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:

The first three bands align with HUD's income limit categories (Extremely Low = 30% AMI, Very Low = 50% AMI, Low = 80% AMI) 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, 0.50, 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 the latest ACS year.

Population-to-Household Conversion

Total household counts are derived from the population projection using age-specific householder (headship) rates — the approach used by state demographers (e.g. California DOF, Washington OFM) and the Harvard Joint Center for Housing Studies. This applies to counties, places (incorporated cities and towns), and county subdivisions. For each geography and householder age band a, the headship rate is the number of householders per person living in households:

h_a = Householders_a / HHPop_a

where:

• Householders_a = householders in age band a (ACS Table B25007, Tenure by Age of Householder)
• HHPop_a = population in age band a living in households (ACS Table B01001, net of group quarters)

Rates in small geographies are partially pooled toward the state age curve (estimated from counties, the exhaustive non-overlapping partition of each state) to stabilize noisy estimates:

h^pooled_a = w × h_a + (1 − w) × h^state_a,   w = N² / (N² + k²)

where N is the geography's household population and k is a pooling-scale constant. Small places and county subdivisions, which have noisier rates, are shrunk more strongly toward the state curve.

The household count is anchored to the actual base-year count and grown by the headship-weighted household-population trajectory from the population projection:

H_t = H_base × ( Σ_a h_a × m_a,t × HHPop_a,t ) / ( Σ_a h_a × HHPop_a,base )

Both the numerator and the base-year denominator use the population model's own household population (total population net of group quarters), so the series is pinned to the actual ACS household count at the base year and then moves only with projected household-population growth by age. Anchoring the base to the population projection rather than the 5-year ACS average avoids a spurious jump at the first forecast year.

Headship trajectory. Each geography's rates are its own, but they are not held constant. Nationally, headship adjusted for the age mix peaked around 2000 and has fallen since at roughly a quarter of a percent a year; the rise from 2019 to 2023 was a pandemic-era exception that the 1-year ACS shows reversing in 2024. The multiplier m_a,t carries that decline forward from the base year:

m_a,t = exp( 0.75 × s_a × (t − base) )

where s_a is the slope of national headship for band a fitted on the 1-year ACS over 2010 to 2019, the decade before the pandemic, ranging from about −0.9% a year for householders under 35 to −0.1% for 65 to 74. Three quarters of that slope is carried because the 2010 to 2019 window is steeper than the long-run rate (its first half contains the post-2008 unwinding of doubled-up households), and three quarters reproduces the 2000 to 2019 rate. The multiplier is 1 at the base year, so the plotted history and the forecast meet without a step. The rule has not been shown to beat constant headship in backtests of county household growth. Over 2019 to 2024 it did worse than holding headship constant on every measure (median absolute error about 4.0 points against 3.3), because headship rose rather than fell. Over 2014 to 2019 the closest out-of-sample version, three quarters of the 2010 to 2014 slope, did worse for the typical county (2.59 points against 2.40) and better when counties are weighted by households (1.93 against 2.36); a full-slope extrapolation overshot the actual decline by about two to one. Carrying the decline forward is a judgment that the long pre-2020 trend resumes after the pandemic-era rise, not a backtested improvement. Nationally the trajectory takes about 1 point off household growth over five years and 2.4 points over ten, concentrated in households under 45.

Group-quarters leverage cap. Where group quarters (prisons, college dormitories, seasonal-worker housing) are a large share of the population, the projection holds the group-quarters count fixed. Left uncorrected, this forces the entire population change onto the household population and exaggerates household growth or decline. Where the group-quarters share s is high, the household trajectory is blended toward the total-population trajectory:

H_t = H_base × [ (1 − λ) × R^hhpop_t + λ × R^pop_t ],   λ = clip((s − 0.25) / 0.75, 0, 1)

where R^hhpop and R^pop are the headship-weighted household-population and total-population growth ratios. Below a 25% group-quarters share (all but a handful of counties) there is no adjustment.

Geographies without an age-structured population projection or ACS householder data (for example, areas with population history only) use the legacy conversion, which derives total households from PUMS household-type distributions and population-to-household ratios:

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

where Prop_age,type is the proportion of the age group living in each household type (person-weighted across both sexes), based on the 2020–2024 ACS 5-Year PUMS (household and person microdata, weighted by WGTP and PWGTP and aggregated to PUMA 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 B25007: Tenure by Age of Householder — householders by age band (headship-rate numerator)
• ACS Table B01001: Population by age and sex — household population by age band (headship-rate denominator, net of group quarters)
• ACS Table B19001: Household Income in the Past 12 Months (16 bins)
• HUD Income Limits: Area Median Income by geography and year (2010-2025)
• Population Forecast: County population by age, with group-quarters netting — from the PEP-anchored cohort-migration methodology (see Population Forecast)
• ACS PUMS 2020-2024 5-Year: Household and person microdata (legacy population-to-household conversion, for geographies without an age-structured projection or ACS householder data)
• FRED: Per capita wage growth for income trend analysis

Coverage Note

The full methodology above applies to counties and municipalities, which have population forecasts. States, the nation, and geographies without a population forecast use a simplified path — ACS B19001 income trends with linear extrapolation — that produces a current-year snapshot rather than a full forecast.