Housing Affordability Methodology

Housing Affordability Methodology

The housing affordability analysis calculates the income required to afford the typical home price in each geographic area, incorporating all major components of homeownership costs.

Monthly Housing Cost Components

Total monthly housing cost is calculated as:

C_monthly = M + T + I_p + I_m

where:

• M = Monthly mortgage payment
• T = Monthly property tax
• I_p = Monthly property insurance
• I_m = Monthly mortgage insurance (if applicable)

Mortgage Payment Calculation

The monthly mortgage payment uses the standard amortization formula:

M = L × [r(1+r)ⁿ / ((1+r)ⁿ − 1)]

where:

• L = Loan amount = P × (1 − d)
• P = Home purchase price
• d = Down payment percentage (default 20%)
• r = Monthly interest rate = R_annual / 12
• n = Number of payments = 360 (30-year mortgage)

Property Tax

Monthly property tax is calculated as:

T = (P × τ) / 12

where τ is the effective property tax rate, calculated from ACS data as:

τ = Selected Monthly Owner Costs (B25103) / Median Home Value (B25077)

Data Sources:

• ACS Table B25103: Selected Monthly Owner Costs
• ACS Table B25077: Median Home Value

Property Insurance

Monthly property insurance is calculated as:

I_p = (P × ρ) / 12

where ρ is the annual insurance rate.

Data Sources:

• Geographic-level insurance rates aggregated from ZIP code-level data
• National average insurance rate used as fallback when local data unavailable

Mortgage Insurance (PMI)

When down payment is less than 20%, private mortgage insurance is required:

I_m = (L × 0.005) / 12    if d < 0.20

I_m = 0    otherwise

Required Income Calculation

The required annual income applies the standard 30% housing cost burden threshold:

I_required = (C_monthly × 12) / 0.30

This assumes that housing costs should not exceed 30% of gross household income, a widely-used affordability standard.

Time Series Construction

The affordability analysis generates monthly time series from 2010 to present by integrating:

1. Home Values: Commercial home value index -- monthly data for middle-tier single-family homes and condos (33rd-67th percentile price range)

2. Mortgage Rates: 30-year fixed mortgage rates from FRED (Federal Reserve Economic Data) series MORTGAGE30US

3. Median Income: ACS Table B19113 (Median Family Income), available annually. Monthly values are interpolated using:

   • Historical ACS data (2010-2023)
   • Per capita wage growth rates from FRED for extrapolation
   • Compound monthly growth rate: (1 + r_annual)^1/12 − 1

4. Property Tax Rates: Calculated annually from ACS data, held constant within each year

The final time series contains:

• date: Month-end date
• median_income: Median family income (annual, inflation-adjusted)
• required_income: Annual income required to afford typical home price at 30% housing cost burden

Contributing Factors to Affordability

The methodology captures the following factors affecting housing affordability:

1. Home Prices: Commercial home value indices reflect market conditions and housing supply/demand
2. Interest Rates: FRED 30-year mortgage rates capture financing costs
3. Property Taxes: Local tax rates from ACS reflect fiscal policy impacts
4. Insurance Costs: Geographic variation in property insurance premiums
5. Income Growth: Median family income trends from Census data
6. Down Payment Requirements: 20% standard, with PMI penalty for lower down payments
7. Loan Terms: 30-year fixed-rate mortgage assumptions

Data Sources