Session 6: Panel Data and Fixed Effects
Date: Thursday, 28 May 2026, 16:00–19:00
Business question
Does rising income make countries happier — and what would it take to interpret that relationship causally?
Learning goals
- Understand the logic of panel data: N units × T time periods, indexed \((i,t)\)
- Distinguish within- from between-unit variation and explain why the difference matters
- Apply fixed effects estimation to control for time-invariant unobserved heterogeneity
- Recognise what fixed effects cannot fix: time-varying confounders and feedback
- Connect the FE identification argument to the causal reasoning framework of Session 5
- Use
fixest::feols()for efficient FE estimation; cluster standard errors at the unit level
Datasets
Slides and live demo — World Happiness Report panel
Country-level panel of life satisfaction and GDP per capita for ~140 countries, 2011–2023. Merges three sources: WHR 2026 (happiness), World Bank WDI (GDP per capita, unemployment, population), and SWIID 9.2 (disposable income Gini).
| Variable | Description |
|---|---|
happiness |
Life satisfaction (0–10, WHR 3-year average) |
GDP_pc |
GDP per capita, PPP (constant 2017 int’l $) |
gini_disp |
Disposable income Gini coefficient |
unemployment |
Unemployment rate (% of labour force) |
Exercise — World Management Survey (WMS)
Manufacturing firms across 24 countries, surveyed in multiple waves 2004–2015 as part of the World Management Survey project.
| Variable | Description |
|---|---|
management |
Management quality score (1–5 scale) |
degree_nm |
Share of non-managers with a college degree |
emp_firm |
Number of employees |
firmid |
Unique firm identifier |
wave |
Survey wave (year) |
Source: Békés & Kézdi (2021). Download: https://osf.io/t6zdp/
Session outline
- Debrief of exercise and previous session (~30 min)
- Input: Motivation — the Easterlin paradox; panel data structure; the FE estimator; two-way FE
- Live demo: the income–happiness panel, model progression, causal interpretation, time-varying confounders
- Break
- In-session exercise: firm-level panel, management quality and workforce education
- Debrief + Quarto skill: reporting panel results with confidence intervals and
modelsummary
Materials
| File | Description |
|---|---|
| Slides | Lecture slides — open in browser, press F for fullscreen |
| Live demo | Coding document built during the session — Easterlin panel analysis |
| Exercise | In-session exercise: firm FE with WMS data (via GitHub Classroom) |
| Exercise solution | Example solution (added after session) |
Further reading:
If you are interested in the relationship between income and happiness, this recent paper is a worthwhile read. Not only does it survey previous results and explain the history of discussions on this topic, it also provides new evidence.:
Killingsworth, M. A., Kahneman, D., & Mellers, B. (2023). Income and emotional well-being: A conflict resolved. Proceedings of the National Academy of Sciences, 120(10), e2208661120. https://doi.org/10.1073/pnas.2208661120
Quarto skill introduced this session
Presenting panel model results: confidence intervals instead of standard errors, the within-\(R^2\), and notes on fixed effects and clustering.
```{r}
modelsummary(
list("Pooled OLS" = m0, "Country FE" = m1, "Two-way FE" = m2),
statistic = "conf.int", # show [lower, upper] instead of (SE)
conf_level = 0.95,
gof_map = c("nobs", "r.squared", "r2.within"),
notes = "95% CIs. FE models clustered at country level.",
output = "flextable"
) |> autofit()
```The within-\(R^2\) (r2.within) measures fit on the demeaned data — the variation the FE model actually uses. Always report it instead of the inflated overall \(R^2\).