using three waves of
the LSMS-ISA data, find similar national-level estimates, but note
higher levels of fertilizer use by maize farmers in the zones covered by
our survey: 31-37\% of maize plots in the Southern Highlands and 16\% of
maize plots in the Northern zone. Of these fertilizer users, there is
considerable variability in fertilizer application rates, with a median
rate of 56 kg ha\textsuperscript{-1} of nitrogen (somewhat below
regional recommendations).22Sheahan and Barrett (2017) found that
fertilizer users applied an average of 32kg/ha in the nationally
representative LSMS-ISA data for Tanzania in 2011. The higher
application rates we find for fertilizer users in our sample reflects
our sample design, as noted above, as well as the fact that fertilizer
use in our sample is dominated by high analysis Urea (46\%N) and was
often applied to very small maize plots.

\subsection*{Agronomic returns to
nitrogen}

{\label{agronomic-returns-to-nitrogen}}

Production function coefficient estimates are shown in Table 2 (we show
only a subset of estimation results; full results are reported in the
supplementary materials). We show six alternative specifications. In
each of these, the dependent variable is maize yield, measured in kg
ha\textsuperscript{-1} during the maize production season. Nitrogen, as
expected, shows a strong positive and non-linear influence on yield
outcomes. Specifications (1) and (2) use pooled OLS (POLS), and only
differ in the interaction term: the first specification interacts N with
active carbon alone, while the second specification interacts N with
active carbon and log rainfall for that growing season. Specifications
(3) and (4) incorporate the Mundlak-Chamberlain device -- i.e. the
correlated random effects (CRE) model -- to address unobserved
heterogeneity, but are otherwise similar to the first two
specifications. Specifications (5) and (6) use Fixed Effects estimation
to address unobserved heterogeneity, but are otherwise similar to the
other specification pairs. All models are cluster robust at the
household level and include controls for plot, household and community
characteristics (including distance to markets), detailed plot
management controls, a year indicator, and, in the POLS and CRE models,
time-invariant controls for the 75 districts in the sample.

Coefficient estimates (Table 2) are fairly consistent across all
specifications, although they differ somewhat in magnitude. Results
correspond with the expected positive returns to N applications, but at
diminishing rates. Interaction terms -- N*POXC and N*POXC*log(rainfall)
-- are significant under all three estimators, indicating that the
agronomic efficiency of N is conditioned by active carbon and rainfall,
as hypothesized. The coefficients on active carbon and its interaction
term is highly significant in all models, even where the individual
coefficient for active carbon is not significant at conventional levels.
The estimated impacts of rainfall and rainfall variability are positive
and negative, respectively, as we would expect.

Average marginal effects are shown for N and POXC in Table 3. The
marginal effects for N are our estimates of marginal physical product
(MP). These estimates differ somewhat across specifications, being
somewhat higher under FE compared with POLS and CRE models. The range in
MP estimates of 10-16 (additional kgs of maize yield per additional kg
of N) are similar to those found elsewhere in the region: 8 kg in
Nigeria (Liverpool-Tasie et al., 2017), 16 kg for Zambia (Xu et al.,
2009), 17 kg for Kenya (Marenya \& Barret, 2009), 23 to 25 kg for Uganda
(Matsumoto \& Yamano, 2013), 21 to 25 kg for Malawi (Harou et al.,
2017), 19 kg for Burkina Faso (Koussoube \& Nauges, 2017). Our results
are somewhat higher than Mather et al. (2016) found for Tanzania using
LSMS-ISA data (7-8kg). However, their data included all plots and
production in marginal areas, and was based on farmer estimates, rather
than crop-cut measures. Because our sample focuses on the most
productive maize plots of farmers in Tanzania's maize producing belt, we
would expect somewhat higher levels of productivity than for the entire
population of smallholders in the nation.

In the analysis that follows, we focus on the results of the Fixed
Effects regression, as the model which has the most plausible controls
for unobserved time-invariant heterogeneity which may otherwise bias our
results. However, we may note that all our results (i.e. limited
agronomic and economic returns to fertilizer) are even stronger when
based on the other model estimates, which indicate lower agronomic use
efficiencies. We return to this point in the discussion.

Table 4 illustrates the diminishing expected MP of nitrogen at different
levels of active carbon (10\textsuperscript{th}, 25\textsuperscript{th},
50\textsuperscript{th}, 75\textsuperscript{th}, and
90\textsuperscript{th} percentile, respectively), holding other factors
constant, focusing on the Fixed Effects model results. The direct impact
of moving from 337 ppm (the 25\textsuperscript{th} percentile of our
sample) to 696 ppm (75\textsuperscript{th} percentile) implies an
increase in MP by 20-25 percentage points, depending upon the
specification (i.e. whether or not log rainfall enters via an
interaction). Moving from the 10\textsuperscript{th} to the
90\textsuperscript{th} percentile of the active carbon distribution is
associated with even larger changes in MP: 43-55 percentage points.

