The role of active soil carbon in influencing the profitability of fertilizer use: Empirical evidence from smallholder maize plots in Tanzania

Abstract We use recent plot‐level panel data from Tanzanian smallholder farmers to investigate maize yield responses to inorganic fertilizer under variable soil carbon conditions. Unlike many prior studies which consider total carbon measurements, we focus on active soil carbon, which is a component strongly related to key soil functions, such as nutrient cycling and availability. Active soil carbon is found to be a strong predictor of maize yield response to nitrogen fertilizer. 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, 39% of farmer plots have an average value‐cost ratio greater than 1.5 at a maize‐nitrogen price ratio of 0.15. That share drops to 4% at a price ratio of 0.12 and 0% at a price ratio of 0.09. Our findings provide insights into the intertwined biophysical and economic underpinnings of low levels of fertilizer use in Tanzania and elsewhere in the region. Raising active carbon stocks in smallholder systems may be a strategic priority in many areas for incentivizing greater use of inorganic fertilizer, reversing land degradation, and achieving sustainable agricultural intensification.


| MOTIVATION
Staple crop yields in subSaharan Africa (SSA) remain very low by international standards, with yield gaps on the order of 80% (van Ittersum et al., 2016). Inorganic fertilizer is widely agreed to be the technology with the greatest potential to raise yields in SSA's smallholder systems (Holden, 2018;Vanlauwe et al., 2014). Inorganic fertilizer also greatly promotes crop biomass and is therefore an important component of an integrated and sustainable soil fertility management strategy.
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 21st century given its pivotal role in food production, and nowhere is this more important than in subSaharan Africa where a strong negative relationship has been observed between soil nitrogen balances and population density (Drechsel, Gyiele, Kunze, & Cofie, 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-that is, 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 farmgate crop and fertilizer prices are applied (Burke, Jayne, & Black, 2017;Jayne & Rashid, 2013;Koussoubé & Nauges, 2017;Liverpool-Tasie, Omonona, Sanou, & Ogunleye, 2017;Marenya & Barrett, 2009;Sheahan, Black, & Jayne, 2013;Theriault, Smale & Haider, 2018;Xu, Guan, Jayne, & Black, 2009). 1 Relatedly, fertilizer is not profitable for many farmers even where the 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 (Drechsel et al., 2001;Marenya & Barrett, 2009), 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, de Janvry, Sadoulet, & Dar, 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 subplot 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 active soil carbon. Our production function estimates indicate that the marginal product (i.e., agronomic efficiency 2 ) of nitrogen increases by 16-21% when moving from the 25th to the 75th percentile of active 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 an average value cost ratio (AVCR) >1.5 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 versus studies relying on farm trials and demonstration plots (e.g., Jama, Kimani, Harawa, Mavuthu, & Sileshi, 2017), which tend to benefit from researcher management protocols that many smallholder farmers may not be able to replicate (Snapp, Jayne, Mhango, Benson, & Ricker-Gilbert, 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 article 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.

| 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).

