Abstract
This paper modifies the Cornwell, Schmidt and Sickles [CSS (J Econom 46:185–200, 1990)] time-varying specification of technical efficiency to allow for switching patterns in temporal changes, which may occur more than once during the sample period. For this purpose, we move from the (second-order) polynomial specification of the standard CSS to a spline function setup, while keeping CSS’s flexibility regarding the cross-sectional dimension. The spline function specification of the temporal pattern of technical efficiency can accommodate more than one turning point and thus can be non-monotonic. This allows the modeler to account for firm or individual efficiency gains that can occur relatively quickly, for example, changes related to regulation or policy changes, as well as those related to ownership/organization changes (e.g., merger or acquisitions).
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Notes
Much more general mixed types of so-called environmental variables can also be controlled for with the CSS model, such as additive effects that impact the slope coefficients of the “environmental” variables. In these specifications of the CSS estimator, the “environmental” variables impact the frontier as well as the level of efficiency, unlike most two-step models, wherein there is separability between the frontier and efficiencies of the cross-sectional units (Wang 2002; Wang and Schmidt 2002; Simar and Wilson 2007).
Details on the efficient IV estimator can be found in the CSS paper.
Firm-specific relative efficiencies can be identified along with the overall growth in innovation that diffuses to all firms for the GLS estimator. Under appropriate orthogonality assumptions, a similar term can be identified for the Hausman–Taylor type efficient IV estimator. Thus, for these two estimators, total factor productivity can be decomposed into technical change and efficiency change. Such a decomposition is not possible for the CSS within estimator as the overall technical change term specified as quadratic in time is not identified after the within transformation if the effects are also specified as quadratic in time.
We conjecture that this is due to the large standard errors estimated under the within model.
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Almanidis, P., Karagiannis, G. & Sickles, R.C. Semi-nonparametric spline modifications to the Cornwell–Schmidt–Sickles estimator: an analysis of US banking productivity. Empir Econ 48, 169–191 (2015). https://doi.org/10.1007/s00181-014-0890-y
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DOI: https://doi.org/10.1007/s00181-014-0890-y
Keywords
- Cornwell–Schmidt–Sickles estimator
- Time-varying efficiency
- Spline functions
- Semi-parametric estimation