Given the uncertainty that farmer face in production environments, these
expected changes in MP are not at all trivial. Recall that rainfall
variability also affects response. Because rainfall is a stochastic
variable, the large impact it has on yields, even after controlling for
other factors, indicates the magnitude of uncertainty in yield outcomes
for farmers operating in these areas.

As a complement to our MP estimate, we computed the average physical
product (AP) of N, calculated as the difference between the estimated
difference in yields resulting from zero fertilizer and yields resulting
from 200 kg ha\textsuperscript{-1} of nitrogen (the level at which
MVCR=1, on average, when using a farmgate maize-nitrogen price ratio of
0.15), with other sample values as observed. The distribution of MP and
AP estimates across the sample is shown in Table 5. These results
indicate substantial variability in agronomic response across the
sample. As an illustration, a farmer at the
75\textsuperscript{th}percentile of the MP distribution has an expected
MP that is 40\% larger than that of a farmer at the
25\textsuperscript{th} percentile.

\subsection*{Economic returns to
nitrogen}

{\label{economic-returns-to-nitrogen}}

To translate these agronomic responses into profitability terms, we
calculate and summarize a number of relative measures of economic
returns on the basis of alternative maize-nitrogen price ratios. In our
farm survey data, the farmer-reported input and output prices were
exceedingly noisy and it was not possible to coherently interpret the
variability of responses within a given area. Data entry problems cannot
be ruled out, but we may also note the wide variety of fertilizer
acquisition and maize sales channels: farmers buy and sell at very
different quantities, in different types of markets, at different
distances from their homestead. For this reason, we base the
profitability analysis in this paper on a set of representative
wholesale prices based on different sources of local market price
information for Tanzania: data on the average maize wholesale prices in
regional markets was taken from FEWSNet for the 2014-2018 period. Data
on the average unsubsidized commercial price of urea (generally the
cheapest source of N) for all local Tanzanian markets reporting prices
for 50kg bags during the 2014-2018 period was obtained
AfricaFertilizer.org. The price for nitrogen was inferred from the urea
price, based on the 46\% N content of urea, as is standard practice in
this type of analysis. Based on these data, we define a representative
market price ratio, as well several indicative farmgate price ratios
(Table 6). The representative maize/nitrogen market price ratio of 0.22,
based on 0.27 and 1.22 USD/kg for maize and nitrogen respectively. These
values are very similar to those used in other studies of fertilizer
profitability for Tanzanian maize farmers (e.g. Kihara et al., 2016).
However, such a market price ratio fails to account for last mile
transfer costs incurred by farmers, in which effective prices of inputs
increase (as the farmer needs to add transport costs to the market price
paid) and the effective prices of marketed output decline (as the farmer
must discount transfer costs between the farm and the market from the
market price received).33Note that this situation does not change when
marketing is done locally via traders. In that case, the trader's
margins will include transfer costs between the village and market, plus
intermediation fees. Thus, we further define farmgate price ratios from
the baseline market price ratio, based on transfer costs of 0.006
USD/kg/km at 5,10,15 and 20 kilometers distance, respectively, between
the wholesale market and the farmgate, resulting in decreasing price
ratios of 0.18, 0.15, 0.12, and 0.09. The transfer cost assumption here
is based on the empirical finding of Benson et al. (2012). Our resulting
farmgate price ratios are in the range of those calculated by Mather et
al. (2016) from LSMS-ISA data for Tanzania (which range from 0.19-0.14).

The marginal value-cost ratio (MVCR) is computed as the MP multiplied by
the input-output price ratio, while the average value-cost ratio (AVCR)
is the AP multiplied by the input-output price ratio. An AVCR value
exceeding 1 indicates profitability, strictly speaking, although an AVCR
value of 2 is often used as a shorthand criterion for gauging the
economic attractiveness of an investment from the perspective of a
risk-averse farmer. Similarly, while an MVCR value of 0 indicates the
optimal input level for a risk-neutral farmer (because marginal returns
are zero), MVCR values of 1 or greater are often used as more reasonable
indicators of acceptable minimum marginal returns, under assumptions of
risk-aversion and imperfectly observed production or transactions costs.

Table 7 summarizes these measures for the different price ratio
assumptions, using the estimation results from the FE model with
N*POXC*log(rainfall) interactions (column 6 in table 2). This
specification produces the highest estimated agronomic response of maize
to N. As such, these results may be taken as an upper bound to the
actual profitability of fertilizer in our survey area.

Results indicate relatively low rates of profitability, regardless of
the assumption: the average MVCR ranges from 2.85 (at the market price
ratio of 0.22) to 1.116 (when the farmgate price ratio is 0.09). While
most farmers apply at rates below the economically efficient rate for a
risk-neutral farmer (i.e. where MVCR=0), the share of farmers with
MVCR\textgreater{}1 drops notably with price ratio reductions, and the
share of farmers with MVCR\textgreater{}2 drops even faster. As
discussed elsewhere (e.g. Sheahan et al., 2013; Xu et al., 2009), an
MVCR of 2 may be a more appropriate ``optimal'' level of input usage,
under the assumption that a risk-averse farmer will require a marginal
return of at least this magnitude.