| 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 (Shepherd, Shepherd, & Walsh, 2015;Walsh & Vågen, 2006). 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 nonfarm 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. We drop observations with fertilizer application rates exceeding 700 kg ha −1 , as implausible and likely to derive from data entry error. 3 Maize yields on focal plots were measured using crop cuts from three 5 × 5 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.
Total organic carbon, despite its well-recognized importance as an indicator of overall soil quality, is not an ideal indicator of nutrient availability because much of the bulk soil organic matter is relatively inert (Drinkwater, Wagoner, & Sarrantonio, 1998). 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 by farmer practices (Zingore, Delve, Nyamangara, & Giller, 2008). Thus, rather than testing for total carbon, as is often the case in standardized soil testing, testing the active organic matter pool provides better insight into how changes in management affect nutrient cycling and potential soil carbon accumulation or loss (Haynes, 2005;Wander, 2004). The active carbon pool, while constituting a small fraction (5-20%) of the soil's total organic matter, is the component that greatly influences key soil functions, such as nutrient cycling and availability, soil aggregation, and soil carbon accumulation (Grandy & Robertson, 2007;Schmidt et al., 2011;Six, Elliott, Paustian, & Doran, 1998;Wander, 2004). Hence, in this analysis, we focus on the factors influencing active carbon.
Developments in laboratory assays to monitor 'active' soil organic matter fractions have highlighted the value of permanganate oxidizable carbon (POXC) as an early indicator of management influence on soil organic carbon (Culman et al., 2012). We acknowledge that there are other laboratory analyses that track this fraction. At the same time, POXC is a widely used indicator and we standardize for the purposes of this study on the term 'active carbon' to refer to POXC results. Total soil organic carbon also provides insights regarding sustainable soil management, although at a slow timestep (5-10 years).
For this work, POXC was determined on a ground (1 mm sieve) subsample, oxidized with 0.02 M KMnO 4 , and subsequently absorbance was read of the liquid phase at a wavelength of 550 nm (Culman et al., 2012). POXC (mg kg −1 ) = [0.02 M − (a + b × Abs)] × (9,000 mg C mol −1 ) × (0.02 L solution/Wt) where 0.02 M is KMnO 4 solution F I G U R E 1 Survey locations initial concentration, a is the intercept, b is the standard curve slope, Abs is the absorbance of the unknown soil sample, 9,000 mg is the amount of C oxidized by 1 mol of MnO 4 changing from Mn 7+ to Mn 2 + , 0.02 L is the volume of KMnO 4 solution reacted, and Wt is the mass of soil (kg) (Weil, Islam, Stine, Gruver, & Samson-Liebig, 2003). To address potential measurement error in our analysis, and under the assumption that the soil properties of interest here are comparatively stable in the very short term, we use the average measure across the two consecutive 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.

| Estimation strategy
The intent of this article 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): Because farmers in Tanzania use a variety of fertilizer blends, we integrate these decisions be decomposing each blend into its macronutrient content, that is, nitrogen (N), phosphorus (P) and potassium (K). Other management factors include improved maize seed, maizelegume 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 (striga asiatica, a.k.a. 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: Where: N is nitrogen, our primary input of interest, i indexes plots, t indexes observations over time, and where, for convenience, we have subsumed M and G in the vector X. As indicated earlier, a priori hypotheses include the possibility of positive interactions between nitrogen, soil organic carbon and rainfall, after controlling for other factors. 4 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: 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. 5 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 unobserved o it is unlikely to be a major issue. Our larger concern is with timeinvariant 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 (Wooldridge, 2010), as well as a fixed effects estimator.

| Descriptive statistics
Summary statistics on our dataset are reported in Table 1. The average farm size is 3.3 ha, and is comprised of four plots. Most of our sample consists of farms in the 1-4 ha range, which is typical for smallholder systems in the region. Only 7% had a single plot, and 14% had more than five plots. The mean and median focal plot sizes are 0.85 and 0.51 ha, respectively. A total of 13% 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 −1 . 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. 6 Of these fertilizer users, there is considerable variability in fertilizer application rates, with a median rate of 60 kg ha −1 of nitrogen (somewhat below regional recommendations). 7

| Agronomic returns to nitrogen
Production function coefficient estimates are shown in Table 2 (we show estimation results for the variables of primary interest in this discussion; full results are reported in Table S1). 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 nonlinear 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-that is, the correlated random effects (CRE) model-to address unobserved heterogeneity, but are otherwise similar to the first two specifications. Specifications (5) and (6)  Note: The dependent variable in all models is maize yield measured in kg ha −1 . Rainfall measured in 10-day periods during the growing season for the survey year. SEs are cluster robust at the household level. Full results shown in Table S1 Abbreviations: CV, coefficient of variation; N, nitrogen; POXC, active carbon *p < .1 **p < .05 ***p < .01 T A B L E 3 Partial effects of nitrogen and active carbon (estimates from fixed effects models) 25 kg for Uganda (Matsumoto & Yamano, 2013), 21-25 kg for Malawi (Harou, Liu, Barrett, & You, 2017), 19 kg for Burkina Faso (Koussoubé & Nauges, 2017). Our results are somewhat higher than Mather, Minde, Waized, Ndyetabula, and Temu (2016) found for Tanzania using LSMS-ISA data (7-8 kg). 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 similar across all model specifications. 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 250 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 75th percentile of the MP distribution has an expected MP that 28% larger than that of a farmer at the 25th percentile.

