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.