Tests and confidence intervals for a class of scientometric, technological and economic specialization ratios

Abstract

In economic, scientometric and innovation research, often so-called specialization indices are used. These indices measure comparative strengths or weaknesses as well as specialization profiles of the observation units with respect to certain criteria, such as patenting and publication or trade activities. They allow question like: is Germany specialized in the export of motor vehicles? Or is the UK specialized in biotech patents? Unfortunately, little is known about their statistical properties, which makes valid inferencing difficult. In this article we prove asymptotic normality for a certain class of scientometric, technological and some economic, though nonmonetary, specialization indices. We provide asymptotic confidence intervals and demonstrate in an example how to obtain statistically sound results. We will also address the problem of normalization of these indicators. All procedures proposed are provided in an add on package for R statistical environment.

Acknowledgements

The research underlying this article was partially supported by the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG) in a project on ‘performance indicators for research groups’ (SCHM 1719/1-2) which is part of a larger research group on ‘international competitiveness and innovation capacity of universities and research institutions–new forms of governance’ (FOR 517). We would also like to thank two anonymous referees who with their comments helped significantly to improve the quality of this article. We would especially like to thank them for the suggestions that gave rise to ‘Influence of the classification’ and the discussion of IIT indicators in Section II. Any remaining errors are of course the authors’ responsibility.

Notes

¹ Note for now that the GLI and, related to it, other IIT indicators are not really specialization ratios, as they are discussed in this article. This will become clear later on.

² http://ec.europa.eu/enterprise/tris/

³ Note that quantities that can be measured on an absolute scale have a natural unit. In our context this will imply that the quantities can be counted (for example, patents).

⁴ The technical definition only requires it to be a ratio of ratios.

⁵ Check that the technical definition applies.

⁶ In this definition denotes total exports of country i.

⁷ Note that (r^k − 1)/(r^k + 1) for any k > 0 has the same properties. Apart from the Moebius transformations there are others with identical normalization properties.

⁸ Also confirmed in a private communication from Dr Markus von Ins, CEST, Switzerland, on 11 September 2006.

⁹ We use either k or v throughout the text to denote the subjects under consideration. Also note that by defining an individual object we make use of the ‘absolute scale’ condition.

¹⁰ To do this, specialization ratios as described above were used along with the second order Moebius transformation. The latter bounds the specialization ratio to the interval −1 and 1. A zero indicates that the country average is identical with the reference group average (often the world average) while positive values indicate above average and negative below average specialization.

¹¹ Aggregation bias in this context means that IIT is overestimated and vanishes after disaggregation.The reason is the ‘opposite sign effect’. (Gray, 1979; Greenaway, 1983; Tharakan, 1984; Balassa, 1987; Doroodian et al., 1999; Bahmani-Oskooee and Harvey, 2006).

¹² Equation A10 of the Appendix.

¹³ In fact, we could use a nested bootstrap to determine the variance. But this is computationally even more intensive. Since we are in the lucky situation of having an asymptotic expression for the variance it is better to use this for practical reasons (see, e.g. Wassermann, 2006).

¹⁴ The precision increases with the number of bootstrap replications. Thus infinite replications would be ideal. Since this is impossible for reasons of finite computation time, a usual recommendation is to choose 1000–5000 replications.

¹⁵ π now denotes the circle constant.