11.4 Repeated Cross-Sectional Data
Repeated cross-sectional data consists of multiple independent cross-sections collected at different points in time. Unlike panel data, where the same individuals are tracked over time, repeated cross-sections draw a fresh sample in each wave.
This approach allows researchers to analyze aggregate trends over time, but it does not track individual-level changes.
Examples
- General Social Survey (GSS) (U.S.) – Conducted every two years with a new sample of respondents.
- Political Opinion Polls – Monthly voter surveys to track shifts in public sentiment.
- National Health Surveys – Annual studies with fresh samples to monitor population-wide health trends.
- Educational Surveys – Sampling different groups of students each year to assess learning outcomes.
11.4.1 Key Characteristics
- Fresh Sample in Each Wave
- Each survey represents an independent cross-section.
- No respondent is tracked across waves.
- Population-Level Trends Over Time
- Researchers can study how the distribution of characteristics (e.g., income, attitudes, behaviors) changes over time.
- However, individual trajectories cannot be observed.
- Sample Design Consistency
- To ensure comparability across waves, researchers must maintain consistent:
- Sampling methods
- Questionnaire design
- Definitions of key variables
- To ensure comparability across waves, researchers must maintain consistent:
11.4.2 Statistical Modeling for Repeated Cross-Sections
Since repeated cross-sections do not track the same individuals, specific regression methods are used to analyze changes over time.
- Pooled Cross-Sectional Regression (Time Fixed Effects)
Combines multiple survey waves into a single dataset while controlling for time effects:
\[ y_i = \mathbf{x}_i \beta + \delta_1 y_1 + ... + \delta_T y_T + \epsilon_i \]
where:
\(y_i\) is the outcome for individual \(i\),
\(\mathbf{x}_i\) are explanatory variables,
\(y_t\) are time period dummies,
\(\delta_t\) captures the average change in outcomes across time periods.
Key Features:
Allows for different intercepts across time periods, capturing shifts in baseline outcomes.
Tracks overall population trends without assuming a constant effect of \(\mathbf{x}_i\) over time.
- Allowing for Structural Change in Pooled Cross-Sections (Time-Dependent Effects)
To test whether relationships between variables change over time (structural breaks), interactions between time dummies and explanatory variables can be introduced:
\[ y_i = \mathbf{x}_i \beta + \mathbf{x}_i y_1 \gamma_1 + ... + \mathbf{x}_i y_T \gamma_T + \delta_1 y_1 + ...+ \delta_T y_T + \epsilon_i \]
- Interacting \(x_i\) with time period dummies allows for:
- Different slopes for each time period.
- Time-dependent effects of explanatory variables.
Practical Application:
If \(\mathbf{x}_i\) represents education level and \(y_t\) represents survey year, an interaction term can test whether the effect of education on income has changed over time.
Structural break tests help determine whether such time-varying effects are statistically significant.
Useful for policy analysis, where a policy might impact certain subgroups differently across time.
- Difference-in-Means Over Time
A simple approach to comparing aggregate trends:
\[ \bar{y}_t - \bar{y}_{t-1} \]
- Measures whether the average outcome has changed over time.
- Common in policy evaluations (e.g., assessing the effect of minimum wage increases on average income).
- Synthetic Cohort Analysis
Since repeated cross-sections do not track individuals, a synthetic cohort can be created by grouping observations based on shared characteristics:
- Example: If education levels are collected over multiple waves, we can track average income changes within education groups to approximate trends.
11.4.3 Advantages of Repeated Cross-Sectional Data
Advantage | Explanation |
---|---|
Tracks population trends | Useful for studying shifts in demographics, attitudes, and economic conditions over time. |
Lower cost than panel data | Tracking individuals across multiple waves (as in panel studies) is expensive and prone to attrition. |
No attrition bias | Unlike panel surveys, where respondents drop out over time, each wave draws a new representative sample. |
Easier implementation | Organizations can design a single survey protocol and repeat it at set intervals without managing panel retention. |
11.4.4 Disadvantages of Repeated Cross-Sectional Data
Disadvantage | Explanation |
---|---|
No individual-level transitions | Cannot track how specific individuals change over time (e.g., income mobility, changes in attitudes). |
Limited causal inference | Since we observe different people in each wave, we cannot directly infer individual cause-and-effect relationships. |
Comparability issues | Small differences in survey design (e.g., question wording or sampling frame) can make it difficult to compare across waves. |
To ensure valid comparisons across time:
- Consistent Sampling: Each wave should use the same sampling frame and methodology.
- Standardized Questions: Small variations in question wording can introduce inconsistencies.
- Weighting Adjustments: If sampling strategies change, apply survey weights to maintain representativeness.
- Accounting for Structural Changes: Economic, demographic, or social changes may impact comparability.