Submitted:
07 April 2026
Posted:
09 April 2026
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Abstract
Keywords:
1.0. Introduction
2.0. Materials and Methods
2.1. Theoretical Framework
2.1.1. Subjective Expected Utility Theory
2.1.2. Theory of Production
2.2. Analytical Framework
2.2.1. Conditional Mixed Process
2.2.2. Stochastic Frontier Analysis
2.2.3. Variables and Measurements
2.3. Data Source
3.0. Results
3.1. Soil Conditions in Malawi
3.2. Maize Input Allocation and Maize Productivity
3.3. Effect of Subjective Soil Assessments on Maize Input Use
3.4. Effect of Knowledge of Soil Quality Attributes on Maize Productivity
4.0. Discussion
5.0. Conclusion and Policy Implications
6.0. Limitations of the study
Author’s contribution
Funding
Availability of data and materials
Acknowledgments
Declaration of Generative AI Use
Competing interests
References
- Abdul Mumin, Y.; Abu, B.M.; Nkegbe, P.K. (2023). Conditional Mixed Process Modeling: Applications from the Agriculture Sector in Ghana (pp. 269–300). [CrossRef]
- AGRA. Assessment of fertilizer distribution systems and opportunities for developing fertilizer blends: Malawi report 2018.
- Ajefu, J.B.; Abiona, O. The Mitigating Impact of Land Tenure Security on Drought-Induced Food Insecurity: Evidence from Rural Malawi 2021.
- Asfaw, S.; Pallante, G.; Palma, A. Distributional. impacts of soil erosion on agricultural productivity and welfare in Malawi. Ecological Economics 2020, 177, 106764. [Google Scholar] [CrossRef]
- Battese, G.E.; Coelli, T.J. A model for technical inefficiency effects in a stochastic frontier production function for panel data. Empirical Economics 1995, 20, 325–332. [Google Scholar] [CrossRef]
- Battese, G.E.; Coelli, T.J. A model for technical inefficiency effects in a stochastic frontier production function for panel data. Empirical Economics 1995, 20, 325–332. [Google Scholar] [CrossRef]
- Belotti, F.; Daidone, S.; Ilardi, G.; Atella, V. Stochastic. Frontier Analysis using Stata. The Stata Journal: Promoting Communications on Statistics and Stata 2013, 13, 719–758. [Google Scholar] [CrossRef]
- Berazneva, J.; McBride, L.; Sheahan, M.; Güereña, D. Empirical. assessment of subjective and objective soil fertility metrics in east Africa: Implications for researchers and policy makers. World Development 2018, 105, 367–382. [Google Scholar] [CrossRef]
- Bocquého, G.; Jacquet, F.; Reynaud, A. Expected. utility or prospect theory maximisers? Assessing farmers’ risk behaviour from field-experiment data. European Review of Agricultural Economics 2014, 41, 135–172. [Google Scholar] [CrossRef]
- Chen, J.; Roth, J. Logs. with Zeros? Some Problems and Solutions. The Quarterly Journal of Economics 2024, 139, 891–936. [Google Scholar] [CrossRef]
- Chikaya-Banda, J.; Chilonga, D. Key challenges to advancing land tenure security through land governance in Malawi: Impact of land reform processes on implementation efforts. Land Use Policy 2021, 110, 104994. [Google Scholar] [CrossRef]
- Cobb, C.W.; Douglas, P.H.A. Theory of Production. The American Economic Review 1928, 18, 135–165, https://doi.org/http://www.jstor.org/stable/1811556. [Google Scholar]
- Colman, D.; Young, T. Economics of agricultural production: theoretical foundations. In Principles of Agricultural Economics: Markets and Prices in Less Developed Countries. In Principles of Agricultural Economics;Wye Studies in Agricultural and Rural Development; Cambridge University PressCambridge University Press, 1989; pp. 5–29. [Google Scholar] [CrossRef]
- COSA. (2024, September 17). Agile Data Insights: From a fertilizer program in Malawi. https://www.theglobaleconomy.com/rankings/fertilizer_use/.
- DCAFS, & TIPDeP. (2025). Soil Health Update: Malawi’s Degradation Crisis and Pathways to Restoration. Development Consortium for Agroecological Food Systems & Technical Implementation Partnership for Development. https://www.dcafs-tipdep-donors-mw.org/update/soil-health-in-mw .
- DeYoreo, M.; Reiter, J.P. Bayesian Mixture Modeling for Multivariate Conditional Distributions. Journal of Statistical Theory and Practice 2020, 14, 45. [Google Scholar] [CrossRef]
- FAO. (2025, August 15). FAOSTAT: Crops and livestock products. https://www.fao.org/faostat/en/#data/QCL.
- Gautam, S. UNDERSTANDING. COBB-DOUGLAS PRODUCTION FUNCTION IN AGRICULTURAL ECONOMICS. Journal of Technology & Innovation 2024, 4, 75–78. [Google Scholar] [CrossRef]
- Harju, M.; Liesiö, J; Virtanen, K. Independent. postulates for subjective expected utility. Theory and Decision 2024, 96, 597–606. [Google Scholar] [CrossRef]
- Jolex, A. Influence. of agricultural extension services on technical efficiency of maize farmers in Malawi. African Journal of Agricultural and Resource Economics 2022, 17, 91–105. [Google Scholar] [CrossRef]
- Karakaplan, M.U. Estimating Endogenous Stochastic Frontier Models in Stata. The Stata Journal 2016. Available online: www.mukarakaplan.com.
- Karakaplan, M.U.; Kutlu, L. Endogeneity. in panel stochastic frontier models: an application to the Japanese cotton spinning industry. Applied Economics 2017, 49, 5935–5939. [Google Scholar] [CrossRef]
- Kemala Dewi, R.; Puji Mumpuni, R.; Iqbal Nurulhaq, M.; Julio Pratama, A.; Wiraguna, E.; Sekar Mardisiwi, R.; Hasian Situmeang, W.; Budiarto, T.; Kasman Hadi Saputra, H. Organic Fertilizer: Indonesia’s Legacy for a Sustainable Future 2025. [CrossRef]
- Kumbhakar, S.C.; Ghosh, S.; McGuckin, J.T.A. Generalized Production Frontier Approach for Estimating Determinants of Inefficiency in U.S. Dairy Farms. Journal of Business & Economic Statistics 1991, 9, 279–286. [Google Scholar] [CrossRef]
- Lalani, B.; Aminpour, P.; Gray, S.; Williams, M.; Büchi, L.; Haggar, J.; Grabowski, P.; Dambiro, J. Mapping. farmer perceptions, Conservation Agriculture practices and on-farm measurements: The role of systems thinking in the process of adoption. Agricultural Systems 2021, 191, 103171. [Google Scholar] [CrossRef]
- Lien, D.; Hu, Y.; Liu, L. Taking. logarithm when the independent variable contains zeros in regression analysis: a new approach. Applied Economics Letters 2025, 32, 630–636. [Google Scholar] [CrossRef]
- Makoni, J.L.; Nyandoro, G.; Shayanewako, Z.; Lotriet, R. Understanding. seed technology adoption and brand switching behavior among small-scale farmers in Southern Africa: A comparative study of Malawi, Mozambique, and Zimbabwe. Outlook on Agriculture 2025, 54, 285–292. [Google Scholar] [CrossRef]
- Marenya, P.P.; Barrett, C.B. Soil quality and fertilizer use rates among smallholder farmers in western Kenya. Agricultural Economics 2009, 40, 561–572. [Google Scholar] [CrossRef]
- Matchaya, G. Land ownership and productivity in Malawi: A conditional recursive mixed process analysis (1; 3) 2010.
- Muyanga, M.; Burke, W.J. The Future of Smallholder Farming in Malawi. ResearchGate 2020. [Google Scholar] [CrossRef]
- NSO. (2020). Integrated Household Panel Survey 2010-2013-2016-2019 (Long-Term Panel, 102 EAs). Living Standards Measurement Study (LSMS). https://doi.org/https://doi.org/10.48529/q5q1-2a34.
- Nyirenda, H.; Balaka, V. Conservation. agriculture-related practices contribute to maize (Zea mays L.) yield and soil improvement in Central Malawi. Heliyon 2021, 7, e06636. [Google Scholar] [CrossRef]
- Nyirenda, H.; Mwangomba, W.; Nyirenda, E.M. Delving into possible missing links for attainment of food security in Central Malawi: farmers’ perceptions and long term dynamics in maize (Zea mays L.) production. Heliyon 2021, 7, e07130. [Google Scholar] [CrossRef] [PubMed]
- Omondi, J. O.; Simwaka, P.; Kamwana, F.; Siyeni, D.; Arega, A.; Sika, G.; Kadwala Peter; Wupe, M.; Kyei-Boahen, S.; Chinwada, P.; Gbenga, A. Climate-smart cropping arrangement and integrated soil fertility technologies for maize and cowpea to enhance soil health, yield, and income in Malawi 2025.