| Economic returns to nitrogen
To translate these agronomic responses into profitability terms, we  for Tanzania: data on the average maize wholesale prices in regional   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 2.52 (at the market price ratio of 0.22) to 1.03 (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., Morris, Kelly, Kopicki, & Byerlee, 2007;Sheahan et al., 2013;Xu et al., 2009), an MVCR of two or more has conventionally been used by agricultural economists as the level of returns required to induce fertilizer adoption by smallholders, based on empirical observations of fertilizer use patterns in the region. However, as Morris et al. (2007) also note, in especially risky production contexts, value-cost ratios of 3 or 4 may be required to incentive adoption by smallholders.
AVCR estimates show similar cross-sectional variability, with mean values ranging between 2.21 (at price ratio = 0.22) to 0.90 (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., Sheahan et al., 2013;Xu et al., 2009). The share of farmers in the sample with AVCR estimates exceeding 1.5 or 2 is very sensitive to price ratio assumptions: at a price ratio of 0.15 only 39 and 2% 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. There is a growing body of evidence from the region that modest MVCR and AVCR returns to fertilizer use on maize is the norm for smallholder agriculture (Burke et al., 2017;Sheahan et al., 2013). This could in large part be due to agronomic practices that are ineffective at maintaining soil productivity or adequate weed control (Burke, Snapp, & Jayne, 2020).
Further, 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, Stifel, & Koro, 2013). The implications of economic remoteness have been well described (e.g., Chamberlin & Jayne, 2013;Stifel & Minten, 2008). 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 nonparametric function of active carbon. This graph illustrates that at lower concentrations of active 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.

