Technical Efficiency and the Role of Crop Diversification among Smallholder Farmers in the Geba Catchment, Tigray Region, Northern Ethiopia

Variables	Variable description	unit
y_i	value of crop output	Birr
x₁	area of cultivated land	hectare
x₂	value of owned farm implements	Birr
x₃	number of oxen days used	oxen-days
x₄	labor used in crop production	labour-days
x₅	fertilizer	kg
x₆	seed used	kg
V_i	a disturbance term with normal properties
U_i	farm specific error term
Z₁	age of the respondent in years	number
Z₂	education, i.e. literacy status of the farmer	dummy	1 = literate, 0 = otherwise
Z₃	sex of the house hold head	dummy	1 = male, 0 = female
Z₄	membership to association	dummy	1 = member 0 otherwise
Z₅	off farm income	dummy	1 = have non-farm income 0 = otherwise
Z₆	access to irrigation	dummy	1 = irrigated, 0 = otherwise
Z₇	credit	dummy	1 = loan taken, 0 = otherwise
Z₈	number of crop type₂	number
Z₉	distance to woreda market	km

[i] Number of crop types is the number of types of crop that a household cultivates. This is taken as a proxy for crop diversification or crop specialization.

[ii] Source: own computation.

Table 2.

Generalized Likelihood ratio test of hypotheses for parameters of stochastic production frontier and technical inefficiency factors

Null hypotheses	LR	Critical value	Decision
Absence of inefficiency H₀: δ_i = 0 = γ	33.5	29.1^a	reject
Production function is Cobb-Douglas H₀: β_ji = 0	29.4	32.7^b	do not reject

a This value is obtained from Table 1 in Kodde and Palm (1986) , which gives critical values for tests of null hypothesis involving values of the boundary of the parameter space.

Source: own elaboration.

Table 3.

Estimates of the conventional inputs

Inputs	Coefficient	Standard-error	t-ratio
Constant	6.83^***	0.3	22.23
Total seed	0.027	0.016	1.6
Oxen-days	−0.02	0.02	−1.32
Fertilizer	0.01^**	0.008	1.33
Farm size	0.26^***	0.075	3.46
Farm equipment	0.09^**	0.036	2.59
Labour-day	0.19^**	0.097	2.002
Sigma-squared	0.82
Log likelihood function	−346.33

*** significant at 1%,

** significant at 5%.

Source: own computation.

Table 4.

Estimates of the inefficiency parameters

Parameter	Coefficient	Standard-error	t-ratio
Constant	1.99^**	0.98	2.02
Head's sex	0.63	0.69	0.90
Head's age	−0.10^**	0.053	−1.96
Off farm income dummy	0.75	0.44	1.52
Extension participation	−0.10	0.77	−0.13
Irrigation	−5.54^**	3.44	−1.69
credit	0.14	0.38	0.38
Distance to market	0.48	1.33	1.83
Number of crop type	−0.89^**	0.50	−1.75
Sigma-squared	2.72	1.02	2.64
Gamma	0.82	0.083	9.83
log likelihood function	−329.5
LR test of the one-sided error	33.5

Credit is measured in terms of whether respondents have taken loans other than the package loan.

** significant at 5%,

* significant at 10%.

Source: own computation.

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DOI: https://doi.org/10.17306/j.jard.2026.2.00010r1 | Journal eISSN: 1899-5772 | Journal ISSN: 1899-5241

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Language: English

Page range: 188 - 194

Accepted on: Apr 29, 2026

Published on: Jun 30, 2026

Published by: Poznań University of Life Science

In partnership with: Paradigm Publishing Services

Publication frequency: 4 issues per year

Keywords:

technical efficiency,

stochastic frontier analysis,

crop diversification,

smallholder agriculture,

Tigray,

Ethiopia

Related subjects:

Business and economics,

Political economics,

Political economics, other,

Business management,

Business management, other,

Life sciences,

Life sciences, other,

Social sciences,

Political science,

Political science, other

© 2026 Mohammed Endris Harun, Indalew Bongase, published by Poznań University of Life Science
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 80 (2026): Issue 2 (June 2026)