Does money buy happiness?

Leilane Cambara 2024-03-15

Introduction

This is an old question and you already probably thought about it at some point in your life, finding your own answer for it. In the past decade, there has been an increasing effort to make happiness a variable to be taken into account in government policymaking. The World Happiness Report, which polls people around the world about their lives, resulting in the Happiness Score, is a reflection of this.

In a dashboard in Tableau Public, I created a visualisation to explore the relationship between the Happiness Score and GDP per capita to try to answer the question.

The GDP per capita is the Gross Domestic Product (GDP) per person in an economy and the GDP, in simple terms, is the monetary value of how much a country produced within its borders in a certain period. It is the main variable used to evaluate the state of an economy.

In this short report, I analyse the data and fit a model to it.

Descriptive statistics

The Happiness Score comes from the World Happiness Report and the GDP per capita comes from Our World in Data and the World Bank. In order to be able to also explore potential regional differences, I group the countries by world regions as categorised by the World Bank, collected from Our World in Data.

I merge the data sets using an inner join, such that I keep only the countries with records in all tables. This results in a sample of 138 countries, with the following distribution by regions:

World Region	Countries
East Asia and Pacific	15
Europe and Central Asia	48
Latin America and Caribbean	18
Middle East and North Africa	15
North America	2
South Asia	6
Sub-Saharan Africa	34

Number of countries per region

Europe and Central Asia is the region with the most number of countries (48), followed by the Sub-Saharan Africa (34). North America is the region with the least number of countries, with only two: United States and Canada. Even though Mexico is geographically located in North America, it is culturally a Latin American country, such that it is included in the Latin America and Caribbean region.

The Happiness Score, by construction, is a number that ranges from zero to ten, while the GDP per capita is expressed in international dollars at 2017 prices and can be any positive number.

In 2022, the average of the Happiness Score around the world was 5.56, just above 50%, with a standard deviation of 1.11. The countries who had the minimum and maximum Happiness Score, or in other words the happiest country and the least happy country in the world were Finland (score of 7.82) and Afghanistan (score of 2.4).

The average GDP per capita in 2022 was 2263.43 international dollars, with a standard deviation of 22013.07. The highest GDP per capita (115683.49, produced by Luxembourg) was almost 100 times higher than the lowest one (1186.58, produced by Niger).

	Mean	Min.	Max.	St. dev.
Happiness Score	5.56	2.40	7.82	1.11
GDP per capita	22263.43	1186.58	115683.49	22013.07

Descriptive statistics of the Happiness Score and GDP per capita

Analysing the Happiness Score by region, we see that North America was the happiest region in 2022, with a score of 7: 7.03 for Canada and 6.98 for the United States. As it was classified, North America is an homogeneous region, which reflects in similar Happiness Scores. South Asia, on the other hand, which includes the least happy country in the world (Afghanistan) was the least happy region, with an average score of 4.27. The happiest country in the region, Nepal, only scored 5.38. Middle East and North Africa is the region with the highest standard deviation and widest Happiness Score range: Lebanon scored the minimum of 2.96 and Israel the maximum of 7.36. The region’s average score was 5.29. After North America, which only includes two countries, Latin America and Caribbean, which had an average score of 6.01, is the region with the smallest standard deviation (0.32) and range in the score: Costa Rica was the happiest country with 6.58 and Ecuador was the least happy with 5.53.

World Region	Mean	Min.	Max.	St. dev.
East Asia and Pacific	5.77	4.39	7.20	0.78
Europe and Central Asia	6.30	4.74	7.82	0.79
Latin America and Caribbean	6.01	5.53	6.58	0.32
Middle East and North Africa	5.29	2.96	7.36	1.20
North America	7.00	6.98	7.03	0.03
South Asia	4.27	2.40	5.38	1.08
Sub-Saharan Africa	4.46	3.00	6.07	0.67

Descriptive statistics of the Happiness Score by world region

World Region	Mean	Min.	Max.	St. dev.
East Asia and Pacific	26882.34	4032.63	106032.23	26977.46
Europe and Central Asia	36021.48	3903.32	115683.49	22577.67
Latin America and Caribbean	15039.49	5572.18	29037.94	6990.52
Middle East and North Africa	24334.56	5643.07	69733.80	20090.58
North America	55781.33	47892.94	63669.71	11155.86
South Asia	6078.36	1516.31	13386.68	4006.95
Sub-Saharan Africa	4597.80	1186.58	20967.95	4653.80

Descriptive statistics of the GDP per capita by world region

The relationship between money (GDP per capita) and happiness

There is a moderate positive correlation (which is linear) between GDP per capita and happiness, of around 0.75, but the scatter plot suggests there is a nonlinear relationship between them.

Fitting a model

It looks like a logarithmic model could be a good candidate to fit the data. Hence, in what follows, I fit the data to:

$Happiness_Score = \beta_0 + \beta_1\ln(GDP_per_capita) + \epsilon$,

where $\beta_0$ is the intercept, $\beta_1$ is the coefficient for the effect of the natural logarithm of GDP per capita on the Happiness Score, and $\epsilon$ is an error term.

## 
## Call:
## lm(formula = unlist(df["Happiness_score"]) ~ log(unlist(df["GDP_per_capita"])))
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.60793 -0.36595  0.02777  0.45745  1.29552 
## 
## Coefficients:
##                                   Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                       -1.70598    0.47924   -3.56 0.000512 ***
## log(unlist(df["GDP_per_capita"]))  0.76753    0.05025   15.27  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6738 on 136 degrees of freedom
## Multiple R-squared:  0.6317, Adjusted R-squared:  0.629 
## F-statistic: 233.3 on 1 and 136 DF,  p-value: < 2.2e-16

The result implies that the relationship between the variables is given by:

$Happiness_Score = -1.7060 + 0.7675\ln(GDP_per_capita) + \epsilon$,

such that, for a country with a GDP per capita of 44,979 (the UK), we would predict a Happiness Score of 6.5170, while the actual was 6.9430. The scatter plot with the predicted line shows that the logarithmic model is a decent approximation, even though it might not be the best.