AVCR estimates show similar cross-sectional variability, with mean
values ranging between 2.60 (at price ratio=0.22) to 1.06 (at price
ratio=0.09). It is common to use an AVCR of 1.5 or 2 as a minimal
threshold of profitability sufficient to incentivize risk-averse
smallholder farmers to use fertilizer, to account for risk aversity and
unobserved transactions costs in production and marketing (e.g. Xu et
al., 2009; Sheahan et al., 2013). While most farmers in the sample have
AVCR estimates exceeding 1, the share with AVCR estimates exceeding 1.5
or 2 is very sensitive to price ratio assumptions: at a price ratio of
0.15 only 71\% and 22\% of our sample has an AVCR exceeding 1.5 and 2,
respectively. Our results suggest that under even moderate uncertainty
about farm gate prices, the magnitude of the MVCR and AVCR estimates may
be insufficient to motivate farmers to make risky fertilizer
investments.

These findings suggest that even where agronomic returns are positive
and of magnitudes generally considered conducive to investment, the
incorporation of ``last mile'' transportation costs may quickly
attenuate the economic attractiveness of these investments (e.g., Minten
et al., 2013). The implications of economic remoteness have been well
described (e.g. Minten \& Stifel, 2004; Chamberlin \& Jayne, 2013).
Adding uncertainty around the actual costs of last mile transportation
(which is the reality for many farmers in rural Tanzania) will only
magnify the disincentivizing effects of these transfer costs on
fertilizer investments. The fact that active soil carbon is an
empirically important driver of agronomic responses may help to target
attention to where these market remoteness effects may be especially
magnified. Figure 2 shows the AVCR calculated at a price ratio of 0.15
as a non-parametric function of active carbon. This graph illustrates
that at lower levels of soil carbon the agronomic use efficiency of
nitrogen is likely to be insufficient to be an attractive investment for
risk averse farmers, even in average rainfall years. When we
additionally consider the estimated impacts on profitability of seasonal
rainfall (Figure 3), we can clearly see the sensitivity of expected
profitability calculations to stochastic factors.

\section*{Discussion}

{\label{discussion}}

Our results indicate that while the marginal and average agronomic
returns to inorganic fertilizer use are generally positive, there are
strong variations in these returns over our sample. We have shown that
both early-season rainfall and available soil carbon are important
conditioners of yield responses to nitrogen. Building on these agronomic
response estimates, our economic analysis has stark implications. Even
under relatively modest assumptions of last-mile transportation costs,
the inclusion of estimated farmgate prices in relative profitability
calculations reduces the attractiveness of fertilizer investments for a
large share of our sample.

Our findings are likely to overestimate Tanzanian smallholders'
agronomic responses to fertilizer use and hence their economic
incentives to use fertilizer, for several reasons. First of all, our
sample consists of farmers in Tanzania's maize belt, where
agroecological conditions are generally more favorable than in most
other parts of the country. Secondly, the fact that this analysis is
based on focal plots, rather than on all plots, means that our analysis
cannot be taken as representative of all maize production conditions,
but rather of preferential conditions within the smallholder maize
system. Farmer preferential allocation of maize crops to higher
fertility, adequate soil organic carbon status field has been well
documented (Mhango et al., 2013; Tittonell et al., 2008). As such, our
estimates of agronomic and economic returns to fertilizer use are likely
an upward bound on the true values for the system. Problems with acute
soil organic carbon depletion and other soil fertility issues are likely
to be much worse on average over the farming system as a whole.

Thirdly, our analysis uses the most favorable production function
estimates, i.e. those resulting from the Fixed Effects estimation.
Profitability analysis using the POLS and CRE estimators is even less
profitable on average (although in most other respects estimation
results are remarkably consistent). When we re-run the same economic
analysis using the estimates of agronomic returns generated from the
POLS and CRE estimation results, the share of farmers for with MVCR and
AVCR estimates exceeding 2 is much lower.11For example, Table 7 shows
that 71\% of the sample has estimated AVCR values greater than 1.5. When
we use POLS and CRE estimates corresponding to columns 2 and 4 in Table
2 as the basis of the calculation, the corresponding share of the sample
with AVCR values great than 1.5 is just 13\% and 1\%, respectively.

Fourth, our estimates of farmgate maize/nitrogen price ratios, upon
which profitability estimates critically depend, are conservative and
likely to overestimate the ratio for many farmers. Our price ratio
assumptions are somewhat higher than those used in other empirical
analysis in the region. Sheahan et al. (2013) find an average
maize/nitrogen price ratio of 0.083 for Kenya. Matsumoto and Yamano
(2011) find ratios of 0.063-0.075 in Kenya and 0.044-0.027 in Uganda.
The price ratio assumptions we employ in our analysis are likely to be
optimistic; many farmers in Tanzania are likely to regularly face
less-favorable farmgate price ratios. As such, our profitability
analysis is likely biased upwards.

