RDP 2023-01: The Effect of Credit Constraints on Housing Prices: (Further) Evidence from a Survey Experiment 4. Method: Finding the Marginal Buyer on the Demand Curve

My aim is to consider the change in the WTP of the marginal buyer between each pair of experimental conditions. To identify the marginal buyer, I aggregate responses to construct a demand curve in each experimental condition. The marginal buyer need not be the same person before and after the change in conditions. Combined with an inferred supply curve, the pair of demand curves allows me to locate the marginal buyer in each condition and determine the price change between conditions.

The WTP data is for owner-occupied housing, which means that each household demands either one or zero houses at a given price. Total market owner-occupier demand at any price is thus given by the number of respondents with a WTP equal to or greater than that price. Fuster and Zafar (2021) assume fixed supply in their representative agent user cost framework. I do the same here, both to make my results comparable with theirs, and to provide an upper bound on price changes.^[4]

To construct the market demand and supply schedules, I follow the same procedure as the illustrative market segments with an extra initial step to allow comparison across different home values:

1. Take the ratio of the WTP to the home value (I term the result the ‘normalised WTP’).
2. Order the normalised WTPs from highest to lowest to show the number of households that will buy at any given price. This forms a demand curve, which can also be thought of as the reverse cumulative distribution function for the normalised WTPs. Applying this step to the 20 per cent down payment baseline condition and the 5 per cent down payment loosening condition shows the outward shift in the demand curve.^[5]
3. Infer the location of the vertical supply curve from the intersection of one of the demand curves with the home value. For normalised WTPs this is always 1 (or zero in logarithms).
4. Find the intersection of the shifted demand curve with the supply curve to determine the price change.

Fixed supply is typically considered as a limited building response rather than inelastic supply of existing houses for resale (see Cusbert (2022)). However, because housing demand in the Fuster and Zafar (2021) approach only accounts for owner-occupiers, supply also includes any houses owned by investors in the baseline condition. The assumption of unresponsive supply means investors do not change the number of houses they own in response to the change in credit conditions. There are two interpretations of this assumption. One is that investors are completely inelastic, and none buy or sell in response to the change in credit conditions or increase in demand. Alternatively, investors could be price elastic and also respond to the easing in credit conditions by increasing the price at which they are willing to sell. If these two effects offset to maintain the number of houses owned by investors, it is equivalent to constant supply.

The experimental data cannot inform the behaviour of investors, and other studies suggest the characteristics of investors vary substantially in different circumstances and over time. Graham (2020), Greenwald and Guren (2021) and Cusbert (2022) explore in detail the consequences of different investor behaviour for price and ownership structure. Broadly speaking, investors that are more price elastic dampen the price response, while investors that are more reliant on credit boost the response. The lack of information about investors is a limitation of the experimental dataset that is worth bearing in mind. I maintain the simple assumption of constant supply from Fuster and Zafar (2021), which maintains the focus on the structure of heterogeneity in the owner-occupier demand curve.

Footnotes

Colwell and Trefzger (2005) also assume a vertical supply curve in their demand curve analysis in the context of modelling the price effect of a disamenity. [4]

A substantial fraction of respondents give a WTP exactly equal to the home value. This may be related to differing interpretations of the question, and makes the interpretation of the curves difficult. For my main results I remove any WTP equal to the home value to eliminate the flat spot in the demand curve. Appendix B.3 shows that the down payment results are not sensitive to this treatment. [5]