Technical efficiency for Colombian small crop and livestock farmers: A stochastic metafrontier approach for different production systems


This paper assesses the efficiency of crop and livestock production in Colombia by using a sample of 1565 households. The study considers households located in different production systems which differ in geography, climate and soil types. These conditions affect technical efficiency and thus render analysis under the same production frontier as inadequate. For this reason, stochastic metafrontier techniques are preferred, allowing the estimation of technical efficiency within each production system and between production systems in relation to the sector as a whole. Results suggest that households in some production systems could be benefiting from better production conditions due to advantages in the availability of natural resources and climate as well as to more favorable socio-economic conditions. Additionally, we found that, in all systems, households with higher production have higher measures of technical efficiency. Thus, significant gains could be achieved in the sector through measures that contribute to improve the efficiency of households within their production systems and by policies that help reduce the technology gap in relation to the meta-frontier. These policies would bring positive impacts on the quality of life of small farmers and on the productivity of the sector.

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  1. 1.

    For more details on Battese and Coelli’s approach (1995) see Coelli et al. (1999), and Melo and Espinosa (2005).

  2. 2.

    In the model, as well as in the empirical application, it is assumed that \({u_j}\sim {N^ + }\left( {{\mu ^j}({Z_j}),\sigma _u^{j2}} \right)\) and \(u_j^M\sim {N^ + }\left( {{\mu ^M}({Z_j}),\sigma _u^{M2}} \right)\) .

  3. 3.

    According to the survey, 83 % of the households carried out their production in one farm, 13 % in two farms and 4 % in three or more farms.

  4. 4.

    The information was converted into US dollars using the average exchange rate of 2011 (1846.9 Colombian pesos per US dollar).

  5. 5.

    The information on local variables comes from a municipal panel database conducted by the Center of Economic Development Studies from Universidad de los Andes.

  6. 6.

    According to IGAC (2012), 35 % of the country’s land is affected by erosion problems. In particular, 4′300.000 hectares are eroded severely and very severely, and 12′916.000 hectares in moderate degree.

  7. 7.

    For a detailed description of production conglomerates see IGAC (2012).

  8. 8.

    Following Battese et al. (2004), the statistic of the likelihood-ratio is defined by \(\lambda = - 2\left\{ {{\rm{ln}}\left[ {\frac{{L\left( {{H_0}} \right)}}{{L\left( {{H_1}} \right)}}} \right]} \right\} = - 2\left\{ {{\rm{ln}}\left[ {L\left( {{H_0}} \right)} \right] - {\rm{ln}}\left[ {L\left( {{H_1}} \right)} \right]} \right\}\), where \({\rm{ln}}\left[ {L\left( {{H_0}} \right)} \right]\) corresponds to the value of the loglikelihood function for the frontier estimated including the households from all systems and \({\rm{ln}}\left[ {L\left( {{H_1}} \right)} \right]\) is the sum of the values of the loglikelihood functions of the frontiers for each of four the production systems.

  9. 9.

    Although this transformation implies a change in units of measurement, it allows a direct interpretation of the first order parameters as production elasticities (Coelli et al. 2003).

  10. 10.

    According to the functional form of Battese and Coelli’s approach (1995), a negative (positive) coefficient means that the variable has a positive (negative) effect on technical efficiency.

  11. 11.

    We assume that \({U_{ji}}\) follows a truncated normal distribution, which has three parameters to be estimated: a placement parameter μ and two spread parameters σ u and σ v . As Kumbhakar and Knox Lovell (2000) indicate, technical efficiency of each producer can be obtained by means of:

    $$TE = E (\exp \{ -{u_{ji}} \}|{\varepsilon_{ji}} ) ={\frac{1-\Phi [{\sigma_*}-({\tilde{\mu}_{ji}}/{\sigma_*})]}{1-\Phi (-{\tilde{\mu}_{ji}}/{\sigma_*})}} * \exp \left\{-{\tilde{\mu}_{ji}}+\frac{1}{2}{\sigma^2_{*}}\right\}$$

    where Φ(.) is the standard normal cumulative distribution function, \({\tilde \mu _{ji}} = \left( { - \sigma _u^2{\varepsilon _{ji}} + \mu \sigma _v^2} \right)/{\sigma ^2}\) and \(\sigma _*^2 = \sigma _u^2\sigma _v^2/{\sigma ^2}\).

  12. 12.

    Vocation indicates whether the main household activity is agriculture, livestock or mixed.

  13. 13.

    According to Ruiz et al. (1975), corn grows in altitudes from sea level to over 3000 m.a.s.l.

  14. 14.

    The Chi2 (3) and the p-value for the metafrontier is 1062 (0.000).

  15. 15.

    It is important to note that by the functional form, the positive coefficient has a negative effect on the metafrontier production function.


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The authors acknowledge Boris E. Bravo-Ureta, Professor of Agricultural and Resource Economics at the University of Connecticut, for his suggestions and guidance to undertake this document; Carlos Gustavo Cano, member of the Board of the Colombian Central Bank, for his recommendations and guidance to find the necessary information for the research; José Gabriel Tafur, from the National Administrative Department of Statistics, for the provision of information and support in processing the database. We also wish to thank Jesus Barrios, Luis Armando Galvis, Jhorland Ayala García and Héctor Zárate for their comments and suggestions, and Helena González and Esteban Larrota for their research assistance. The opinions expressed herein belong to the authors and do not necessarily reflect the views of Banco de la República or its Board of Directors.

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Correspondence to Ligia Alba Melo-Becerra.

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Melo-Becerra, L.A., Orozco-Gallo, A.J. Technical efficiency for Colombian small crop and livestock farmers: A stochastic metafrontier approach for different production systems. J Prod Anal 47, 1–16 (2017).

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  • Stochastic frontier analysis
  • Technical efficiency
  • Metafrontier production function
  • Colombia

JEL Classification

  • C14
  • Q12
  • D24