Finally, our results highlight important sources of uncertainty in both
agronomic and economic returns to fertilizer investments. We see this
particularly in the role of seasonal rainfall and rainfall distribution
parameters in the production functions, but may also note that the large
uncertainty around input, output and transportation prices faced by
farmers means that calculating expected returns on fertilizer
investments is highly uncertain even under optimal biophysical
production contexts. The fact that soil carbon stocks have such a strong
effect on yield responses in our sample is all the more striking given
these considerations. What this means is that even for the most
productive smallholders, the agronomic and economic returns to
fertilizer use are quite variable, which would further impede the
incentives of risk averse farmers to incur high capital outlays on
fertilizers.

Taken together, these results indicate that efforts to spur fertilizer
usage by smallholder farmers in Tanzania should not focus exclusively on
blanket agronomic targets, which are based on average responses over
large areas, but rather should carefully consider localized response
rates. This is in alignment with conclusions from other studies, e.g.
Nord \& Snapp (2020), who studied soil fertility variability in the same
geography. Investments in extension and promotion of integrated use of
organic management practices in combination with fertilizer are urgently
required if maize based systems are to be productive, which has clear
implications for reform of input based agricultural subsidies (Lal 2006;
Adowla et al., 2019). Such policies will often miss the mark, as there
is growing evidence -- including this study -- regarding the
accumulation of soil carbon as being necessary to raise yield responses
sufficiently for nitrogen fertilizer to be economically attractive. This
may be particularly valid for risk adverse farmers in areas facing high
transport costs to regional input and output markets. Implications are
also stark in the face of highly variable weather and a changing
climate, complementary investments in soil organic carbon can help
buffer risk (Williams et al., 2016). Our analysis suggests that
agronomic returns to nitrogen will have to increase substantially in
order to offset the low and variable price margins that smallholder
farmers typically face in countries like Tanzania.

\section*{Conclusions}

{\label{conclusions}}

Many areas of smallholder cultivation in sub-Saharan Africa have been
systematically experiencing reductions in soil organic carbon levels,
particularly where continuous maize cultivation without legume rotations
and/or application of inorganic or organic fertilizer is common
(Shepherd \& Soule, 1998; Drechsel et al., 2001; Tittonell et al., 2005;
Lal 2006; Marenya \& Barrett 2009). Soil organic carbon stocks are known
to affect plant uptake of nutrient supplies, and figure into
low-responsiveness of yields to nitrogen supply in some areas. Farmers
in such areas are much less likely to find fertilizer investments to be
economically attractive, regardless of how well fertilizer markets are
performing.

This paper has assembled evidence on the ways in which maize yield
responses to inorganic fertilizer are affected by soil organic carbon
and other factors. We have shown that the marginal product of nitrogen
is positively associated with both soil organic carbon stocks (measured
as active carbon), as well as by seasonal rainfall. When farmgate prices
for maize and fertilizer are incorporated into calculations of average
and marginal cost-benefit ratios, we find that economic returns -- as
measured by MVCR and AVCR -- drop drastically over price-ratio ranges
that are representative of those likely faced by many smallholders in
Tanzania. For example, assuming a price ratio of 0.15, only 22\% to
farmers could utilize fertilizer profitably (using AVCR\textgreater{}2).
However, even under more favorable assumptions, the high year-to-year
variability around these expected returns would discourage many farmers
from investing in fertilizer even if it were profitable to do so on
average across all years. Our results indicate that the sensitivity of
fertilizer profitability to such outcome uncertainty will be to be
particularly acute in areas of depleted organic matter.

An important implication of our analysis is the importance of
investments and policy interventions which address the systematic
depletion of soil organic carbon stocks. This study adds to the growing
evidence that cereal crop response to fertilizer requires that attention
to be paid to soil health, as indicated by active soil carbon. There
have been previous calls by soil scientists and economists for
integrated soil fertility management to complement inorganic fertilizer,
yet few previous studies have examined this at scale. Our research,
conducted across a broad range of soil types and market contexts across
Tanzania, reasserts the urgency of this proposition to better inform
discussions of how to stimulate fertilizer investments by African
smallholders. Farmer incentives to make such investments will be
promoted by efforts to raise the agronomic efficiency of fertilizer
sufficiently for fertilizer to be profitable.



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\section*{Conflict of Interest
Statement}

{\label{conflict-of-interest-statement}}

The authors declare that they have no known conflicts of interest in the
preparation or publication of this research.



