The Functional Demography of Aging: Principal Components of Age Pyramids

The Power of Dimensionality Reduction

Principal Component 1 alone explains 43.1% of all variation in county age structures. This means that nearly half of the demographic diversity across American counties can be captured by a single underlying dimension. Adding the second and third components brings us to 71.1% of total variation.

This remarkable parsimony suggests that the seemingly infinite ways populations can age actually follow predictable patterns that can be mathematically described and geographically mapped.

PC1: Youth versus Age (43.1% of variation)

The dominant pattern distinguishes counties by their balance of young versus old populations. Counties with high PC1 scores concentrate in working ages (25-65), while counties with low PC1 scores concentrate in senior ages (65+).

This captures the fundamental demographic choice facing American communities: attract and retain young workers and families, or serve as destinations for retirees. The mathematics reveal this as a zero-sum relationship where gains in one life stage correspond to losses in another.

Examples of high PC1 (young) counties include military bases with concentrated service members, university towns, and growing suburban areas. Low PC1 (aging) counties include retirement destinations, rural areas experiencing out-migration, and post-industrial regions losing young workers.

PC2: Working-Age Concentration (18.3% of variation)

The second pattern identifies counties with concentrated middle-aged populations. These places show pronounced peaks in ages 40-60, reflecting economic forces that attract workers at their career peaks.

Counties high on PC2 include energy boom areas, suburban employment centers, and places with specialized industries requiring experienced workers. The pattern reflects economic migration—people moving for career opportunities during their prime earning years.

This eigenfunction captures how economic geography shapes demographic structure. Places that offer high-paying jobs for experienced workers develop characteristic age profiles that persist across economic cycles.

PC3: Age Structure Complexity (9.8% of variation)

The third pattern captures more subtle variations in how different life stages balance within communities. While the first two components show clear youth-age and economic patterns, PC3 reflects the complex ways that families, students, workers, and retirees combine in different places.

This component distinguishes communities with unusual age distributions that don’t fit the simple young-old or economic concentration patterns. It identifies places where multiple demographic forces create unique community profiles.

Technical Note: This analysis adapts functional PCA principles using base R rather than specialized packages, employing spline smoothing followed by standard PCA on continuous age functions.

The National Age Divide

Figure 3: Principal Component 1 reveals the fundamental geographic divide between young and aging America

The first principal component creates a stark geographic division across the United States. Young counties (blue) cluster in the Mountain West, military regions, and suburban growth areas. Aging counties (red) concentrate in Florida, rural areas experiencing out-migration, and post-industrial regions.

Young America (Blue) includes: - Utah and surrounding areas with high birth rates and young religious populations - Military counties with concentrated service members and families - University towns with student populations - Suburban growth areas attracting young families

Aging America (Red) includes: - Florida retirement destinations - Rural Midwest and Northeast counties losing young adults - Former industrial areas without economic renewal - Agricultural regions experiencing demographic decline

The pattern reflects economic opportunity, institutional presence, and cultural factors that either attract young people or serve aging populations.

Working-Age Concentration

Figure 4: Principal Component 2 identifies counties with concentrated working-age populations

The second component maps economic geography through demographics. Counties with high PC2 scores show concentrated working-age populations, reflecting specific economic functions that attract career-stage workers.

High PC2 counties include: - Energy boom areas in North Dakota, Texas, and Colorado - Suburban employment centers like Loudoun County, Virginia - Military installations with career personnel - Agricultural processing and industrial centers

These patterns reflect how economic opportunities create demographic concentrations. Industries requiring experienced workers naturally attract people in their peak earning years, creating distinctive age profiles that persist across economic cycles.

The Working-Age Specialists

The counties with extreme PC2 scores reveal specialized economic geographies:

High PC2 (Concentrated Working-Age): - Loudoun County, Virginia: Washington D.C. suburban tech corridor - Duchesne County, Utah: Oil and gas boom region - Counties with specialized industries that attract career-stage workers

The Great Aging Acceleration

Between 2010 and 2020, American counties showed systematic aging patterns:

PC1 Changes (Youth→Age Direction): - Most counties shifted toward aging (positive PC1 changes) - Particularly pronounced in rural areas losing young adults - Suburban counties showed more stability as they maintained family attraction

PC2 Changes (Working-Age Concentration): - Greater variability in working-age patterns - Energy boom counties showed dramatic swings based on economic cycles - Technology centers gained working-age concentration

Regional Aging Patterns

Figure 6: Distribution of county scores reveals clear clustering along demographic dimensions

The distributions of component scores show:

1. PC1 (Youth-Age): Normal distribution centered slightly toward aging, indicating most counties are moderately aging
2. PC2 (Working-Age): Wider distribution with longer tails, showing greater specialization in working-age concentration
3. PC3 (Age Balance): Tighter distribution around zero, indicating most counties have similar age balance patterns

Industry and Age Patterns

The extreme counties on each component often reflect specialized economic functions:

Military Counties dominate PC1 extremes: - Young military personnel create artificial age bulges - Career military families concentrate in working ages - Base closures or expansions dramatically alter age structures

