# RDP 2023-01: The Effect of Credit Constraints on Housing Prices: (Further) Evidence from a Survey Experiment Appendix C: Modelling

## C.1 Preference parameters and the nonlinear mapping

The fitted distributions are narrower than the distributions inferred from the WTP data. The fitted distribution can be thought of as the heterogeneity that can be accounted for by the observable financial and demographic data, while the inferred distribution captures all heterogeneity in responses. The rent/own preference parameter distribution is reasonably well captured in the fitted distribution. The heterogeneity of the time preference parameter that governs the increase in WTP is not well captured by observable variables. Idiosyncratic heterogeneity is clearly important. There are two modes in the actual distribution but none of the explanatory variables capture this feature of the distribution. Figure C1: Distribution of Inferred Rent versus Own Parameter Histogram, distribution of rental penalty factor ( ω ) estimates Figure C2: Distribution of Inferred Discount Rate Parameter Histogram, distribution of discount factor ( β ) estimates

## C.2 User cost prediction equations

(C1) $ϕ ^ i = X i Ψ ^ i$
(C2) $β ^ i = X i ζ ^ i$

where the ${\stackrel{^}{\Psi }}_{i}$ and ${\stackrel{^}{\zeta }}_{i}$ coefficients are estimated in regressions

(C3) $ϕ i = X j Ψ i e j for j≠i$
(C4) $β i = X j ζ+ u j for j≠i$

The willingness to pay in each condition (WTP20 and WTP5) are then found by plugging ${\stackrel{^}{\varphi }}_{i}$ and ${\stackrel{^}{\beta }}_{i}$ into the heterogeneous user cost equation (Equation (2)) with the two values of the down payment constraint, $\theta$.