Results
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-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.
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-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 (10th, 25th,
50th, 75th, and
90th percentile, respectively), holding other factors
constant, focusing on the Fixed Effects model results. The direct impact
of moving from 337 ppm (the 25th percentile of our
sample) to 696 ppm (75th 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 10th to the
90th 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-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 75thpercentile of the MP distribution has an expected MP that is 40% larger
than that of a farmer at the 25th percentile.
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>1 drops notably with price ratio reductions, and the
share of farmers with MVCR>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.