# Guide to calculating and interpreting the HDI

The Human Development Index (HDI) is an indicator of progress. It is increasingly important to measure the capacities of a society and not only from an economic point of view. In this article we develop the concept of HDI in depth.

The Human Development Index (HDI) is a combined indicator with a different profile than the indicators traditionally used to measure progress. Historically, the indicator most used as well as criticized to elaborate this task has been the gross domestic product (GDP). At the same time, the GDP since it began to be used around 1930 by its creator (Simon Kuznets) has undergone different variations.

Among the variations are some such as comparing countries not only in the same currency, but also taking into account the price level and purchasing power. For example, taking into account purchasing power parity (PPP).

Be that as it may, Kuznets himself, who was awarded the Nobel Prize in Economics in 1971, recognized that some measures, including the one created by him, present many limitations to measure the well-being of a country.

## Does the HDI replace GDP?

No, absolutely not. They are two different indicators. The GDP aims to measure economic growth, while the HDI aims to measure human development through other indicators.

In the same way that there are indicators for inflation, for the unemployment rate or for the poverty line, there are indicators for human development.

Another issue would be the reliability of the index. A detail that we will comment in depth later.

## Components of the HDI

As described by the United Nations Development Program (UNDP), the Human Development Index (HDI) contains the following components:

- Long and healthy life: Life expectancy at birth is taken into account.
- Access to education: Expected years of schooling and average years of schooling.
- Decent standard of living: Through per capita gross domestic product (GDPpc), adjusted for purchasing power parity.

Despite the fact that it is closer to the well-being of society than gross domestic product, since it includes it in its calculation — in addition to other variables that are also important — it is far from perfect.

One of the great criticisms has been not taking inequality into account. Hence, UNDP has developed an Adjusted Human Development Index (IDHA). In this, the variables to take into account are the same, but when calculating the indices that lead us to the final result, inequality is taken into account.

## How is the HDI calculated?

Data are needed to calculate the Human Development Index (HDI). Data that we can collect from different sources. Thus, UNDP indicates in its methodological note its data sources:

- Life expectancy at birth: UNDESA
- Expected years of schooling: UNESCO, ICF Macro Demographic and Health Surveys, UNICEF, OECD surveys.
- Average years of schooling: UNESCO, ICF Macro Demographic and Health Surveys, UNICEF and OECD surveys.
- Gross domestic product per capita: World Bank, IMF and United Nations Statistics Division.

### Steps to calculate it

Once we know the data to use, we must create what the UNDP calls dimension indexes. That is, the indices with which we will calculate the final index.

Below is a table of dimensions from which the dimension of each index is calculated:

Dimension | Indicator | Minimum | Maximum |

Health | Life expectancy (years) | 20 | 85 |

Education | Hope for years of schooling Average years of schooling | 0 0 | 18 15 |

Entry | Gross domestic product per capita (2011 PPP $) | 100 | 75000 |

This table is the indicative table to calculate the indices of any country. Thus, for a given country, the way to calculate each dimension index is used the following formula:

Dimension index = (current value - minimum value) / (maximum value - minimum value)

Where the current value is the data of the dimension chosen for a country. Then we will see an example, so do not worry because we can see it in detail. But, before going with the example, we would like to indicate some details about the minimum and maximum values.

The table above is the reference table. If a country has the maximum in everything, its HDI will be 1, while if it has the minimum values, its HDI will be zero. Therefore, the HDI will always be between 0 and 1. The higher the better.

You may wonder why the minimum value of life expectancy is 20, or the minimum GDP per capita in PPP $ is 100. Let's explain it:

In the first place, it is assumed that the minimum life expectancy is 20, since during the 20th century there is evidence that no country on the face of the earth had a life expectancy of less than 20 years, the maximum is 85 percent. This is a realistic measure, according to the UNDP.

Regarding education, the minimum is obviously zero for both components. The expectation of years of schooling sets its maximum limit at 18 years, which is equivalent to obtaining a university degree in most countries. On the other hand, schooling sets its maximum at 15 years, which is the maximum projected for this indicator for the next few years.

Lastly, the GDP per capita sets its minimum figure at 100 constant dollars under purchasing power parity (PPP) and the maximum at 75,000 PPP dollars. The minimum is set at $ 100 PPP because even those countries that do not collect data need at least this figure to survive. On the opposite side, that of the maximum, the limit of $ 75,000 per capita PPP is set since according to the studies by Kahneman and Deaton there are no significant gains in human development and well-being when GDP per capita in PPP exceeds these figures.

Finally, once the indices of each dimension have been calculated, the final index is calculated. That is, the number that we see as the final result:

HDI = (IShealth · IEducation · Income) 1/3

Note: In the case of the education index, the arithmetic mean of the two components is performed. In the index on income, the variables in logarithms base 10 are taken into account to adjust the calculations.

## Example of HDI calculation

To calculate the HDI of a certain country, we are going to follow the steps that we have described above:

- Obtaining data
- Calculation of dimension indices
- HDI calculation

Suppose the data for country X are as follows:

Indicator | Value |

Life expectancy (years) | 73,3 |

Hope for years of schooling Average years of schooling | 10,5 8,5 |

Gross domestic product per capita (2011 PPP $) | 10,300 pc PPP $ |

Once we have the data, we calculate the index of each dimension

- IShealth

IShealth = (73.3 - 20) / (85 - 20) = 0.82

- IEducation

Years of schooling expectancy = (10.5 - 0) / (18 - 0) = 0.583

Average years of schooling = (8.5 - 0) / (15 - 0) = 0.567

IEducation = 0.567 + 0.583 / 2 = 0.575

- Income

Income = log (10,300) - log / log (75,000) - log = 0.70

Once all the dimension indices have been calculated, we have to calculate the final HDI.

HDI = (IShealth · IEducation · Income) 1/3

We substitute in the formula:

HDI = (0.82 0.575 0.70) 1/3 = 0.692

## Criticism of the HDI

The HDI has been a highly criticized indicator since its inception. Not a few people indicate that it is not a totally reliable quantity. And, indeed, they are partly right.

As an indicator, it cannot cover all reality and leaves out variables that may reflect a delicate situation in a country. For example, a country that has an abrupt fall in GDP per capita, whose population begins to starve, will not automatically see its variations in the HDI reflected. Life expectancy, to name the first variable, will fall but gradually. Therefore, the HDI, assuming that the data on which it is calculated are reliable, offers us an overview of long-term evolution.

In addition, it is not only important to understand that the variables on which it is calculated can be rigid in the short term, but also the reliability of the data. The UNDP, contrary to what many people believe, does not base its data exclusively on the metrics offered by the countries. Compare the data from different institutions and offer a final combined data. For example, regarding GDP per capita, it collects data from the World Bank, IMF and United Nations Statistics Division. However, these organisms are not infallible and their estimates differ from each other, since it is not easy to calculate these metrics.

Another important point is the adjustment for inequality. Suppose a country with 100 inhabitants. 50 have a life expectancy of 40 years and another 50 of 90 years. The average life expectancy will be 65 years, but there is enormous inequality. The same would happen with education or income. Adjusting for inequality has been a great advance in the development of this indicator. Its calculation is complicated and the data does not make it easy, but it was necessary.

Although there are many more criticisms, we will name the composition of the index last. More indicators could be added, indicators that reflect in a more up-to-date and reliable way the levels of education, health and income. It is useless to have an average of 10 years of schooling, if the education is of poor quality. In the same way, a high life expectancy does not guarantee that those years of life will be with a good quality of life.

In order for you to better document yourself, we have created the following articles:

HDI calculator HDI ranking
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