- Ozaki, R.; Tsujimoto, Y.; Andriamananjara, A.; Rakotonindrina, H.; Sakurai, T. Optimizing. fertilizer use by providing soil quality information: experimental evidence from Madagascar. Agriculture & Food Security 2024, 13, 45. [Google Scholar] [CrossRef]
- Park, S.Y. Effect. of zero imputation methods for log-transformation of independent variables in logistic regression. Communications for Statistical Applications and Methods 2024, 31, 409–425. [Google Scholar] [CrossRef]
- Phillips, M.A. Inefficiency. in Japanese water utility firms: a stochastic frontier approach. Journal of Regulatory Economics 2013, 44, 197–214. [Google Scholar] [CrossRef]
- Reifschneider, D.; Stevenson, R. Systematic. Departures from the Frontier: A Framework for the Analysis of Firm Inefficiency. International Economic Review 1991, 32, 715. [Google Scholar] [CrossRef]
- Roodman, D. Fitting Fully Observed Recursive Mixed-process Models with cmp. The Stata Journal: Promoting Communications on Statistics and Stata 2011, 11, 159–206. [Google Scholar] [CrossRef]
- Salam, M.; Rukka, R.M.; Samma, M.A.N.K.; Tenriawaru, A.N.; Rahmadanih Muslim, A.I.; Ali, H.N.B.; Ridwan, M. The causal-effect model of input factor allocation on maize production: Using binary logistic regression in search for ways to be more productive. Journal of Agriculture and Food Research 2024, 16. [Google Scholar] [CrossRef]
- Savage; L.J. The foundations of statistics. Naval Research Logistics Quarterly 1954, 1, 236–236. [Google Scholar] [CrossRef]
- Smale, M.; Thériault, V.; Mason, N.M. Does. subsidizing fertilizer contribute to the diet quality of farm women? Evidence from rural Mali. Food Security 2020, 12, 1407–1424. [Google Scholar] [CrossRef]
- Soko, J.J. Agricultural Pesticide Use in Malawi. Journal of Health and Pollution 2018, 8. [Google Scholar] [CrossRef]
- Troosters, W.; Heinrich, G.; Pearson, L.; Chiwaula, L.; Burke, W.J. The Economic and Social Cost of Land and Soil Degradation in Malawi 2024.
- Wang, H.; Schmidt, P. One-Step. and Two-Step Estimation of the Effects of Exogenous Variables on Technical Efficiency Levels. Journal of Productivity Analysis 2002, 18, 129–144. [Google Scholar] [CrossRef]
- Zuza, E.J.; Maseyk, K.; Bhagwat, S.A.; Chemura, A.; Brandenburg, R.L.; Emmott, A.; Rawes, W.; Hancock, W.; Mnthambala, F.; Araya, Y.N. Factors. affecting soil quality among smallholder macadamia farms in Malawi. Agriculture & Food Security 2023, 12, 17. [Google Scholar] [CrossRef]


| Variable | Description | Measurement unit |
|---|---|---|
| Crop productivity | Total maize output obtained from the plot | Kg |
| Plot area | Total area of the cultivated plot | Acres |
| Organic fertilizer | Quantity of organic manure or compost applied to the plot. | Kg |
| Inorganic fertilizer | Quantity of chemical fertilizer applied to the plot. | Kg |
| Labour | Total household and hired labour used on the plot. | Man-hours |
| Seed quantity | Total seed used for planting the plot. | Kg |
| Pesticides/herbicides use | Indicates whether a farmer applied pesticide or herbicide during the production season. | 1=Yes; 0=No |
| Improved variety | Indicates whether an improved maize seed variety was planted. | 1 = Improved variety; 0 = Local |
| Soil quality | Farmer’s subjective assessment of soil fertility condition. | 1 = Poor; 2 = Fair; 3 = Good |
| Soil erosion rate | Self-reported rate of soil erosion observed on the plot. | 1 = Severe ; 2 = Moderate; 3 = Low; 4 = No erosion |
| Agro-ecological zone | Climatic zone determined by temperature and rainfall regime. | 1 = Tropic-warm/semi-arid; 2 = Tropic-warm/sub-humid; 3 = Tropic-cool/semi-arid; 4 = Tropic-cool/sub-humid |
| Region | Administrative region where the plot is located. | 1 = Northern; 2 = Central; 3 = Southern |
| Extension contact on inorganic fertilizer | Household received extension advice on inorganic fertilizer use. | 1 = Yes; 0 = No |
