# DHDI Analytics

## Comparison of HDI vs. DHDI

The DHDI helps rank countries based on how well they improved overtime on the combination variables chosen to measure the quality of life in countries. This is opposed to the HDI, which ranks countries based on how well they are doing based on the combination of variables chosen to measure the quality of life in countries. While the HDI tells you the ranks of countries based on how ‘developed’ they are at a point in time, the DHDI tells you how countries are improving over time (hence, Dynamic). The DHDI is the measure of development as opposed to the HDI, which is a measure of how developed.

A simple analogy will clarify the difference. Assume two runners Quick and Quicker who need to rank. Note, we haven’t told you to rank based on what. Assume that Quick ran the 100 meters in 20 seconds in 2017 (year), and Quicker ran the same 100 meters in 12 seconds in 2017. Now assume that in 2019 Quick ran the 100 meters in 14 seconds, and Quicker ran the same 100 meters in 13 seconds. In both years, if we were to rank them based on how fast they ran, Quicker will be first and Quick second.

On the other hand, if we were to rank them on how much they improved between 2017 and 2019, then Quick will be first (improved from 20 seconds to 14 seconds), and Quicker will be second (became worse by going from 12 to 13 seconds). Note that Quicker needn’t run slower in 2019 than 2017 to be ranked second on the improvement scale. It is reasonable to say that if Quicker had gone from 12 seconds to 11 seconds, even though there was an improvement, we would say that Quick improved a lot more than Quicker.

The HDI ranks countries based on how fast they run. The DHDI ranks countries based on how much they improve in their running speeds.

The DHDI seeks to rank countries based on their combined improvement given a set of variables appropriate to measure well-being and quality of life. In its basic HDI calculation, the UNDP uses health, education, and income, each weighted by a third. It calculates the HDI by taking the geometric means of the indexes for each variable. Details for how the HDI is calculated can be found here.

The DHDI follows a methodological structure similar to, but different from, the way the HDI is calculated. It is similar in the variables it uses (see the last paragraph for more on this) and sets up an index for each variable and combines it. But given what is being calculated, it is different from the HDI, as discussed below.

To calculate the DHDI we take the weighted arithmetic mean in the improvement in the three variables (again, the UNDP variables are health, education, and income, and the weights of each are a third) as opposed to the geometric mean. In comparison, it is appropriate to use the geometric mean for the HDI (intuitively suggesting that if you are the worst in any development-related variable, then you are last in the ranking. Put another way, a country which is ranked moderately in all three variables will be ranked higher than a country that in principle can be spectacular in two variables and really, really bad in the third). On the other hand, the arithmetic mean is more appropriate for the DHDI. Intuitively this suggests that if you improve a lot in two of the three variables and do not improve at all in the third, you can be ranked higher than a country that improves moderately in all three.

## How is the relative improvement in any single variable (income, education, etc.) calculated?

The number of years n is a choice variable. Typical values for n are 5, 10, 15, or 20 years period.

The amount any year is weighted decreases the further the year is away. So if the improvement from one year away is weighted δ, the improvement from 2 years away is weighted δ², and the improvement from 3 years away is weighted δ³, etc. Note:

The calculation for the relative improvement for each year is a little trickier. While it seems natural to simply calculate a percentage increase in the units of a variable for a country, this does not pass the smell test. For example, using this method, if the life expectancy of a country improves from 25 to 35, and another country improves from 60 to 70, it will seem that the first country does better – improving by 40% as opposed to the second country that simply improves by 16.66%. But we know going from 60 to 70 is more difficult to achieve and therefore a better improvement than going from 25 to 35. So we calculate how well a country improves by calculating .

The amount improved is what the actual data tells us. The potential for improvement is the difference between the max for the variable (determined by the UNDP for each of the variables used in the HDI) – where a country is in the year the improvement is being calculated from. Once this measure is obtained for each country, we follow the methodology used by the HDI to rank a count on an index from 0 to 1 for each year of the n years. 0 will signify the least improvement and 1 for the greatest improvement.

So we now have an index score for each year and a weight to be attached to each year. The Relative DHDI score for each variable is obtained by the formula: