# RDP 2023-01: The Effect of Credit Constraints on Housing Prices: (Further) Evidence from a Survey Experiment Appendix A: General Equilibrium Effects for Interest Rates

## A.1 Modelling

Given that the interest rate effect seems to apply evenly across the market, it is possible that the survey response to the interest rates an individual faces is an underestimate of the effect of an interest rate cut that applies to all households. One way of getting a handle on that is to consider the following WTP model, which is a simplified version of the regression model in Table 2 of Fuster and Zafar (2021). The regressions are estimated in logs, but I transform back to the original variables here for ease of explanation.

(A1) $E( WT P t )= X i βHomeValu e 1 α ( 1+γCut )$

where ${X}_{i}\beta$ is the effect of household characteristics, HomeValue is the value of the home given in the survey, $\alpha$ is the log-linear coefficient from an OLS regression, and Cut is a binary variable with a value of 1 for low rates. The $\gamma$ parameter then represents the effect of the cut on an individual's WTP as measured by the survey (i.e. $\gamma$ = 0.04 for a 4 per cent increase in WTP). If we take $\gamma$ as the effect on an individual's WTP holding the rest of the market constant, we can calculate the whole market effect as the fixed point of Equation (A1) with WTPi = HomeValuei:

(A2) $E( WT P i | Cut=1 WT P i | Cut=0 )= ( 1+γ ) 1 1−α$

The estimated $\alpha$ coefficient in Table 2 (column 3) of Fuster and Zafar (2021) is 0.72, which implies the general equilibrium effect by this method is around 3.8 times larger than the individual effect at around 15 per cent. Fuster and Zafar note that their estimate of the effect of interest rate response is at the lower end of estimates in other studies. This ‘general equilibrium’ transformation gives a value around the top of the range of estimates in previous literature.