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Measuring performance, development and growth when restricting flexibility

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In industries with heterogeneous firms and fast-changing productivity, it is necessary to consider both firm and time effects if one is interested in technology adoption and efficiency. Since it is not possible to estimate individual firm effects for each time period due to degree-of-freedom problems, a trade-off is necessary with respect to where one is employing a flexible specification and where one is more restrictive. While most studies choose to account for variation, either in cross-sectional or temporal dimensions, we are in this paper, by clustering firms together in groups, allowing for variation in both cross-sectional and temporal dimensions. By modifying a shadow cost system, we are able to measure group-specific temporal patterns of technical and allocative efficiency and technological change without restricting the patterns to any parametric form.

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Notes

  1. Economic agents can be firms, regions, countries or industries.

  2. In this type of studies it is common to model the temporal pattern of inefficiency by using a time trend model over a more flexible general index model, i.e. by variants of the approach introduced by Cornwell et al. (1990) or Kumbhakar (1990).

  3. Färe et al. (1994), Baumol et al. (1994), Bernard and Durlauf (1995), and Gouyette and Perelman (1997) are only a few of the studies that undertake productivity convergence between countries. Regional differences are investigated by, among others, Barro and Sala-i-Martin (1992, 1995), Bernard and Jones (1996), Rey and Montouri (1999), Sachs et al. (2002) and Ahluwalia (2000). Studies investigating convergence between individual sectors is conducted by, among others, Barro and Sala-i-Martin (1991).

  4. An alternative way to gain degrees of freedom would be to use the multiple time-trend representation of Heshmati and Nafar (1998), where time periods are clustered together.

  5. Hence, change in technical efficiency is modelled in the same flexible way as Lee and Schmidt (1993) and technological change in the same flexible way as Baltagi and Griffin (1988).

  6. As anonymous referee pointed out, the unit if interest could be a firm if multiple observations per time period are available or if time periods are clustered together.

  7. Since this observation is assumed to be technically efficient and makes use of the best available technology over the sample period, the input distance function for this reference observation is 1 (ϕ eT  = 1).

  8. Equation (7) does not fully reflect TFP growth, since the scale effect is not included in the expression.

  9. The choice of the input as numeraire has no impact on the estimate of the log-likelihood function (Atkinson and Cornwell 1994b).

  10. This distance function is found post-estimation, and is given by the lowest predicted intercept.

  11. Since 1973 a license has been required to operate a salmon farm in Norway. The government has used this instrument as a device to ensure regional dispersion of farms.

  12. The quantity of feed is not given directly, but is calculated as the product of output and the feed conversion ratio (Salvanes 1989).

  13. TSP(5.0) software was used for estimation.

  14. See e.g., Guttormsen (2002), Tveteras (2002), Kumbhakar and Tveteras (2003) and Asche et al. (2009).

  15. \( R_{vc}^{2} = 0.978 \) and \( R_{f}^{2} = 0.651 \) for the variable cost function and the share equation for feed, respectively. The log likelihood value was found to be 8,338.

  16. A Wald test for the hypotheses that the all the distance functions are equal to 1 is rejected at 1% level of significance.

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Acknowledgments

I want to acknowledge Frank Asche and Ragnar Tveteras for their valuable support and comments.

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  1. University of Stavanger, 4036, Stavanger, Norway

    Kristin Helen Roll

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Correspondence to Kristin Helen Roll.

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Roll, K.H. Measuring performance, development and growth when restricting flexibility. J Prod Anal 39, 15–25 (2013). https://doi.org/10.1007/s11123-012-0265-3

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