| DISCUSSION
Our results indicate that while the marginal and average agronomic returns to inorganic fertilizer use are generally positive, there are Note: Calculations based on the MP and AP estimates shown in Table 5, against each of the price ratio assumptions in Table 6 Abbreviations: AVCR, average value-cost ratio; MVCR, marginal value-cost ratio F I G U R E 2 Estimated average value-cost ratio (AVCR) over distribution of active carbon in sample. Vertical red lines indicate 10% and 90th 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. POXC is measured as mg kg −1 [Colour figure can be viewed at wileyonlinelibrary.com] strong variations in these returns over our sample. We have shown that both early season rainfall and active soil carbon are important conditioners of yield responses to nitrogen. The active soil carbon as indicated by POXC has been shown to be correlated with soil nitrogen availability, and vigorous maize growth (Culman, Snapp, Gentry, & Green, 2013). 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.
One caveat to our analysis is the fact that we do not observe long-term historical patterns of management. A plot which has received relatively high levels of organic and inorganic fertilizers in the past may benefit from the residual effects of those soil amendments, as well as have higher levels of organic carbon (Njoroge, Schut, Giller, & Zingore, 2019). While we cannot entirely rule out this possibility, our panel estimation framework does address time-invariant unobserved heterogeneity as well as effects that change slowly over time, which may include cumulative nutrient buildup. 11 On balance, the findings we present in this article 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, Snapp, & Kanyama-Phiri, 2013;Tittonell, Vanlauwe, Corbeels, & Giller, 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, that is, 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 rerun 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 even lower. 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 active soil carbon has 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, for example, Nord and Snapp (2020) F I G U R E 3 Estimated average value-cost ratio (AVCR) over distribution of seasonal rainfall in sample. Vertical red lines indicate 10% and 90th 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 [Colour figure can be viewed at wileyonlinelibrary.com] Lal, 2006). New technologies that can measure active carbon using handheld spectral devices on farmer's fields will move this project forward, as information will be provided in real time using nonlaboratory, inexpensive methods (TerAvest, Austic, Tu, & Snapp, 2019).
Current agricultural policies often miss the mark, as there is growing evidence-including this study-regarding the accumulation of active soil carbon as being necessary to raise yield responses sufficiently for nitrogen fertilizer to become economically attractive. This may be particularly valid for risk adverse farmers in areas facing high transport costs to regional input and output markets. Failure to address these issues may continue to stall the process of sustainably raising fertilizer use on the majority of Africa's smallholder farms.
There is rising urgency in this challenge, as the closure of the land frontier in many African farming areas has led to more frequent continuous cropping of plots, which, without greater usage of fertilizers, will certainly contribute to land degradation and rural poverty (Barbier & Hochard, 2012). Our analysis aligns with other assessments of soil carbon depletion as a major soil degradation concern within the region's smallholder farming systems (Lal, 2006). There is need for more evidence regarding smallholder farm practices that are feasible to adopt, and that increase active soil carbon. Long-term field experimentation has shown that promising options include crop residues and mixed cropping systems that provide enhanced vegetative cover, although economic assessments have been limited to date (Beedy, Snapp, Akinnifesi, & Sileshi, 2010;Cong et al., 2015).
Success in investing in soil organic carbon can also help mitigate the variability of yields in the face of highly variable weather and a changing climate (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.
Low 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. Because of its role in promoting greater crop biomass (including roots), inorganic fertilizer is usually a crucial component of a sustainable agricultural intensification strategy, and its use will need to rise rapidly to arrest the land degradation processes already evident in areas where the land frontier has been reached and where continuous cultivation has become the norm.
This article 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 agronomic efficiency of nitrogen is positively associated with both soil organic carbon stocks (measured as active carbon), as well as by seasonal rainfall.

CONFLICT OF INTEREST
The authors declare no conflicts of interest. (such as nitrogen fertilizer) is referred to by economist as marginal product or marginal physical product; in the agronomy literature this is referred to as agronomic efficiency.
3 However, we may note that this does not affect our results qualitatively. We obtain similar results from models run on the entire sample, models run on the sample with outliers dropped, and models run on the sample with winsorized outliers. In the case of winsorizing, we replaced N application rates exceeding 700 kg ha −1 with that value, which is tantamount to winsorizing at the 99th 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). However, as noted, these outlier management choices do not materially affect our analytical conclusions. 4 Our assumption of positive interactions between nitrogen, soil organic carbon and rainfall is grounded in the context of no excessive rainfall, which was the case in our study. However, it should be acknowledged that such interactions may be negative at excessively high levels of rainfall. Such interactions may also be negative under conditions of very high organic matter content, especially when the latter derives from nitrogen fixing trees or excessive green manuring. The latter conditions are also unlikely to be the case in our study sample. We thank an anonymous reviewer for raising this issue. 5 Burke et al. (2017) provide a useful, detailed discussion of these issues and corresponding identification strategies in survey data settings. 6 Sheahan and Barrett (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. 7 Sheahan and Barrett (2017) found that fertilizer users applied an average of 32 kg ha −1 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. 8 For comparison, we also estimated models which used total carbon instead of POXC. Coefficient estimates and marginal effects of N and carbon from these models are shown in Tables S2 and S3. The results with total carbon show a smaller direct association with carbon on yield outcomes and show less significant interaction effects with yield response to N, although the direct yield responses to N in these models were otherwise very similar. It is possible that in some other empirical settings, well-measured estimates of total carbon may give useful insights into interaction effects, although in our analysis it proved to be of little analytical value, despite the positive correlation between total carbon and active carbon.