Comparison of GDP per Capita & HDI in Developed vs. Developing Countries, Monografías, Ensayos de Matemáticas Aplicadas

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Does the overall Human Development Index depend on its GDP per

capita?

Page count: 38

1. Introduction During our economics class, we started talking about the importance of equity and how lucky we are to have health, education and decent economic standards. As a result, I started thinking about all those countries that do not have such opportunities and started to ponder how vital it is for a country to grow since without development, there are low levels of skills or knowledge; preventing a country's potential progress. Thereby, I wondered to what extent there is a relationship between the GDP of a country and its development index. The Human Development Index provides a better picture of a nation’s development, and I was keen on comparing it with the country’s GDP per capita to see if or how a nation’s economy has an influence on the development of it. Thus, I came up with investigating the following question: Does the overall Human Development Index depend on its GDP per capita? The following calculations will be vital in order to answer the research question: Firstly, as big samples offer more accurate values, a list of 60 randomly chosen countries will be subdivided into 2 groups: 30 developed and developing countries with its Human Development Index. A random sample will provide more precision and every country will have an equal chance of being selected.

World Bank , which are international organizations which provide reliable statistical^2 information. Secondly, the Human Development Index is defined as “Three basic goals of development that can be measured”. 3 A healthy life, increased education, and a fair level of living are the three essential aims. To collect all the necessary data, I have used the World Population Review.^4 Thirdly, the list of the 60 countries will be subdivided into two groups. On the one hand, a list of 30 developed countries, which refers to “A country with a relatively high level of economic growth and security”. On the second hand, another list of 30 developing countries, which refers to “ Countries that do not enjoy the same level of economic security, industrialization, and growth as developed countries ”. 5 The countries will be subdivided in order to see how the level of economic development of a country will affect its HDI value. Lastly, it is worth noting that the three most significant goals for a country’s Human Development Index are as follows. On the basis that those who live longer have benefitted from good health, life expectancy at birth is used to assess a long healthy life. (^5) Majaski. C.M. Investopedia. (2021, September 21). Developed Economy. Retrieved from https://www.investopedia.com/terms/d/developed-economy.asp (^4) World Population Review: Human Development Index (HDI) by Country. (2022). Retrieved from https://worldpopulationreview.com/country-rankings/hdi-by-country (^3) Blink, J., Dorton, I. (2012). IB Economics Course book: 2nd Edition: Oxford IB Diploma Program (International Baccalaureate) (2nd ed.). Oxford University Press. (^2) The World Bank & OECD (n.d). World Development Indicators / DataBank. The World Bank: GDP per capita (current US$). (2020). Data. Retrieved from https://data.worldbank.org/indicator/NY.GDP.PCAP.CD?name_desc=false

Furthermore, education is assessed by the average number of years spent in school for children of school-age. The GNI per capita is used to determine the level of life, or the capacity to satisfy basic necessities. These three indicators are added together to provide a 0 to 1 index (with higher values representing a higher level of development). Exploration The following are the countries that will be utilized throughout the exploration, along with their GDP per capita (US$) and HDI value: Table 1: The GDP per capita (US$) and the average Human Development Index of developed and developing countries Developed countries Developing countries Country GDP per capita HDI Country GDP per capita HDI Australia 51,693 0.938 Bolivia 3,133 0. Canada 43,258 0.922 Eritrea 643 0. Austria 48,587 0.914 Ethiopia 936 0. Belgium 45,159 0.919 Gabon 6,882 0. Costa Rica 12,141 0.794 Mexico 8,329 0. Japan 40,193 0.915 Iraq 4,146 0. Kuwait 24,812 0.808 Armenia 4,221 0. Qatar 50,124 0.848 Colombia 5,335 0. Romania 12,896 0.816 China 10,435 0. Spain 27,063 0.893 Burundi 239 0. United Kingdom 41,125 0.920 Cameroon 1,537 0. Cyprus 26,624 0.873 Cambodia 1,544 0. France 39,030 0.891 Chad 659 0. Germany 46,208 0.939 Ecuador 5,600 0. Chile 13,232 0.847 Eritrea 643 0.

