Key Assumptions

The market demand model relies on six key assumptions that shape how housing affordability and demand are estimated. These assumptions reflect established practices in housing economics and demographic analysis.

1. Willingness-to-Pay Scenarios: The model produces two distinct scenarios. The 30% expenditure rule scenario assumes all households spend exactly 30% of gross income on housing, reflecting federal housing policy guidelines. The 85th percentile WTP scenario incorporates observed market behavior where households in different income-tenure groups spend varying percentages of income on housing.

2. Log-Normal Income Distribution: Within each income bin, household incomes are assumed to follow a log-normal distribution, a standard assumption in income modeling that captures right-skewness and provides a realistic representation of income heterogeneity.

3. Stable Preferences: Household preferences for bedroom counts and WTP behavior are assumed to change gradually according to observed historical trends, forecasted using compositional time series methods.

4. Regional Market Behavior: Households within a 30-minute drive time search for housing across the entire regional market area, competing for available units regardless of municipal boundaries.

5. Fixed-Rate Mortgages: Home price affordability calculations assume standard fixed-rate mortgages with constant monthly payments over the loan term, using current market interest rates from FRED data.

6. Compositional Stationarity: Time series forecasting of compositional data (shares) assumes that historical trends in relative proportions continue into the future. Compositional variables (e.g., shares of households by bedroom count) are transformed using the Centered Log-Ratio (CLR) before modeling:

   CLR(x) = [log(x₁/g(x)), log(x₂/g(x)), ..., log(x_p/g(x))]

   where g(x) = (x₁ × x₂ × ... × x_p)^1/p is the geometric mean.

   Inverse: x_i = exp(CLR_i) / Σ exp(CLR_j)

   This transformation maps compositions from the simplex to unconstrained real space, where standard linear time series models (with trend) can be applied. The inverse transformation maps forecasted values back to valid shares that sum to one.