Household Growth by Income Group

Household Growth by Income Group Methodology

This methodology forecasts household growth segmented by Area Median Income (AMI) categories, enabling analysis of housing needs across different income levels.

AMI Group Definitions

Households are classified into six AMI groups based on their income relative to the HUD-defined Area Median Income:

These thresholds align with HUD income limit categories used in affordable housing policy.

Census Income Data Rebinning

ACS Table B19001 provides household income in 16 predefined bins:

Bins: [0, 10k), [10k, 15k), [15k, 20k), ..., [200k, ∞)

These must be rebinned to the 6 AMI-based categories, which have dollar thresholds that vary by geography and year:

AMI Threshold_i,g,t = AMI_g,t × α_i

where:

• AMI_g,t = Area Median Income for geography g in year t (from HUD)
• α_i = AMI percentage threshold (0.30, 0.60, 0.80, 1.00, 1.20)

Rebinning Algorithm: Households are redistributed from Census bins to AMI bins using proportional allocation based on overlap between bin ranges:

H_new,j = Σ_i H_census,i × overlap(B_census,i, B_AMI,j) / width(B_census,i)

where:

• H_new,j = households in AMI bin j
• H_census,i = households in Census bin i
• overlap() = dollar range overlap between bins
• width() = bin width

Inflation Adjustment

Historical AMI thresholds are adjusted for inflation to maintain consistent real income categories:

Threshold_real,t = Threshold_nominal,t / (CPI_t / CPI_base)

This ensures that an "80% AMI" household in 2010 represents the same purchasing power as in 2023.

Population-to-Household Conversion

Total household counts are derived from population forecasts using PUMS (Public Use Microdata Sample) data:

H_type,t = Σ_age,sex P_age,sex,t × Prop_age,sex,type / Ratio_pop/hh,type

where:

• P_age,sex,t = population forecast by age and sex
• Prop_age,sex,type = proportion of (age, sex) in household type
• Ratio_pop/hh,type = population-to-household ratio for household type

Household Types (13 categories based on size and children):

• 1-person households (no children)
• 2-person households (with/without children)
• 3-7+ person households (classified by number of adults and children)

PUMS Data Sources:

• 2019-2023 ACS 5-Year PUMS: Household and person microdata files
• Weighted by WGTP (household weight) and PWGTP (person weight)
• Aggregated to PUMA (Public Use Microdata Area) geographies

Income Distribution Forecasting

The share of households in each AMI group is forecasted using:

1. Historical Trend Estimation: Linear regression of income shares over time

S_i,t = β₀ + β₁ × t + ε_t

2. Constraint and Normalization: Forecasted shares are clipped to [0, 1] and renormalized:

S^normalized_i,t = max(0, min(1, S_i,t)) / Σ_j=1..6 max(0, min(1, S_j,t))

3. Blended Forecast: Combine base year distribution with trend forecast:

S^blend_i,t = (1 − w) × S_i,base + w × S^trend_i,t

where w = 0.30 (30% weight on trend, 70% on base year) to dampen extreme extrapolations.

Final Household Projection by AMI Group

H_AMI,i,t = S^blend_i,t × H_total,t

where H_total,t is the total household forecast from population projections.

Data Sources

• ACS Table B19001: Household Income in the Past 12 Months (16 bins)
• HUD Income Limits: Area Median Income by geography and year (2010-2025)
• ACS PUMS 2019-2023 5-Year: Household and person microdata
• FRED: Per capita wage growth for income trend analysis
• Population Forecasts: From Leslie Matrix methodology (see Population Forecast section)