Into the bargain, what will be firstly calculated is the GDP per capita of the 30 developed and 30 developing countries. The graphs were done with GeoGebra^6 Figure 1. Box and Whiskers plot of developed and developing countries GDP per capita GDP per capita (US$) In order to draw the Box and Whiskers, the following calculations are required. Outliers An outlier is considered when a number is above the third quartile + 1.5 x the interquartile range (Q 3 + 1.5 x IQR) or below the first quartile - 1.5 x the interquartile range (Q 1 - 1.5 x IQR). This means that they are the extreme numbers compared to the other values. Additionally, IQR refers to the difference between the upper and lower quartile. (^6) GeoGebra. (2022). GeoGebra Classic. Retrieved from https://www.geogebra.org/classic?lang=en

Outliers for developed countries IQR = Q3 - Q 1 = 48,773.3 - 22,932.2 = $25,841.1 US Upper boundary outliers UB → 48,773.3 + 1.5 x 25,841.1 = $87,534.95 US In this case, as the maximum GDP per capita value for developed countries is 85,267.8, there are no upper boundary outliers. Lower boundary outliers LB → 22,932.2 - 1.5 x 25,841.1 = $-15,829.45 US The minimum GDP per capita value for developed countries is 12,140.9, therefore there are no lower boundary outliers. Outliers for developing countries IQR = Q3 - Q1 → 4,266.7 - 797.9 = $3,468.8 US Upper boundary outliers: UB → 4,266.7 + 1.5 x 3,468.8 = $9,469.9 US As already seen in the box and whisker diagram, the cross indicates that there is an outlier. The maximum GDP per capita value for the developing countries is $10,434. US, hence there is an upper boundary outlier.

STANDARD DEVIATION ( ) σ To calculate the standard deviation, the following formula will be used. σ = Σ(𝑥𝑖− μ) 𝑁 For this formula, N represents the number of values collected, 𝑥 are all the values of 𝑖 data, and lastly, μis the mean of the data. σ = (51,692.80 − 36,664.0567) 2

• (43,258.20 − 36,664.0567) 2
• (48,586.80 − 36,664.0567) 2
• (...) 2 30 σ ≈ $17,765 US Developing countries MEDIAN 𝑀𝑒𝑑𝑖𝑎𝑛 = = 1,903. 1,878.6 + 1,927. 2 MEAN ( 𝑥 ) → 3,133.10 + 642.5 + 936.3 + 8,329.30 + 4,145.90 + (...) 30 ( 𝑥 ) ≈$ 2,888 US STANDARD DEVIATION σ = (3,133.10 − 2,887.9367) 2
• (642.5 − 2,887.9367) 2
• (936.3 − 2,887.9367) 2
• (...) 2 30

σ ≈$2,517 US Now that the calculations are measured, I have checked it in Geogebra and it shows that the calculations were correctly done: Table 2. Measures of central tendency and variation of GDP per capita (current US$) Countries n (^) Mean ( )𝑥 Standard deviation ( )σ Minimum value Q1 Median Q3 Maximum value Developed 30.0^ 36,664^ 17,765^ 12,141^ 22,932^ 39,612^ 48,773^ 85, Developing 30.0^ 2,888^ 2,517^239 798 1,903^ 4,267^ 10, Analysis As it can be observed in the box and whiskers diagram, developed countries have a higher GDP per capita overall. The diagrams are not symmetrical nor have the same skewness. On the one hand, developed countries’s box plot is negatively skewed, representing that the mean( ) ($36,664.0567 US) which takes into consideration all𝑥 values to calculate the average, is higher than the median ($39,611.85 US). However, it is more stretched, which can also be seen by their high standard deviation ( ) of $17,765σ US, thus, representing a higher variation which is advantageous when comparing the data. On the other hand, for developing countries is positively skewed, meaning that the mean( ) ($𝑥 2,888US), is higher than the median ($1,903 US). Nevertheless, the standard

Box and Whisker plot for HDI Figure 2. Box and Whiskers plot of HDI value Outliers for developed countries IQR = Q3 - Q1 → 0.925 - 0.857 = 0. Upper boundary outliers

UB → 0.925 + 1.5 x 0.068 = 1.027 HDI value

Since the maximum HDI value for the developed countries is 0.95, there are no upper boundary outliers. Lower boundary outliers

LB → 0.857 - 1.5 x 0.068 = 0.755 HDI value

Since the minimum HDI value for the developed countries is 0.794, there are no lower boundary outliers. Outliers for developing countries IQR = Q3 - Q1 → 0.724 - 0.495 = 0. Upper boundary outliers UB → 0.724 + 1.5 x 0.229 = 1,0675 HDI value As the maximum HDI value for the developing countries is 0.786, there are no outliers. Lower boundary outliers LB → 0.495 - 1.5 x 0.229 = 0.1515 HDI value The minimum value for the HDI value is 0.786, thus there are no lower boundary outliers for the developing countries.

