econ2041-income-happiness

ECON 2041

Introductory Econometrics

Income & happiness

Plan for the semester

1 What is econometrics?

2 Basic mathematical tools

3 Stats fundamentals

4 Stats fundamentals II

5 Simple regression

6 OLS properties & fit

7 Flavors of OLS & OVB Quiz

8 Causality

9 Regression inference

10 Inference, continued PS due 16 Oct

11 Diagnostics

12 Measurement error & IRL

13 Revision

Happiness

Cantril Ladder score

Source: Gallup World Poll

Please imagine a ladder, with steps numbered from 0 at the bottom to 10 at the top. The top of the ladder represents the best possible life for you, and the bottom of the ladder represents the worst possible life for you. On which step of the ladder would you say you personally feel you stand at this time?

GDP per capita

GDP per person, adjusted for inflation and purchasing power

Total value added from the production of G&S in country
Divided by population
PPP-adjusted
In "international dollars"
Source: World Bank

Cross-sectional data

144 countries in 2024
GDP per capita (X) & happiness (Y) are both continuous RVs
Why? They're draws from a larger conceptual population

Experiment

draw a set of respondents from each country
calculate their average life satisfaction

Sample space

set of all possible tuples of country averages you could get
X maps each outcome of that process to a number

Now let's open the data!

Open this week's lecture notebook and follow along:

https://emiliatjernstrom.com/econ2041/lectures/w03

It will open directly in Colab

Click Copy to Drive first, so you can save any edits

The notebook reproduces every figure in today's slides

The mean and the median disagree about GDP

happy[['Happiness', 'GDP_pc']].describe()

	count	mean	std	min	25%	50%	75%	max
Happiness	144	5.58	1.15	1.36	4.71	5.87	6.47	7.74
GDP_pc	144	27,642	26,296	1,409	7,057	17,796	42,378	134,549

Most countries rate between 4 & 7

Data: Gallup World Poll & World Bank, via Our World in Data

GDP per capita is strongly right-skewed

Each picture is one line of code

sns.histplot(happy['GDP_pc'], bins=15)

Happiness, given GDP

\mathbb{E}[\,\text{Happiness} \mid \text{GDP per capita}\,]

Conditioning is a Boolean

median_gdp = happy['GDP_pc'].median()
mask = happy['GDP_pc'] > median_gdp

Entity	GDP_pc	mask
Afghanistan	1,964	False
Albania	21,641	True
Algeria	15,502	False
Argentina	26,772	True
Armenia	20,079	True

Happiness conditional on GDP

Happiness conditional on GDP: independent?

The joint distribution: one dot per country

Data: Gallup World Poll & World Bank, via Our World in Data

The joint distribution is one line of code, too

sns.scatterplot(data=happy, x='GDP_pc', y='Happiness')

The median split, in color

Is the median the right split?

Richer half vs poorer half
Top third vs bottom third
Top quarter vs bottom quarter
Top tenth vs bottom tenth

More extreme comparisons

Rule	N high	N low	Mean high	Mean low	Gap	s.e.(gap)
Richer half vs poorer half	72	72	6.35	4.82	1.53	0.14
Top third vs bottom third	48	48	6.58	4.47	2.11	0.14
Top quarter vs bottom quarter	36	36	6.73	4.33	2.41	0.16
Top tenth vs bottom tenth	15	15	6.88	4.03	2.85	0.26

The humps pull apart, and get bumpier

What each rule throws away

Nothing in the data tells you which cut is correct

Some take-aways

We can tell stories with data

Visualization is powerful
Always explore first

Before you go: forecast your semester

One more portal round, open now

Open your portal link
https://emiliatjernstrom.com/econ2041/portal.html

OR scan the QR code, then enter your code
Forecast your own final mark, then judge three hypothetical students

Portal answers are anonymous & ungraded

Results revealed next week

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