BDO International Business Compass

International Location Index for the Medium-Sized Companies

Normalisation

The indicators, which are included in the three dimensions and the two sub-indices respectively, are scaled differently. Initially, the different scales had to be made comparable, before the data could be aggregated. For this purpose, all indicators were normalised on a scale of 0 to 100 in order to get a comparable unit of size. The minimum value of the indicator for all countries was subtracted from the observed value of the indicator for a country x, divided by the difference between maximum and minimum value of this indicator for all countries and the result multiplied by 100. The closer this value is to 100, the better the country performs in terms of this indicator.[1]

The distribution of the "market potential" indicator is very lopsided due to extremely high values for Singapore, Taiwan and the United Arab Emirates. Yet, it has no further impact on the country ranking even with this lopsided distribution transferred to the normalised values and a significant accumulation close to zero. We tested this by setting the values for these three countries to 100 and normalising the remaining measures to values between 0 and 100 by the usual method. As a result, the values of the index were slightly higher; a logical consequence of the higher value of the "market potential" indicator. However, the variations were relatively minor and the rank order remained unchanged and so, an ad hoc adjustment of these values seemed to be unnecessary.[2] 

The complete country sample is very heterogeneous, because it includes all industrial, emerging and developing countries. In order to particularly demonstrate the potential of perhaps less visible countries, we used a second normalisation method, which is suitable to highlight both above- and below-average performance. Accordingly, the indicators included in the sub-indices "sales market" and "production site" were normalised for a second time by calculating the distance to a point of reference. The second normalisation establishes the relative position of a country within the reference group for the complete country sample. In this case, the countries were divided into the two main groups of OECD member states and non-OECD member states. In the first group, the observed indicator value was put in relation to the average of the OECD member states of this indicator. In the second group, the relevant observed indicator value was put in relation to the average observed value of the relevant continent. A value of more than 1 signifies an above-average and a value of less than 1 a below-average performance of a country for the indicator in question. Hence, this value indicates the relative performance of an OECD-member in relation to all other OECD member states, irrespective of the continent. In the case of a non-OECD member state, the value reflects the relative performance in relation to other non-OECD member states of the same continent.[3]



1 With some indicators, a high value of the not yet normalised indicator reflects a poorer relative performance, i.e. the opposite logic applies. Therefore, in the case of "gross national debt", "inflation rate", "aggregate tax rate", "labour costs" and "unemployment rate", the minimum value of the indicator for all countries was subtracted from the observed value of the indicator for a country x, divided by the difference between minimum and maximum value of this indicator for all countries and the result multiplied by 100. This ensures that a higher value after normalisation reflects a better performance of a particular country, even in the case of these indicators.

2 Following the normalisation to values between 0 and 100, we replaced the minimum value of zero by 1010. This enabled the calculation of the geometric mean in the next step. As opposed to the arithmetic mean, the calculation of the geometric mean involves multiplication of the values. If at least one value is zero, the final product is also zero. The exact value itself is irrelevant, because the primary purpose is to replace the zero value with a value that equals zero approximately, but does not actually equal zero. Additional tests showed that a slightly greater (10-8) or lower (10-12) value does not affect the calculation of either the index or the sub-indices.

3 We measured the indicators "political stability", "regulatory quality", "rule of law" and "control of corruption" on a scale of approx. -2.5 to approx. +2.5. These values were first converted to a scale with exclusively positive values in order to avoid distortions in the distance calculation.