Standard Deviation Method
As distinct criteria exhibit different scales and units, a comparable standard measure – the Standard Deviation Method (SDM) – is used to compute the overall, factor and sub-factor results. It measures the relative difference between the economies’ performances, resulting in a more accurate assessment of each country’s relative position in the final rankings.
First, for each criterion, we compute the average value for the entire population of economies. Then, the standard deviation is calculated using the following formula:
x = original value
x ̅= average value of all the economies
N = number of economies
S = standard deviation
Subsequently, we compute each of the economies’ STD values for the all the ranked criteria. The STD is calculated by subtracting the average value of the 64 economies from the economy’s original value and then dividing the result by the standard deviation.
The STD value for criteria i is calculated as follows:
x = original value
x ̅= average value of all the economies
N = number of economies
S = standard deviation
Subsequently, we compute each of the economies’ STD values for the all the ranked criteria. The STD is calculated by subtracting the average value of the 64 economies from the economy’s original value and then dividing the result by the standard deviation.
The STD value for criteria i is calculated as follows:
Aggregation of Data and Rankings
In the WCY some criteria are provided as background information only and are not included in the determination of the rankings. Some background data, however, are presented in ranking order while others are shown alphabetically.
STD values are calculated for each individual criterion, based on the STD method described above. All hard data indicators are reviewed to determine the shape of the distribution. Non-normally distributed data is normalized by taking the log. The STD is then calculated using the logged values.
The sub-factor rankings are determined by calculating the average of the STD values of all criteria comprising the sub-factor. All the hard data have a weight of 1. The survey data are weighted so that the survey accounts for one- third in the determination of the overall ranking. When data are unavailable for a particular economy, the missing values are replaced by STD values that are imputed from the average of existing data within the sub-factor. Taking the average for each sub-factor enables us to “lock”
the weight of all the sub-factors irrespective of the number of criteria they contain so that each sub-factor has an equal impact on the overall rankings.
Next, we aggregate the sub-factor STD values to determine the factor rankings. Only ranked criteria are aggregated to obtain these rankings. The STD values of the factors are then aggregated to determine the overall rankings. All the ranked criteria comprised in the factors are thus included in the consolidation of data.
Since all the statistics are standardized, they can be aggregated to compute indices. We use these index values, which we call “scores,” to compute the Factors and the Overall Rankings. It should be noted that across the factors, only one economy has a value equal to 100 and one economy a value equal to 0. To calculate the overall rankings, we take the average of the factors’ scores of the respective ranking (Competitiveness, Digital or Talent) and then convert them into an index with the leading economy given a value of 100.
Survey Criteria
Each year we conduct a survey to quantify issues related to competitiveness for which there are no hard statistics. The survey is an in- depth 92-point questionnaire sent to middle and upper level managers in the economies included in the rankings. The distribution reflects a breakdown of industry by sectors: primary, industry/manufacturing and services/finance.
In 2023 we received 6,400 responses for an average of approximately 100 replies per economy. The target list is determined by IMD and has been developed over many years with the collaboration of our Partner Institutes worldwide. Confidentiality is ensured and the list is updated every year. Respondents answer only for the economy in which they have worked and resided in the past year. Results, therefore, reflect widespread knowledge about each economy and draw on the wealth of their international experience.
The respondents assess the competitiveness issues by answering the questions on a scale of 1-6, with 1 indicating a negative perception and 6 indicating the most positive perception. The WCY calculates the average value for each economy, then the data is converted from a1-6 scale to a 0-10 scale, using the formula below.
Finally, the survey responses are transformed into their standard deviation values, from which the rankings are calculated.
where X = average value.
Trends
A trend or growth rate offers a more dynamic assessment than absolute values. The formulas used to calculate trends and growth rates are explained below:
1. Annual real growth rate (i = inflation rate):
2. Average annual percentage growth rate (n = number of periods):
Growth formulas, however, may have shortcomings. The average annual growth rate fails to reveal the real extent of changes, as it flattens or inflates year-to-year growth rates. For example, an average growth rate over two years might be calculated at 15%, while in reality there was 5% growth between the first and second years, and 25% between the second and third years. The average annual growth is used only when data vary widely in the middle years of a period, and less widely between the first and last years of the period. It is also used in cases where it is impossible to combine negative and positive initial and final values. This approach gives a more accurate picture than the compound rate under these circumstances.
Deflated Values
The following formula is used when calculating real growth rates from nominal values, because it takes into account cumulative inflation (e.g., real growth in Household Consumption Expenditure). The final deflated value is then used to obtain the annual real growth rate.
Taking a five-year time span as an example: Deflated final value (i = inflation rate):