Farm Size, Soil Investment, and Quality: Theory and Evidence from a Panel Data Set in Tanzania

Abstract

Achieving sustainable agricultural development is a vital concern as soil degradation poses a growing threat to the livelihoods of smallholder farmers in the developing world. Previous literature has highlighted the potential for rural population growth to exacerbate this concern by leading to smaller farm sizes and crop production on marginal land. This paper uses a theoretical model to demonstrate a countervailing effect consistent with the work of Esther Boserup: Smaller farm sizes can encourage greater intensification and investment in the soil. Using panel data from the Tanzania National Panel Survey, I test the model and find some evidence consistent with this effect. Smaller farms are associated with greater organic, but not inorganic, fertilizer application, and higher levels of some soil quality proxies. These results suggest that if key resource and information constraints are overcome, population growth need not be an obstacle, and can be a boon, to sustainable agricultural development.

Keywords:

• farm size
• soil quality
• soil investment
• fertilizer

JEL Classification Codes:

• O12
• O13
• Q12
• Q15
• Q56

Acknowledgements

I’m deeply thankful to Leah Bevis, Corinne Bocci, Jian Chen, Julie Laudick Dougherty, Jon Einar Flatnes, Richard Gallenstein, Mario Miranda, Khusbhu Mishra, and Abdoul Sam for their helpful comments.

Disclosure statement

No potential conflict of interest was reported by the author.

Data availability statement

The data are publicly available at https://microdata.worldbank.org/index.php/home and the code is included as a supplementary file, please feel free to contact me at [email protected] with any questions.

Notes

1 While applying inorganic fertilizer is fastest and most labor efficient of restoring key nutrients, especially Nitrogen, ISFM practices are key for promoting long-term soil health, water retention, and increasing the agronomic efficiency of inorganic fertilizer (Jayne et al., 2019, Vanlauwe et al., 2011).

2 An important caveat is that self-reported labor-per-acre measurements have been shown to be very inaccurate, with Arthi, Beegle, De Weerdt, and Palacios-López (2018) finding that farmer recall estimates in Tanzania can vary by as much as a factor of 3.7 from weekly surveys. If this bias was greater for smaller farms it could weaken or eliminate this effect. However, the authors show this bias is larger for plots with greater area, so here I may actually understate the relative difference in labor per acre between smaller and larger farms.

3 First, I assume there is an efficient labor market, such that labor per acre remains constant as L increases. Second, I allow the total factor productivity parameter $\varphi$ to be a function of L. There are reasons to expect $\varphi$ may decrease with L at smaller values, such as the edge effect described in Bevis and Barrett (2020), and also reasons why $\varphi$ may increase in L at larger values, as a larger area under cultivation can make fixed investments such as mechanization more profitable. These effects could lead to the possible U-shaped relationship described in recent literature (Omotilewa et al., 2021).

4 A more realistic assumption would be that the effect of fertilizer would be a function of soil quality such that $\psi (q)>0$ and $\psi \prime (q)<0.$ While this would certainly change the magnitudes of effects, the main qualitative result that greater farm output per acre on smaller farms due to an incomplete labor market (or some other factor) leads to a higher return to soil quality and thus a greater level of steady state fertilizer application per acre on smaller farms would remain true.

5 This is the case as long as the steady state optimum is an interior solution. This is not a concern for this model however, since the only corner solution is at f = 0 which implies q = 0 and zero consumption.

6 Total days of farm labor worked on a given plot per acre is the sum of family and hired labor. Roughly 63.32% of households used only family labor, consistent with the assumption in the theoretical model of imperfect labor markets.

7 The weather data from the first three waves and the robustness check output is available upon request.

8 I likewise find qualitatively similar results when using only the GPS-measured plots, with results available upon request.

9 For organic and inorganic fertilizer per acre, most households report using 0 units. To preserve this data when taking the log, I use the log of fertilizer per acre plus one. If fertilizer use is not logged or I simply take the log and drop the zero observations, the negative effect of farm size on organic fertilizer per acre is larger and more significant (the effect on inorganic fertilizer per acre becomes negative and significant when the zero observations are dropped). The effect of farm size on the incidence (as a binary variable as opposed to application rate per acre) of organic fertilizer application is insignificant and for inorganic fertilizer is positive and significant. Summarizing, farm size does not appear to impact whether farmers use organic fertilizer, but conditional on using it, smaller farms apply more per acre. Larger farms are more likely to use inorganic fertilizer than smaller ones, but conditional on using it, smaller farms apply more per acre.

10 Appendix B presents a robustness check using GPS-measured farm sizes, with missing farm sizes imputed through multiple imputation (Kilic et al., 2017). All of the main results presented here are robust except for these findings on fallowing and intercropping. Using multiple imputation on the GPS-measured farm size, fallowing becomes negatively and significantly associated with farm size and intercropping becomes negatively but insignificantly associated with farm size.

11 For an in-depth analysis of the factors leading to changing land prices in Tanzania, see (Wineman & Jayne, 2018).

12 Quintile regressions on farm size, available upon request, demonstrate that the impact of farm size on many key variables such as yield, crop value, land value, and labor inputs are relatively consistent with a linear model. The impact of land size on fertilizer use and the perceived soil quality variable appears to be more heavily concentrated in the smallest quintile.