EMET8002 Chap.8 Panel Data With Fixed and Random Effects
Panel Data With Fixed and Random Effects
Panels and their advantages
Panel data follow many units over time.
The chapter covers long and wide formats, cohort and panel studies, attrition, and pooled OLS with clustered standard errors, then shows how differencing and fixed effects remove time-invariant omitted variables, using the lecture's case of beer taxes and traffic deaths.
Choosing and extending the model
Random effects, the Hausman test and the practical rules for choosing between the two estimators are set out, along with time fixed effects, the HILDA survey, and the difference and system GMM estimators for models with a lagged dependent variable.
Portfolios and wage panels in Week 9
The Week 9 lab reshapes daily industry portfolio returns from wide to long format, declares the panel, and tests whether the Great Depression, the Second World War and the global financial crisis moved returns.
It then runs a wage panel through a Hausman test, time fixed effects and the addition of schooling. Marks follow from justifying each model choice in words, since the lab notes that often no model satisfies every assumption.
What this chapter covers
- 01
Cross-section, time series and panel data
- 02
Long and wide format
- 03
Pooled OLS with clustered standard errors
- 04
Two-period differencing
- 05
Fixed and random effects
- 06
The Hausman test
- 07
State and time fixed effects
- 08
Difference and system GMM
- 09
The HILDA survey
Worked example · free
Why pooling hides the within-unit slope
- 1Within entity A, the outcome rises by 7.5 − 6.5 = 1.0 as X rises by 3 − 1 = 2, a slope of 0.5.
- 1Entities with higher X have lower intercepts, so pooling mixes the between-entity pattern with the within-entity one.
- 1Fixed effects give each entity its own intercept and recover the within slope of 0.5.
Key terms
- Balanced Panel
- A panel in which every unit is observed in every time period.
- Random Effects
- A panel estimator that treats the unit effect as random and uncorrelated with the regressors.
- Hausman Test
- A test of whether the unit effect is correlated with the regressors, used to choose fixed or random effects.
- Difference GMM
- A dynamic panel estimator that instruments the differenced lag with earlier levels.
- Sample Attrition
- The loss of panel members over time, which can make a sample unrepresentative.
Panel Data With Fixed and Random Effects FAQ
When should I use fixed effects instead of random effects?
Use fixed effects when the unobserved unit characteristic is likely correlated with the regressors, which a Hausman rejection supports. Prefer random effects when that correlation is implausible, when units change little over time, or when you need to estimate a time-invariant variable.
Why does a cross-section regression of traffic deaths on beer taxes mislead?
States differ in many fixed ways, such as road quality and drinking culture, that correlate with taxes. Comparing changes within states over time removes those factors, and the lecture's before-and-after regression then finds that higher beer taxes go with fewer deaths.
What problem do the GMM estimators solve?
With a lagged dependent variable, the lag is correlated with the unit effect, so fixed effects are biased. Difference GMM removes the unit effect by differencing and instruments the differenced lag with an earlier level; system GMM adds the level equation for extra efficiency.
What is the difference between long and wide panel format?
Wide format has one row per unit with a column for each period's value, while long format has one row per unit and period. Stata's panel commands need long format, so data in wide format are reshaped first and then declared as a panel with xtset.
What does HILDA offer for a research project?
HILDA is a household panel that began in 2001 and interviews all adult household members every year. It tracks economic and subjective wellbeing, labour market and family dynamics, which makes it suitable for fixed effects designs. Students apply individually through the Australian Data Archive and may use only General Release 22.
Assessment move
Run the full Stata sequence once on a small panel: xtset, fixed effects, random effects, the Hausman test and time effects. For each step, write one sentence saying what it assumes and what it removes. Finally, state in one sentence the unobserved factor that motivates fixed effects in your own project, and one time-varying factor that fixed effects would not remove.
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