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Measuring input-specific productivity change based on the principle of least action

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Abstract

In for-profit organizations, efficiency and productivity measurement with reference to the potential for input-specific reductions is particularly important and has been the focus of interest in the recent literature. Different approaches can be formulated to measure and decompose input-specific productivity change over time. In this paper, we highlight some problems within existing approaches and propose a new methodology based on the Principle of Least Action. In particular, this model is operationalized in the form of a non-radial Luenberger productivity indicator based on the determination of the least distance to the strongly efficient frontier of the considered production possibility sets, which are estimated by non-parametric techniques based upon Data Envelopment Analysis. In our approach, overall productivity change is the sum of input-specific productivity changes. Overall productivity change and input-specific changes are broken up into indicators of efficiency change and technical change. This decomposition enables the researcher to quantify the contributions of each production factor to productivity change and its components. In this way, the drivers of productivity development are revealed. For illustration purposes the new approach is applied to a recent dataset of Polish dairy processing firms.

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Notes

  1. Input-oriented radial models search for equiproportional reductions in all the inputs. In this way, these models are not prepared to allow the decomposition of the “global” productivity change into the different effects of inputs on this change. This is probably the reason why the previous literature devoted to input-specific productivity did not resort to radial models to deal with input-specific productivity change.

  2. These authors really use one good output and one bad output. Nevertheless, they mathematically deal with the bad output as an input in their approach.

  3. Model (13) assumes the production of just one output under Constant Returns to Scale. In practice, this is not a great limitation since, on the one hand, most applications devoted to input-specific productivity change utilized only one output and, on the other hand, Constant Returns to Scale is the correct assumption for determining productivity regardless of the actual returns to scale (see, e.g., Kapelko et al. 2015a). However, any deviation of these assumptions implies that our approach, based on the models by Aparicio et al. (2007), does not work correctly. Aparicio et al. (2016) have studied in detail least distance models for oriented frameworks, proposing an innovative and general methodology that always correctly performs based upon Bi-Level Linear Programming and moving away, therefore, from the well-known Aparicio et al. (2007) approach. Moreover, our model is in line with the original idea of input-specific productivity change that is rooted in the growth accounting literature (cf. Solow 1957). Growth accounting measures the contribution of different production factors (such as capital, labor and materials) to the growth of total output and indirectly computes the change of total factor productivity (or technical progress). It is based on the traditional production function relating the production of a single output to multiple inputs assuming Constant Returns to Scale.

  4. The Luenberger indicator utilized in this section is not the standard indicator but an input-specific version that depends on \({\delta _{i,h}}\left( {{{x\,}_{i0}^p},{{y\,}_0^p}} \right)\).

  5. Regarding fixed assets, model (13) may be adapted to short run situations where some inputs cannot be altered by the decision maker and, therefore, must be assumed fixed. To do this, it is enough to remove the respective input slack from the objective function of (13). Nevertheless, in our empirical application, we assume a long run production function, where fixed inputs can be also modified. In fact, in most studies on input-specific efficiency and productivity, fixed inputs are considered as one of the inputs in empirical applications for which efficiency and productivity are calculated (see, e.g., Chang et al. 2012; Skevas and Oude Lansink 2014).

  6. In the related literature on efficiency and productivity in the food manufacturing industry, it is common to use inputs and outputs measured in monetary values as quantity data are often not available (see, e.g., Doucouliagos and Hone 2001; Soboh et al. 2012; Kapelko et al. 2015b, 2016). In our empirical application, we deflated the inputs and the output in order to convert the nominal values to real input and output measures. In this way, we avoided a bias due to inflation and generated implicit quantity indexes as the ratio of the value to price index.

  7. The computation times of the new approach varied between 3 seconds (for 2004/2005) and 12 seconds (for 2010/2011). The computations were undertaken with a PC with an Intel Xeon Dual Core processor of 2.33 GHz, with 8.5 GB of RAM. The optimization software package CPLEX v11.0 was used in computations. Additionally, the code can be downloaded at http://deacode.blogspot.com.es/.

  8. In fact, when we compute average values of indicators for these two sub-periods, we would find these trends exactly as described.

  9. Recent literature questions the results of technical regress found in DEA studies (see, e.g., Diewert and Fox 2016) and proposes the methods to reveal “true” findings. However, the development or application of such methods is out of the scope of this paper.

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Acknowledgements

We would like to express our gratitude to the editor and two anonymous referees for their helpful comments. Magdalena Kapelko would like to acknowledge the funding by the National Science Centre in Poland, decision number DEC-2013/11/D/HS4/00252. Juan Aparicio would like to express his gratitude to the Spanish Ministry for Economy and Competitiveness for supporting this research under grant MTM2013-43903-P. We also thank the comments of participants at the 14th European Workshop on Efficiency and Productivity Analysis (EWEPA 2015) in Helsinki and the OR2015 International Conference on Operations Research in Vienna. The usual disclaimer applies.

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Authors and Affiliations

  1. Center of Operations Research, University Miguel Hernandez, Elche (Alicante), 03202, Spain

    Juan Aparicio & Jose L. Sainz-Pardo

  2. Institute of Applied Mathematics, Department of Logistics, Wroclaw University of Economics, Wroclaw, Poland

    Magdalena Kapelko

  3. Institute for Industrial Research, Mittersteig 10/4, Vienna, 1050, Austria

    Bernhard Mahlberg

  4. Vienna University of Economics and Business, Welthandelsplatz 1, Vienna, 1020, Austria

    Bernhard Mahlberg

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  1. Juan Aparicio
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Correspondence to Bernhard Mahlberg.

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Aparicio, J., Kapelko, M., Mahlberg, B. et al. Measuring input-specific productivity change based on the principle of least action. J Prod Anal 47, 17–31 (2017). https://doi.org/10.1007/s11123-016-0488-9

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