Allocative and scale efficiency among maize farmers in Zambia: a zero efficiency stochastic frontier approach

ABSTRACT

The commonly used stochastic frontier model assumes that all firms are inefficient. In this specification, inefficiency is non-negative, and the probability of inefficiency being exactly zero is also zero. To the extent that efficiency varies widely across farms in under-developed economies, it is important to employ techniques that account for both inefficiency and full efficiency to ensure unbiased efficiency estimates. In this study, we employ a zero-inefficiency stochastic frontier model to examine allocative efficiency and scale economies, as well as key determinants of efficiency among Zambian maize farmers. The results show that, unlike the stochastic frontier model, the zero-inefficiency stochastic frontier model successfully allows for both fully efficient and inefficient firms to be accounted for in the estimation procedure. The estimates also reveal the presence of scale economies, with the zero-inefficiency stochastic frontier model better predicting scale efficiency compared to the stochastic frontier model. The findings also show that inefficiency is explained by the level of education, access to extension services, distance to markets and access to credit.

KEYWORDS:

• Zambia
• efficiency measurement
• zero-inefficiency

JEL CLASSIFICATIONS:

• C31
• D24
• D61

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ This terminology is used by Kumbhakar, Parmeter, and Tsionas (2013).

² For example, although maize production in Zambia between the 2000/2001 and 2010/2011 increased from 957,437 to 2,786,896 MT, the corresponding farm land also increased from 748,314 ha to 1,311,295 ha within the same period (Mason et al. 2011).

³ For example, transport costs alone in the production of maize in Zambia are more than double those of Thailand (World Bank 2009).

⁴ We use the male form because majority of the farmers are males.

⁵ λ is defined in Table 1.

⁶ Returns to scale and economies of scale are equivalent measures, if and only if the product is homothetic (Chambers 1983).

⁷ Agricultural camp in Zambia is a management unit of agricultural camp officer, comprising a catchment area of up to eight different zones of different villages.

⁸ The opportunity cost is the monetary value of owner-operated land that the household would have received or paid for renting the land.

⁹ The opportunity cost of family labour is the monetary value of wages that the household would have received or paid for hiring equivalent unit of family labour.

¹⁰ We tested this against the Cobb–Douglas specification and Cobb–Douglas specification rejected at the 1% level of significance in both the SF and ZISF specifications.

¹¹ R packages including, ‘frontier’ (Coelli and Henningsen 2013), ‘minqa’ (Bates et al. 2014), and ‘numDeriv’ (Gilbert and Varadhan 2012) were used.

¹² For which the variance is zero

¹³ This supports the axiom that the cost function monotonically increases with output and factor prices.