\section*{Tables}

{\label{tables}}

Table 1: Summary statistics of sample

{\label{table-1-summary-statistics-of-sample}}\selectlanguage{english}
\begin{longtable}[]{@{}lllllllll@{}}
\toprule
\textbf{Variable} & \textbf{units} & \textbf{25th} & \textbf{50th} &
\textbf{50th} & \textbf{75th} & \textbf{75th} & \textbf{mean} &
\textbf{mean}\tabularnewline
\midrule
\endhead
\emph{farm/farmer characteristics} & \emph{farm/farmer characteristics}
& & & & & & &\tabularnewline
farm size & ha & 1.11 & 2.02 & 2.02 & 3.64 & 3.64 & 3.30 &
3.30\tabularnewline
\# of plots & count & 2 & 3 & 3 & 4 & 4 & 4 & 4\tabularnewline
focal plot size & ha & 0.26 & 0.51 & 0.51 & 1.03 & 1.03 & 0.85 &
0.85\tabularnewline
household size & members & 4 & 5 & 5 & 7 & 7 & 6 & 6\tabularnewline
farmer age & years & 38 & 48 & 48 & 59 & 59 & 49 & 49\tabularnewline
farmer education & years & 8 & 8 & 8 & 8 & 8 & 7 & 7\tabularnewline
female & binary & - & - & - & - & - & 0.13 & 0.13\tabularnewline
\emph{focal plot characteristics} & & & & & & & &\tabularnewline
yield & kg ha\textsuperscript{-1} & 1,112 & 2,748 & 2,748 & 4,464 &
4,464 & 2,996 & 2,996\tabularnewline
used fertilizer & binary & - & - & - & - & - & 0.32 &
0.32\tabularnewline
N (for fertilizer users) & kg ha\textsuperscript{-1} & 38 & 60 & 60 &
101 & 101 & 84 & 84\tabularnewline
P (for fertilizer users) & kg ha\textsuperscript{-1} & 0 & 10 & 10 & 55
& 55 & 38 & 38\tabularnewline
K (for fertilizer users) & kg ha\textsuperscript{-1} & 0 & 0 & 0 & 0 & 0
& 3 & 3\tabularnewline
available carbon & ppm & 341 & 472 & 472 & 632 & 632 & 513 &
513\tabularnewline
total carbon & ppm & 4,673 & 6,604 & 6,604 & 9,919 & 9,919 & 8,604 &
8,604\tabularnewline
topsoil pH & pH & 5.6 & 6.1 & 6.1 & 6.5 & 6.5 & 6.1 & 6.1\tabularnewline
intercropped & binary & - & - & - & - & - & 0.54 & 0.54\tabularnewline
legume rotation & binary & - & - & - & - & - & 0.09 &
0.09\tabularnewline
compost & binary & - & - & - & - & - & 0.01 & 0.01\tabularnewline
manure & binary & - & - & - & - & - & 0.19 & 0.19\tabularnewline
crop residues retained & binary & - & - & - & - & - & 0.06 &
0.06\tabularnewline
herbicide & binary & - & - & - & - & - & 0.01 & 0.01\tabularnewline
pesticide & binary & - & - & - & - & - & 0.01 & 0.01\tabularnewline
improved seed & binary & - & - & - & - & - & 0.33 & 0.33\tabularnewline
n. weedings & count & 1 & 2 & 2 & 2 & 2 & 1.57 & 1.57\tabularnewline
disease & binary & - & - & - & - & - & 0.12 & 0.12\tabularnewline
striga & binary & - & - & - & - & - & 0.03 & 0.03\tabularnewline
fallowed w/in 3 years & binary & - & - & - & - & - & 0.05 &
0.05\tabularnewline
erosion control structures & binary & - & - & - & - & - & 0.14 &
0.14\tabularnewline
terraced & binary & - & - & - & - & - & 0.04 & 0.04\tabularnewline
sloped & binary & - & - & - & - & - & 0.77 & 0.77\tabularnewline
rainfall & mm & 322 & 383 & 383 & 759 & 759 & 528 & 528\tabularnewline
rainfall CV & CV & 0.49 & 0.65 & 0.65 & 0.85 & 0.85 & 0.66 &
0.66\tabularnewline
\bottomrule
\end{longtable}

Notes: Summary statistics calculated for the 553 observations recorded
in year 2017.

