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In this paper we use a sub-vector input distance frontier function based on economic foundations.
In the non-parametric approach, such as DEA, the frontier function is a decision function of several variables.
The null hypothesis on technological homogeneity between the two organisational forms is also not rejected, so private firms and cooperatives lie on the same frontier function.
The preferred model is thus a Cobb-Douglas frontier function in which the parameter δ0 is equal to zero (see last column of Table 1).
This model is similar to the Battese and Coelli (1995) model, with a non-neutral specification for the production frontier function.
Over the last half century efficiency has been calculated relative a frontier function using either non-parametric mathematical programming methods such as the Data Envelopment Analysis DEAA) or econometric/regression methods.
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The results relevant to the estimated coefficients of stochastic frontier functions are reported in Table 2.
If the null hypothesis H0 : βp = 0 is rejected, this means that cooperatives and private firms use different technologies and lie on different frontier functions.
The estimated value of sigma are significant at less than 1% probability level for all frontier functions indicating the conventional average production function is not an adequate representation of the data.
Noting that in Table 3, the maximum of TGR in various scales of manufacturing firms equals with 1, and thus, it can be concluded that stochastic frontier functions of these two groups are tangent to the metafrontier function.
The results related to the kinds of efficiency and technology and technology gap ratio are presented in Table 3 where TE k indicates the technical efficiency of stochastic frontier functions for small, medium and large firms.
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