STANDARD DEVIATION

Developed countries: σ = (0.938 − 2,887.9367) 2 + (0.922 − 2,887.9367) 2 + (0.914 − 2,887.9367) 2 + (...) 2 30 σ = 0.0449 HDI value Developing σ = (0.703 − 2,887.9367) 2 + (0.434 − 2,887.9367) 2 + (0.470 − 2,887.9367) 2 + ( ...) 2 30 σ = 0.1222 HDI value Table 3. Measures of central tendency and variation of HDI values Countries n (^) Mean ( )𝑥 Standard deviation ( )σ Minimum value Q1 Median Q3 Maximum value Developed 30 0.8901^ 0.0449^ 0.794^ 0.857^ 0.892^ 0.925^ 0. Developing 30 0.5984^ 0.1222^ 0.401^ 0.495^ 0.580^ 0.724^ 0.

Analysis As shown, both box plots are quite symmetrical. Developed countries contain a normal distribution with a standard deviation( ) ofσ 0.0449. This means that the mean ( ) of𝑥 0.8901 and a median of 0.892, is practically the same. Additionally, it is also important to highlight that the HDI is less varied and all values stay at a high level. On the other hand, developing countries is more positively skewed with a higher standard deviation ( ) ofσ 0.1222. This indicates that the mean ( ) (𝑥 0.5984), is higher than the overall median (0.580). In relation to both box plots (GDP and HDI), it can be seen that the GDP in developing countries is less varied as they all have a low country prosperity. However, developed countries have a less varied HDI value, indicating that they all stay in the high values with a minimum of 0.794. As a result, let's respond to the following question: How is the overall HDI value connected to a country’s GDP per capita? By definition, GDP defines the size and performance of a country's economy. The influence of human power resources is shown in the HDI value, which is influenced by the level of economic growth. In fact, when GDP grows rapidly, firms are likely to recruit more workers for their factories, thus raising people's living standards (one of the HDI components), since they are able to spend and consume more. However, as already noted, in certain circumstances, such as China, the economy may develop but not quickly enough to provide enough jobs for everyone, thus keeping its HDI at a lower level.

Figure 3. Scatter graph to show correlation between GDP per capita and HDI value of developing countries DEVELOPING COUNTRIES As can be observed, the HDI value and the GDP per capita of emerging nations are linked. Pearson's moment correlation coefficient will be calculated to find the strength of the linear correlation. Calculating PMCC for developing countries In order to do this calculation, we firstly have to find the 𝑅 which is seen in the 2 diagram above (0.681). To determine the PMCC, we have to square root the mentioned number.

2

2. PMCC (R) = 0. 681
3. R= 0.825 (3 sf) An R value of 0.825 indicates that there is a strong and positive linear correlation. This shows that a line of regression can be conducted in order to interpret the scatter graph in more detail. Calculating the Equation of the Line for developing countries The formula for the equation of the line is as follows, where y represents the HDI value, and x the GDP per capita. y = mx + c
4. HDI value = m x GDP per capita (US$) + c
5. y = 0.0000401x + 0. To do this calculation, I have chosen a random country with the website Random Lists.^8 Mexico has been the chosen developing country with a GDP per capita of $3,133 US. HDI value = m x GDP per capita (US$) + c Given the formula y = 0.0000401x + 0.483, x has to be substituted with Mexico’s GDP per capita. y = 0.0000401 ×8,329 + 0. y = 0.8169929 ≈0. Mexico = 0.817 HDI value and according to the table of the data basis, Mexico’s HDI (^8) Unknown. (n.d). Generate Random Countries. Random Lists. Retrieved from https://www.randomlists.com/random-country