Table 2: Production function estimates

{\label{table-2-production-function-estimates}}\selectlanguage{english}
\begin{longtable}[]{@{}llllllllllllll@{}}
\toprule
& & (1) & (1) & (2) & (2) & (3) & (3) & (4) & (4) & (5) & (5) & (6) &
(6)\tabularnewline
\midrule
\endhead
& & POLS & POLS & POLS & POLS & CRE & CRE & CRE & CRE & FE & FE & FE &
FE\tabularnewline
N & N & 9.430*** & 9.430*** & 9.180*** & 9.180*** & 7.474** & 7.474** &
7.196** & 7.196** & 12.99*** & 12.99*** & 12.00*** &
12.00***\tabularnewline
& & (2.764) & (2.764) & (2.821) & (2.821) & (3.097) & (3.097) & (3.158)
& (3.158) & (4.360) & (4.360) & (4.356) & (4.356)\tabularnewline
N\^{}2 & N\^{}2 & -0.0155*** & -0.0155*** & -0.0153*** & -0.0153*** &
-0.0133*** & -0.0133*** & -0.0131*** & -0.0131*** & -0.0256*** &
-0.0256*** & -0.0259*** & -0.0259***\tabularnewline
& & (0.00470) & (0.00470) & (0.00465) & (0.00465) & (0.00479) &
(0.00479) & (0.00476) & (0.00476) & (0.00923) & (0.00923) & (0.00884) &
(0.00884)\tabularnewline
POXC & POXC & 0.438 & 0.438 & 0.432 & 0.432 & 0.483 & 0.483 & 0.475 &
0.475 & & & &\tabularnewline
& & (0.349) & (0.349) & (0.350) & (0.350) & (0.352) & (0.352) & (0.353)
& (0.353) & & & &\tabularnewline
N*POXC & N*POXC & 0.00481*** & 0.00481*** & & & 0.00443** & 0.00443** &
& & 0.00767*** & 0.00767*** & &\tabularnewline
& & (0.00172) & (0.00172) & & & (0.00194) & (0.00194) & & & (0.00221) &
(0.00221) & &\tabularnewline
N*POXC*log(rain) & N*POXC*log(rain) & & & 0.000819** & 0.000819** & & &
0.000767** & 0.000767** & & & 0.00153*** & 0.00153***\tabularnewline
& & & & (0.000330) & (0.000330) & & & (0.000362) & (0.000362) & & &
(0.000440) & (0.000440)\tabularnewline
log(rain) & log(rain) & 3,162*** & 3,162*** & 3,172*** & 3,172*** &
4,188*** & 4,188*** & 4,201*** & 4,201*** & 4,092*** & 4,092*** &
4,112*** & 4,112***\tabularnewline
& & (955.1) & (955.1) & (954.8) & (954.8) & (1,108) & (1,108) & (1,108)
& (1,108) & (1,175) & (1,175) & (1,174) & (1,174)\tabularnewline
CV(rain) & CV(rain) & -1,167 & -1,167 & -1,168 & -1,168 & -943.4 &
-943.4 & -940.2 & -940.2 & -2,077** & -2,077** & -2,042** &
-2,042**\tabularnewline
& & (875.1) & (875.1) & (874.4) & (874.4) & (907.6) & (907.6) & (907.1)
& (907.1) & (1,006) & (1,006) & (1,003) & (1,003)\tabularnewline
Observations & Observations & 607 & 607 & 607 & 607 & 607 & 607 & 607 &
607 & 498 & 498 & 498 & 498\tabularnewline
R-squared & R-squared & 0.343 & 0.343 & 0.343 & 0.343 & 0.358 & 0.358 &
0.358 & 0.358 & 0.261 & 0.261 & 0.263 & 0.263\tabularnewline
Estimator & Estimator & POLS & POLS & POLS & POLS & CRE & CRE & CRE &
CRE & FE & FE & FE & FE\tabularnewline
HH, farm \& plot controls & Yes & Yes & Yes & Yes & Yes & Yes & Yes &
Yes & Yes & Yes & Yes & Yes &\tabularnewline
Plot management controls & Yes & Yes & Yes & Yes & Yes & Yes & Yes & Yes
& Yes & Yes & Yes & Yes &\tabularnewline
Mundlak-Chamberlain controls & No & No & No & No & Yes & Yes & Yes & Yes
& -- & -- & -- & -- &\tabularnewline
District fixed-effects & Yes & Yes & Yes & Yes & Yes & Yes & Yes & Yes &
-- & -- & -- & -- &\tabularnewline
Year fixed-effects & Yes & Yes & Yes & Yes & Yes & Yes & Yes & Yes & Yes
& Yes & Yes & Yes &\tabularnewline
\bottomrule
\end{longtable}

Notes: The dependent variable in all models is maize yield measured in
kg ha\textsuperscript{-1}. N = nitrogen; POXC = active carbon; CV =
coefficient of variation. Rainfall measured in 10-day periods during the
growing season for the survey year. Standard errors are cluster robust
at the household level. Significance denoted by * (p\textless{}0.1), **
(p\textless{}0.05) and *** (p\textless{}0.01). Full results shown in
appendix (table A1).

