Method

Introduction
The JustJobs Index is built following a hierarchal framework. The top level is the index itself, the second tier consists of five main dimensions, which in turn may or may not consist of sub dimensions.. The sub dimensions group sets of indicators.

Index Dimensions

The framework of the JustJobs Index

Based on the framework the index is constructed in five steps.

Step one: Selection of Indicators and Data Collection
The quality of a good index is partly a function of the quality of the underlying indicators. The choice of indicators is based on the JustJobs conceptual framework and covers the five dimensions. Data were gathered from publicly available secondary sources, such as the World Bank, the ILO, the OECD etc. In some cases, data have also been gathered from national statistical bureaus.

Step two: Imputation of missing data
Missing data was a major challenge for constructing the index. Nothing can be done in the case of countries with no data for an indicator. However, many countries have missing data for some years for some indicators. In order be able to construct the index despite missing data, imputation was used, i.e. assigning missing data points reasonable values.
In the case of country series with only one or a few missing data points imputation was conducted by use of the loess regression. Loess regression is a local regression model that can take into account both the overall trend and the particular values around specific data points. Some countries have only one measurement for an indicator for the whole time series. In such cases we set the value to a constant equal to the obtained measure for all years. The effect of that is an underestimation of change. A complete data without missing values was obtained.

Step three: Normalization of data
Indicators are measured in different ways. Some are expressed as percentages, others as money, and yet others as ratios. In order to make it possible to make a composite index each indicator must be normalized, i.e. transformed so that all indicators have a common scale.

Common scales can be constructed through different normalization methods, each having its own characteristics. For example, normalization by ranking brings out the relative position of countries with regard to each other, but does not use information about how much countries differ from each other, while Min-max rescale uses such information.

For each indicator we had to determine what we considered as positive or negative developments. For example, an increase in people covered by pensions schemes is good, while an increase in unemployment is bad. Similarly any deviation from equal rates of employment for men and women is bad, regardless of direction. Therefore, the each indicator was normalized taking into account if the preferable outcome was high, low, or equal to a particular value.

Ranking
This method of standardization measures the performance of the countries over time in terms of relative positions, which constitute the rankings.
form-1

Standardization (z-scores)
The indicators are converted into a scale with a mean of zero and standard deviation of one. Extreme values have a greater effect on the index, and hence this method highlights exceptional behavior.
form-2

Min-max rescale
With this method, the indicators are given an identical range, from 0 to 1.
form-3

Distance to a reference (base year 2000)
This method measures the position of an indicator relative to a reference point.
form-4

Step four: Aggregation and construction of composite index
We have employed a simple arithmetic using an additive average of all the normalized indicators associated with each of the just jobs index dimensions and constructed an additive index. All the indicators are given equal weights.

Step five: Sensitivity analysis and selection of final index
Sensitivity analysis helps in evaluating the robustness an index by assessing the contribution of each indicator to the index variance. Sensitivity tests were conducted in order for the index to include the appropriate variables and to make sure that they are added and normalized in the most appropriate way.

The formula used for the sensitivity test is:
form-5
After conducting a series of sensitivity analysis on the results, the rescale method was selected and the JustJobs Index was established.