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Estimation and decomposition of inefficiency when producers maximize return to the outlay: an application to Norwegian fishing trawlers

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Abstract

This paper deals with estimation of a production technology where endogeneous choice of input and output variables is explicitly recognized. In particular, we assume that producers maximize return to the outlay (RO). For simplicity and tractability we start with a Cobb–Douglas transformation function with multiple inputs and outputs and show how the first-order conditions of RO maximization can be used to derive an estimating equation which is nothing but a partial input productivity equation. This equation does not suffer from the econometric endogeneity problem although the output and input variables are endogenous. First, we consider the case where producers are fully efficient allocatively but technically inefficient. The model is estimated using a single equation stochastic frontier approach. The model is then extended to allow allocative inefficiency and it is estimated as a system using generalized method of moment. Algebraic expressions are derived to decompose the effect of technical and allocative inefficiencies on RO. We also consider translog specifications that are estimated as (1) a single equation frontier model as well as (2) a system. We use a panel of Norwegian fishing trawlers data to estimate the model. Outputs are different species caught while inputs are labor and vessel size. We also control for number of days of operation, age of the vessel and year effects. Empirical results show that the average rate of RO is reduced by about 20 to 30 % due to technical inefficiency. On the other hand, average allocative efficiency is found to be about 78 %. The average overall efficiency is found to be around 60 %.

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Notes

  1. There are many efficiency papers published in the operational research journals (for example, Reinhard et al. (2000), Brissimis et al. (2010), among many others). Since most of these papers use data envelopment analysis, which is a linear programming technique, there is no endogeneity issue in estimation even if some explicit economic behaviors are modeled.

  2. For example, endogeneity issue is discussed in many papers (Coelli 2000; Kumbhakar 2001, 2011, among many others) under profit maximization behavior. Endogeneity in the context of a distance function using system approach under profit maximization behavior is discussed in Karagiannis et al. (2006) and Coelli et al. (2007).

  3. We are excluding the cases in which technical and/or allocative inefficiency are formulated as either fixed parameters or deterministic functions. These are often labeled as shadow price models, and are discussed under revenue and profit maximization behaviors. See chapter 6 of Kumbhakar and Lovell (2000) for a discussion of these models. Although the shadow system with RO maximization might be somewhat similar to the system under cost minimization and profit maximization, we are not aware of any such paper.

  4. Note that these normalizing constraints make the transformation function homogeneous of degree one in outputs. In the efficiency literature one starts from a distance function (which is the transformation function with inefficiency built in) and imposes linear homogeneity (in outputs) constraints to get the ODF. Here we get the same end-result without using the notion of a distance function to start with.

  5. These normalizing constraints make the transformation function homogeneous of degree one in inputs. In the efficiency literature one defines the IDF as the distance (transformation) function which is homogeneous of degree one in inputs. Here we view the homogeneity property as identifying restrictions on the transformation function without using the notion of a distance function.

  6. See Coelli (2000) for a discussion on the endogeneity issue under profit maximizing, cost minimizing and revenue maximizing behaviors.

  7. The basic idea of this goes back to Georgescu-Roegen’s (1951) notion of “return to the dollar”.

  8. The restrictions ∑ j β j  =  −1 and ∑ m α m  = 1 make RTS unity. Note that unitary RTS is not an assumption. It is an implication of maximizing RO. If RTS is unity, the inefficiency can be given a hyperbolic interpretation as shown in Section 2. RTS in terms of the transformation function without inefficiency is defined as \(\sum_j \partial \ln f(\cdot)/ \partial \ln x_j \div \sum_m \partial \ln f(\cdot)/ \partial \ln y_m\) (Panzar and Willig 1977), where \(f(\cdot)\) is the transformation frontier.

  9. Although the inefficiency term in our estimating equation is exactly the same as the inefficiency term in the hyperbolic ODF in (5), from estimation point of view the specification in (11) is preferred because the regressors in it are all in ratio forms and they can be treated as exogenous under RO maximization.

  10. Alternatively one can use OLS or 2SLS to (11) in which ratios of input and output prices and the Z variables can be used as instruments. This is suggested in Kumbhakar and Lovell (2000) as well several other papers such as Kumbhakar and Hjalmarsson (1995), Kumbhakar and Heshmati (1997), among others. It is also possible to use the system approach such as 3SLS. The advantage of GMM is that it is robust to heteroskedastic errors.

  11. Individual parameters of the translog function do not have any direct meaning/interpretation. Because of this we have not reported the estimated parameters. However, we used the estimated parameters to compute output elasticities and technical change. These results are discussed later in this section.

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Authors and Affiliations

  1. Department of Economics, State University of New York at Binghamton, Binghamton, NY, 13902, USA

    Subal C. Kumbhakar

  2. Department of Industrial Economics, University of Stavanger, Stavanger, 4036, Norway

    Frank Asche

  3. University of Stavanger Business School, Stavanger, 4036, Norway

    Subal C. Kumbhakar & Ragnar Tveteras

Authors
  1. Subal C. Kumbhakar
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  2. Frank Asche
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  3. Ragnar Tveteras
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Correspondence to Subal C. Kumbhakar.

Appendix

Appendix

In this appendix we report plots of output and input elasticities as well as TC based on the translog system GMM.

See Appendix Figs. 9 and 10.

Fig. 9
figure 9

Histogram of output elasticities (translog system GMM)

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Fig. 10
figure 10

Histogram of input elasticities and TC (translog system GMM)

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Kumbhakar, S.C., Asche, F. & Tveteras, R. Estimation and decomposition of inefficiency when producers maximize return to the outlay: an application to Norwegian fishing trawlers. J Prod Anal 40, 307–321 (2013). https://doi.org/10.1007/s11123-012-0336-5

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