\par\null{\label{section-2}}

Table 3: Partial effects of nitrogen and active carbon (estimates from
Fixed Effects models)

{\label{table-3-partial-effects-of-nitrogen-and-active-carbon-estimates-from-fixed-effects-models}}\selectlanguage{english}
\begin{longtable}[]{@{}lll@{}}
\toprule
& (1) & (2)\tabularnewline
\midrule
\endhead
& Fixed Effects estimates & Fixed Effects estimates\tabularnewline
& w/ N*POXC interaction & w/ N*POXC*log(rainfall)
interaction\tabularnewline
MP at POXC=220 (10th pctile) & 13.20*** & 12.59***\tabularnewline
& (3.921) & (3.882)\tabularnewline
MP at POXC=337 (25th pctile) & 14.09*** & 13.69***\tabularnewline
& (3.936) & (3.884)\tabularnewline
MP at POXC=481 (50th pctile) & 15.20*** & 15.07***\tabularnewline
& (3.979) & (3.923)\tabularnewline
MP at POXC=696 (75th pctile) & 16.85*** & 17.11***\tabularnewline
& (4.088) & (4.053)\tabularnewline
MP at POXC=954 (90th pctile) & 18.84*** & 19.57***\tabularnewline
& (4.286) & (4.311)\tabularnewline
\selectlanguage{greek}Δ \selectlanguage{english}MP: 25th-75th POXC pctile & 20\% & 25\%\tabularnewline
\selectlanguage{greek}Δ \selectlanguage{english}MP: 10th-90th POXC pctile & 43\% & 55\%\tabularnewline
\bottomrule
\end{longtable}

Notes: Table shows partial effects of nitrogen (N) and active carbon
(POXC) from Fixed Effects models in table 2. Standard errors are cluster
robust at the household level. Standard errors are cluster robust at the
household level. Significance denoted by * (p\textless{}0.1), **
(p\textless{}0.05) and *** (p\textless{}0.01).

Table 4: Partial effects of nitrogen at different levels of active
carbon in sample (estimates from Fixed Effects models)

{\label{table-4-partial-effects-of-nitrogen-at-different-levels-of-active-carbon-in-sample-estimates-from-fixed-effects-models}}\selectlanguage{english}
\begin{longtable}[]{@{}lll@{}}
\toprule
& (1) & (2)\tabularnewline
\midrule
\endhead
& Fixed Effects estimates & Fixed Effects estimates\tabularnewline
& w/ N*POXC interaction & w/ N*POXC*log(rainfall)
interaction\tabularnewline
MP at POXC=220 (10th pctile) & 13.20*** & 12.59***\tabularnewline
& (3.921) & (3.882)\tabularnewline
MP at POXC=337 (25th pctile) & 14.09*** & 13.69***\tabularnewline
& (3.936) & (3.884)\tabularnewline
MP at POXC=481 (50th pctile) & 15.20*** & 15.07***\tabularnewline
& (3.979) & (3.923)\tabularnewline
MP at POXC=696 (75th pctile) & 16.85*** & 17.11***\tabularnewline
& (4.088) & (4.053)\tabularnewline
MP at POXC=954 (90th pctile) & 18.84*** & 19.57***\tabularnewline
& (4.286) & (4.311)\tabularnewline
\selectlanguage{greek}Δ \selectlanguage{english}MP: 25th-75th POXC pctile & 20\% & 25\%\tabularnewline
\selectlanguage{greek}Δ \selectlanguage{english}MP: 10th-90th POXC pctile & 43\% & 55\%\tabularnewline
\bottomrule
\end{longtable}

Notes: Table shows partial effects of nitrogen at
10\textsuperscript{th}, 25\textsuperscript{th}, 50\textsuperscript{th},
75\textsuperscript{th} and 90\textsuperscript{th} percentile of active
carbon in the sample, from the Fixed Effects models reported in table 2.
Standard errors are cluster robust at the household level. Standard
errors are cluster robust at the household level. Significance denoted
by * (p\textless{}0.1), ** (p\textless{}0.05) and ***
(p\textless{}0.01).

Table 5: Distribution of MP and AP estimates

{\label{table-5-distribution-of-mp-and-ap-estimates}}\selectlanguage{english}
\begin{longtable}[]{@{}llllllll@{}}
\toprule
physical product & 10th & 25th & 50th & 75th & 90th & mean &
std.dev.\tabularnewline
\midrule
\endhead
MP & 7.77 & 11.35 & 13.65 & 15.84 & 18.22 & 12.87 & 5.46\tabularnewline
AP & 9.09 & 10.03 & 11.50 & 13.45 & 14.97 & 11.73 & 2.49\tabularnewline
\bottomrule
\end{longtable}

Note: MP and AP estimates come from the Fixed Effects model
corresponding to column 5 in table 2. MP is calculated for each
household using sample values. AP is calculated as the difference
between the estimated difference in yields resulting from zero
fertilizer and yields resulting from 200 kg ha\textsuperscript{-1} of
nitrogen (the level at which MVCR=1, on average, when using a farmgate
maize-nitrogen price ratio of 0.15), with other sample values as
observed.