Energy Counties feature prominently in PC2: - Oil and gas development attracts working-age adults - Boom-bust cycles create dramatic age structure swings - Remote locations prevent family settlement, concentrating specific age groups

University Counties show unique age signatures: - Student populations create youth bulges that may not reflect permanent demographics - Faculty and staff create secondary working-age concentrations - College towns often age rapidly when student populations aren’t counted

Policy Implications

The functional approach to age analysis reveals policy insights invisible in traditional demographic analysis:

Service Planning: Understanding age distribution shapes rather than just median age helps plan services more effectively

Economic Development: Counties can identify whether their age profile supports growth industries or requires demographic intervention

Housing Policy: Age distribution functions predict housing demand better than simple age categories

Transportation Planning: Functional age analysis reveals commuting and mobility patterns across the life course

What Functional Analysis Adds

Traditional Approach: Analyzes age groups separately (% under 18, % over 65, median age)
Functional Approach: Treats entire age distribution as an integrated shape, revealing relationships between age groups

Key Advantages: 1. Captures age structure complexity that summary statistics miss 2. Reveals mathematical relationships between different life stages 3. Enables prediction of future age patterns through component dynamics 4. Identifies similar counties based on complete age profiles, not just single metrics

Technical Adaptations

Due to package availability limitations, we adapted the functional data analysis approach:

• Spline smoothing converted discrete age bins to continuous functions
• Standard PCA applied to smoothed data rather than specialized FPCA
• Base R implementation maintained analytical rigor while ensuring reproducibility

Limitations and Caveats

Data Constraints: - 12-year observation window may miss shorter-term demographic cycles - County-level aggregation masks sub-county age variation - ACS sampling creates noise in smaller counties

Methodological Limitations: - Smoothing assumptions may obscure genuine discontinuities in age distributions - Linear PCA may miss non-linear relationships in age structure - Component interpretation requires demographic knowledge beyond mathematical results

Geographic Bias: - Population thresholds exclude many rural counties - Military and university counties create artificial age concentrations - Migration timing may create temporary age structure artifacts

Expanding the Functional Framework

Temporal Extensions: - Multi-period functional analysis to model age structure evolution - Forecasting age pyramid shapes using component trends - Policy intervention analysis using difference-in-differences on age functions

Geographic Refinements: - Sub-county functional analysis using tract or block group data - Metropolitan area age systems analyzing urban-suburban-rural age complementarity - Regional age networks modeling how counties exchange populations across age groups

Economic Integration: - Industry-specific age functions relating economic structure to demographic patterns - Housing market analysis using age structure functions as demand predictors - Labor market modeling with functional age supply curves

Methodological Advances

Advanced Functional Methods: - Functional regression with age distributions as predictors - Functional clustering to identify age structure typologies - Functional time series for demographic forecasting

Policy Applications: - Service demand forecasting using age structure dynamics - Economic development modeling with demographic constraints - Retirement migration prediction using age transition functions

Key Findings

The functional approach reveals several important patterns:

Mathematical Parsimony: Just three dimensions capture most age structure variation across American counties. This suggests that demographic diversity, while complex, follows systematic rules rather than random variation.

Geographic Clustering: Similar counties form coherent regions with shared age patterns. Youth concentrates in the Mountain West and military areas, aging in retirement destinations and areas experiencing out-migration, and working-age populations in economic centers.

Institutional Effects: The most extreme counties reflect specialized institutions (military bases, universities, energy centers) that create distinctive demographic signatures. These places show how organizational needs can override typical community age patterns.

Temporal Stability: Component patterns remain consistent between 2010 and 2020, indicating fundamental structures that persist despite individual county changes.

Policy Applications

Functional age analysis offers practical tools for community planning:

Service Planning: Understanding complete age distribution shapes helps predict service needs better than summary statistics like median age.

Economic Development: Counties can assess whether their age profiles support target industries or require demographic interventions.

Regional Coordination: The clustering of similar counties suggests opportunities for coordinated planning across demographic regions.

Methodological Contributions

This analysis demonstrates that functional data analysis techniques can illuminate demographic patterns invisible to traditional approaches. The adaptation using base R shows that sophisticated analytical insights don’t require specialized software packages.

The functional perspective transforms demographic analysis from counting people in categories to understanding the mathematical relationships between age groups. This reveals patterns that discrete age analysis misses while providing a foundation for more sophisticated modeling and forecasting.

Future research could extend this framework to other demographic dimensions, incorporate temporal dynamics more fully, and develop predictive models based on functional components. The approach offers a path toward more mathematical rigor in demographic analysis while maintaining practical relevance for policy and planning.

Technical Notes

Data Sources: 2010-2014 and 2018-2022 American Community Survey 5-year estimates
Geographic Coverage: 2,491 U.S. counties with ≥10,000 population
Functional Analysis: Spline-smoothed age distributions with standard PCA
Age Range: 0-90 years at 100 equally-spaced points
Components Analyzed: First 5 principal components (80.4% cumulative variance)
Visualization: Geographic maps use shift_geometry() for proper CONUS display