| Extension contact on organic fertilizer | Household received extension advice on organic fertilizer. | 1 = Yes; 0 = No |
| Extension contact on seed variety | Household received extension advice on improved seeds. | 1 = Yes; 0 = No |
| Fertilizer coupon | Household accessed government fertilizer subsidy. | 1 = Yes; 0 = No |
| Livestock ownership | Household owns livestock. | 1 = Yes; 0 = No |
| Household size | Number of household members residing in the household. | Number of persons |
| Variable | Mean | Linearised Standard Error |
|---|---|---|
| Plot area (acres) | 0.88 | 0.01 |
| Seeds (kg) | 7.70 | 0.08 |
| Organic fertilizer (kg) | 208.02 | 48.17 |
| Fertilizer total | 56.02 | 0.77 |
| Labour man-hours | 31.26 | 0.28 |
| Pesticides | 0.04 | 0.003 |
| Variety | 0.48 | 0.01 |
| Maize output (kg) | 442.20 | 8.85 |
| Variable | Pesticide use | Improved variety | Organic Fertiliser (ln) | Inorganic Fertiliser (ln) | Labour hours (ln) |
|---|---|---|---|---|---|
| Soil quality | Probit (dy/dx) | Probit (dy/dx) |
Censored Tobit (Coefficient) | Linear (Coefficient) | Linear (Coefficient) |
| Fair | 0.05 (0.06) |
-0.04 (0.04) | 0.24 (0.22) |
-0.11*** (0.03) |
-0.07 (0.02) |
| Poor | 0.01 (0.09) |
-0.03 (0.05) | 0.57* (0.31) |
-0.22*** (0.04) |
-0.14** (0.01) |
| Soil erosion | |||||
| Low | 0.09 (0.06) |
-0.01 (0.04) | 0.56** (0.23) |
0.02 (0.52) |
0.09 (0.03) |
| Moderate | -0.02 (0.10) | -0.12** (0.06) | 0.57 (0.35) |
0.03 (0.04) |
0.11 (0.02) |
| High | 0.14 (0.11) |
-0.11 (0.07) |
-0. 16 (0.45) |
0.09 (0.27) |
0.09 (0.02) |
| Region | |||||
| Central | -0.02 (0.12) | -0.13** (0.08) | |||
| Southern | -0.07 (0.11) | -0.51*** (0.07) | |||
| Extension on pest control | 0.31*** (0.06) | ||||
| Agro-ecological zone | |||||
| Tropic-warm/subhumid | 0.22*** (0.07) | -0.11*** (0.04) | -0.787*** (0.22) |
-0.23*** (0.04) |
0.13*** (0.02) |
| Tropic-cool/semi arid | -0.01 (0.01) | -0.26*** (0.05) | -1.63*** (0.33) |
0.24*** (0.03) |
0.09** (0.02) |
| Tropic-cool/subhumid | 0.19 (0.14) |
-0.12 (0.08) | -3.50*** (0.42) |
0.67*** (0.04) |
0.04 (0.02) |
| Extension on new seed varieties | 0.27*** (0.04) | ||||
| Livestock ownership | 0.04 (0.22) |
||||
| Extension on organic fertilizer | 1.66*** (0.21) |
||||
| Extension on inorganic fertilizer use | 0.10*** (0.03) |
||||
| Inorganic fertilizer coupon | 0.10*** (0.03) |
||||
| Household size | 0.11*** (0.01) |
||||
| Observations | 6370 | 6370 | 6370 | 6370 | 6370 |
| Crop productivity | Production function | Inefficiency model |
|---|---|---|
| Acreage (ln) | 0.24 (0.02) |
|
| Pesticides | 0.14** (0.04) |
|
| Improved variety | 0.22*** (0.02) |
|
| Seed(ln) | 0.33*** (0.02) |
|
| Inorganic fertiliser (ln) | 0.47*** (0.01) |
|
| Organic fertilizer (ln) | 0.01*** (0.003) |
|
| Labour (ln) | 0.08 (0.02) |
|
| Soil quality: | ||
| Fair | 0.19*** (0.0.07) |
|
| Poor | 0.42*** (0.10) |
|
| Soil erosion: | ||
| Low | 0.11 (0.08) |
|
| Moderate | 0.49*** (0.11) |
|
| High | 0.68*** (0.13) |
|
| Constant (ln σ²ᵤ) | 5.222** (1.529) |
|
| Constant (ln σ²ᵥ) | 11.932*** (0.018) |
| Soil assessment | Technical Efficiency | ANOVA p-value | ||||
|---|---|---|---|---|---|---|
| N | Mean | p25 | p50 | p75 | ||
| A. Soil quality | ||||||
| Poor | 836 | 0.57 | 0.47 | 0.62 | 0.72 | 0.000 |
| Fair | 2,041 | 0.61 | 0.52 | 0.66 | 0.74 | |
| Good | 3,493 | 0.64 | 0.66 | 0.68 | 0.76 | |
| B. Erosion rate | ||||||
| Severe | 366 | 0.54 | 0.41 | 0.58 | 0.68 | 0.000 |
| Moderate | 579 | 0.57 | 0.46 | 0.61 | 0.72 | |
| Low | 1,750 | 0.62 | 0.53 | 0.66 | 0.74 | |
| No erosion | 3,675 | 0.64 | 0.57 | 0.68 | 0.76 | |
| Total | 6,370 | 0.62 | ||||
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| 1 | The model was estimated using sfcross Stata command (Belotti et al., 2013)(Belotti et al., 2013) |
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