\par\null{\label{section-3}}

Table 6: Maize and N price assumptions used in profitability
calculations

{\label{table-6-maize-and-n-price-assumptions-used-in-profitability-calculations}}\selectlanguage{english}
\begin{longtable}[]{@{}llll@{}}
\toprule
Price ratios used for profitability analysis & maize (USD/kg) & nitrogen
(USD/kg) & maize/N price ratio\tabularnewline
\midrule
\endhead
wholesale price ratio: 0.22 & 0.27 & 1.22 & 0.22\tabularnewline
farmgate price ratio: 0.18 & 0.24 & 1.33 & 0.18\tabularnewline
farmgate price ratio: 0.15 & 0.21 & 1.44 & 0.15\tabularnewline
farmgate price ratio: 0.12 & 0.18 & 1.55 & 0.12\tabularnewline
farmgate price ratio: 0.09 & 0.15 & 1.66 & 0.09\tabularnewline
\bottomrule
\end{longtable}

\par\null{\label{section-4}}

Table 7: Profitability distributions under alternative maize-N price
ratios

{\label{table-7-profitability-distributions-under-alternative-maize-n-price-ratios}}\selectlanguage{english}
\begin{longtable}[]{@{}lllllllllll@{}}
\toprule
MVCR & 10th & 25th & 50th & 75th & 90th & mean & std.dev. &
MVCR\textgreater{}0 & MVCR\textgreater{}1 &
MVCR\textgreater{}2\tabularnewline
\midrule
\endhead
wholesale price ratio: 0.22 & 1.72 & 2.51 & 3.02 & 3.51 & 4.03 & 2.85 &
1.21 & 96\% & 94\% & 88\%\tabularnewline
farmgate price ratio: 0.18 & 1.40 & 2.05 & 2.46 & 2.86 & 3.29 & 2.32 &
0.99 & 96\% & 94\% & 77\%\tabularnewline
farmgate price ratio: 0.15 & 1.13 & 1.66 & 1.99 & 2.31 & 2.66 & 1.88 &
0.80 & 96\% & 92\% & 48\%\tabularnewline
farmgate price ratio: 0.12 & 0.90 & 1.32 & 1.58 & 1.84 & 2.12 & 1.49 &
0.63 & 96\% & 88\% & 16\%\tabularnewline
farmgate price ratio: 0.09 & 0.70 & 1.03 & 1.23 & 1.43 & 1.65 & 1.16 &
0.49 & 96\% & 78\% & 1\%\tabularnewline
AVCR & 10th & 25th & 50th & 75th & 90th & mean & std.dev. &
AVCR\textgreater{}1 & AVCR\textgreater{}1.5 &
AVCR\textgreater{}2\tabularnewline
wholesale price ratio: 0.22 & 2.01 & 2.22 & 2.55 & 2.98 & 3.31 & 2.60 &
0.55 & 99\% & 98\% & 90\%\tabularnewline
farmgate price ratio: 0.18 & 1.64 & 1.81 & 2.08 & 2.43 & 2.70 & 2.12 &
0.45 & 99\% & 95\% & 56\%\tabularnewline
farmgate price ratio: 0.15 & 1.33 & 1.46 & 1.68 & 1.96 & 2.18 & 1.71 &
0.36 & 98\% & 71\% & 22\%\tabularnewline
farmgate price ratio: 0.12 & 1.06 & 1.16 & 1.34 & 1.56 & 1.74 & 1.36 &
0.29 & 94\% & 30\% & 2\%\tabularnewline
farmgate price ratio: 0.09 & 0.82 & 0.91 & 1.04 & 1.22 & 1.35 & 1.06 &
0.22 & 56\% & 2\% & 0\%\tabularnewline
\bottomrule
\end{longtable}

Note: Calculations based on the MP and AP estimates shown in table 5,
against each of the price-ratio assumptions in table 6.

\section*{Figures}

{\label{figures}}

Figure 1: Survey locations

{\label{figure-1-survey-locations}}

{[}Figure 1 here{]}

\par\null

Figure 2: Estimated AVCR over distribution of active carbon in sample

{\label{figure-2-estimated-avcr-over-distribution-of-active-carbon-in-sample}}

{[}Figure 2 here{]}

Note: Vertical red lines indicate 10\% and
90\textsuperscript{th}percentiles of the distribution of POXC measures
in the sample. AVCR estimates use AP estimates from the fixed effects
model with N*POXC*log(rainfall) interaction (column 6 in table 2), and a
farmgate maize-nitrogen price ratio of 0.15.

Figure 3: Estimated AVCR over distribution of seasonal rainfall in
sample

{\label{figure-3-estimated-avcr-over-distribution-of-seasonal-rainfall-in-sample}}

{[}Figure 3 here{]}

Note: Vertical red lines indicate 10\% and
90\textsuperscript{th}percentiles of the distribution of seasonal
rainfall totals in the sample. AVCR estimates use AP estimates from the
fixed effects model with N*POXC*log(rainfall) interaction (column 6 in
table 2), and a farmgate maize-nitrogen price ratio of 0.15.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure-1/Figure-1}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure-2/Figure-2}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure-3/Figure-3}

\end{center}
\end{figure}

\selectlanguage{english}
\FloatBarrier
\end{document}

