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Radar scanning the world production frontier

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Abstract

In this paper we report the results from a detailed investigation of the shifts of the world production frontier function over the period 1980–2010. Analogous to a radar we implement a novel measurement approach for these shifts using nonparametrically computed directional distance functions to scan the frontier shifts across the entire input–output space. The shifts of the frontier function measured in this way are analyzed by regression methods. The results point towards substantial non-neutrality of technological progress and furthermore show that technological progress is more pronounced in regions of high output and in regions where human capital is intensely used.

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Notes

  1. See Färe and Primont (1995) and Hackman (2008) for detailed expositions of the axiomatic approach.

  2. For the computations of the linear programs in this paper the solver in the R-package “lpSolve” is used.

  3. This procedure is much more straightforward and less problematic to implement compared to the different approach chosen in the working paper version of this article, see Krüger (2015).

  4. Constant returns to scale are regularly imposed in other work relying on two-dimensional representations of the frontier function, cf. e.g. Henderson and Russell (2005), Jerzmanowski (2007), Badunenko et al. (2013).

  5. The measure is related to the difference \(\delta _{2j}-\delta _{1j}\) since \(\hat{Y}_{tj}=Y_{0}+\delta _{tj}g_{yj}\Rightarrow \hat{Y}_{2j}-\hat{Y}_{1j}=(\delta _{2j}-\delta _{1j})g_{yj}\Rightarrow \nabla \hat{Y}_{j}=(\delta _{2j}-\delta _{1j})g_{yj}/\hat{Y}_{1j}\) for the output and likewise (with opposite signs) for the inputs. Thus, \(\hat{\gamma }_{j}\) can be readily interpreted as the sum of the relative output enhancements and input reductions which is easily interpreted and directly related to \(\delta _{2j}-\delta _{1j}\) without being arbitrarily scaled.

  6. Here again the solution values of program (5) are denoted with the direction index j, i.e. \(\delta _{j}\), \(\varvec{\alpha }_{xj}\) and \(\varvec{\alpha }_{yj}\).

  7. This goal is achieved by using an initial M-estimator searching for the regression parameters associated with the smallest robust measure of scale of the residuals (actually an S-estimator), followed by a second M-estimation which can be computed by the iteratively reweighted least squares (IRWLS) algorithm. Maronna et al. (2006, pp. 124ff.) provide a formal exposition.

  8. The SMDM-estimator is implemented in the R-package “robustbase” and readily available upon using the option setting=’KS2011’ in the lmrob command.

  9. The alternative way to compute \(\mathtt {rk}=(\mathtt {rkna}/\mathtt {rgdpna})\cdot \mathtt {rgdpo}\) with the series rgdpna as the real GDP at constant 2005 national prices leads to a real capital stock series which is very highly correlated (correlation coefficient \(\approx 0.99\)) with the variant we have chosen here.

  10. Recall from (4) that the \(\gamma\)-measures are just relative measures of the extent of the frontier shifts computed as the (positive) growth rate of the output minus the (negative) growth rates of the inputs (in the case of a forward shift of the frontier function). There is no straightforward interpretation of the numerical magnitudes pretty much as there is no direct interpretation of the numerical value of a standard deviation.

  11. Recall the famous quote from Solow (1987): “You can see the computer age everywhere but in the productivity statistics”.

  12. The Great Recession officially ended in 2009 but the recovery was still incomplete in the following years, see e.g. Ng and Wright (2013) for more on that issue.

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Acknowledgments

I am grateful to the participants of the 15th International Schumpeter Conference 2014 in Jena for their suggestions. Benny Hampf also provided many insightful comments. In the previous version of the paper I used generalized additive models for estimating the response surfaces. Simon Wood provided generous advice on these models which is gratefully acknowledged. I am also grateful to the inspiring comments of three anonymous referees which triggered a complete reconsideration of the approach and substantially improved the paper. Of course, all errors are mine.

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  1. Department of Law and Economics, Darmstadt University of Technology, Hochschulstr. 1, 64289, Darmstadt, Germany

    Jens J. Krüger

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Correspondence to Jens J. Krüger.

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Krüger, J.J. Radar scanning the world production frontier. J Prod Anal 46, 1–13 (2016). https://doi.org/10.1007/s11123-015-0462-y

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