ILLUSTRATIVE EXAMPLE
Panel Data Analysis for a
Labor Economics Study
Two-way fixed effects with a Mundlak comparison, clustered standard errors and a staggered-timing check for an annual panel of about 300 regions over 15 years.
This example does not describe a real client or project. Every engagement is confidential, during the project and after it ends.
RESEARCH QUESTION
What the Study Set Out to Test
This panel data analysis example follows a labor economics research team that wants to know whether regional minimum wage increases are associated with changes in teen employment. They have an annual panel of regions observed over 15 years, in which different regions raised their minimum wage in different years.
The question is framed as a within-region association: when a region raises its minimum wage, does its own teen employment move differently from its own earlier level, after common yearly shocks are accounted for? The plan fixes the specification before estimation and makes no causal claim beyond what the design supports.
STUDY DESIGN AND DATA
A Long Regional Panel With Staggered Adoption
A balanced annual panel of around 300 regions over 15 years, about 4,500 region-year observations. The dataset holds the teen employment rate, the minimum wage level and the year of each increase, and regional controls such as overall unemployment and population. Regions adopted increases in different years, so the timing of the policy is staggered, and observations within a region are correlated over time.
- Design: annual regional panel with staggered policy changes
- Outcome: teen employment rate, with the region as the unit of analysis
- Software requested: Stata, with do-files and logs
METHOD AND ASSUMPTIONS
Why Two-Way Fixed Effects, and What Must Hold
Stable unobserved regional traits, such as long-run industry mix or local labor norms, plausibly go with local policy, so the plan specifies a two-way fixed effects model with region and year effects. This identifies the association from changes within regions. A conventional Hausman test cannot be used when errors are clustered, so the plan names a Mundlak model, which adds each region's mean of the time-varying regressors, as the comparison with a random-effects specification. Serial correlation is tested, and standard errors are clustered by region.
Because adoption dates differ, two-way fixed effects can mix comparisons between early and late adopters in ways that bias the estimate when effects vary over time or across regions. The plan therefore prespecifies a heterogeneity-robust difference-in-differences estimator for staggered adoption, with each region's first increase as the adoption event, as a robustness check, and the two sets of estimates are reported together. Where they diverge, the divergence is itself a finding and is explained, not averaged away.
OUTPUT AND INTERPRETATION
How the Results Are Read
The output has a table of within-region estimates with 95% confidence intervals and region-clustered standard errors, the Mundlak comparison against the random-effects specification, and the staggered-timing estimates beside the main model. Each coefficient is described in plain language as a within-region association, with the interval, not the p-value, showing how precisely it is estimated.
Sensitivity analyses vary the choices that matter most: alternative control sets, an event-study version to look at the years before each increase, and dropping regions that changed policy more than once. The write-up states what the estimates do and do not support for a policy question, and why no causal effect is claimed beyond the within-region associations.
REPORTING
What the Researcher Received
A methods section justifying the specification and the choice of standard errors, results tables formatted for the target journal, and a short account of the robustness checks. The research question, the interpretation and the conclusions remain with the research team.