RDP 2023-01: The Effect of Credit Constraints on Housing Prices: (Further) Evidence from a Survey Experiment 1. Introduction

The importance of collateral constraints in determining housing prices is contested, in part because constraints rarely vary in a way that permits causal inference. One way of dealing with this difficulty is to introduce exogenous variation using survey experiments that ask people about their behaviour in hypothetical scenarios. A survey experiment asking US households about their willingness to pay (WTP) for housing under different financing conditions was reported in Fuster and Zafar (2021). Their analysis of the experimental data focused on the average change in WTP among households in response to changes in financing conditions. My paper extends their analysis by estimating the response of the marginal buyer, which should give a better sense of the effect on housing prices.

Fuster and Zafar (2021) find a large average effect of easing collateral constraints on the stated WTP of survey respondents and a relatively small effect of changes in interest rates. But because the marginal buyer sets the price, these average changes in WTPs need not coincide with changes in price. Using the same experimental data to construct market demand curves, I find that the effect of easing collateral constraints on price is systematically smaller than the average effect on a household's WTP. Constrained households tend to be more responsive to changing collateral constraints. These households rarely affect prices though, because they tend to have WTPs well below the market price even under loose collateral constraints. For changes in mortgage rates, the average change in WTP and the change in the marginal WTP are similar.

I can describe the experimental data and illustrate my analytical technique with an example. In the data there are five households from Michigan that live in a home valued at US$140,000. The households are asked to imagine a hypothetical situation in which they are moving to a different town and have found a home they like that is similar in value to their current home. They are then asked how much they would be willing to pay for the house given they need a 20 per cent down payment and can use a loan for the balance of the price.[1] The five responses range from US$40,000 to US$200,000. As long as each household demands at most one dwelling to live in, the WTPs ordered from highest to lowest form a market demand curve that shows demand for homes at any given price. Figure 1 shows this demand curve, as well as the demand curve with a 5 per cent down payment required, constructed in the same way.

As expected, the looser collateral constraint shifts the demand curve outward, but the shift is not uniform. Demand at the upper end barely shifts from the baseline 20 per cent down payment to the looser requirement of 5 per cent. At the lower end of the demand curve, the shift in demand is much larger. This pattern is consistent with constraints binding more at the lower end of demand. As the constraint is loosened, these households responds by raising their WTPs.

Translating these demand curves into a price change requires a supply curve. The supply curve is not observable but it must intersect the demand curve at the price, which is available in the data as the estimated home value. I illustrate the price effect using a vertical supply curve that intersects the demand curve with tighter constraints at the market price. The change in price can then be determined as the change in the marginal WTP. In the example in Figure 1, the average change in WTP is US$28,000 while the change in the marginal WTP is US$10,000.

Figure 1: Example of Effect of Easier Collateral Constraints on Demand
US$140,000 homes in Michigan
Figure 1: Example of Effect of Easier Collateral Constraints on Demand

Sources: Author's calculations; Fuster and Zafar (2021)

The rest of the paper shows how this same pattern seen for US$140,000 homes in Michigan is borne out in the aggregate data and within most market segments. Constrained households have low WTPs, typically below the marginal WTP, and tend to respond most to collateral constraints. As a result, the average change in WTP is greater than the change in the marginal WTP. For the average change in demand to equal the change in price the shifts in demand would need to be even across the curve.

Analysing the demand curves across the full dataset in Fuster and Zafar (2021) follows the same principle as the above example, but is complicated by aggregation. The relatively small size of the survey means it is not feasible to recreate local housing markets in detail. To analyse the full dataset I aggregate household demand for homes of different values in different locations. In aggregate, my estimate of the change in market price caused by a loosening of collateral constraints is a 6 to 8 per cent increase compared with the average WTP increase of 16 per cent reported in Fuster and Zafar (2021). Analysing disaggregated subsets of the data shows the same pattern. Within each segment, more-constrained households tend to have low WTPs that have little effect on prices despite their larger responses to looser collateral constraints.

For the mortgage rate cut experiment, analysing the demand curves does not show systematic differences between the average effect of interest rates and the effect on the marginal buyer. This demonstrates that the collateral constraint result is not an artefact of the method, and also makes sense in the context of the experiment. There is no servicing constraint in the experiment so a changing mortgage rate does not change any constraint. As such, there is less reason to expect a different effect across the demand curve.

To help interpret the results of the empirical analysis of the demand curves, I consider a heterogeneous-agent user cost framework. In this framework households vary in their subjective discount rate and their relative preference for renting versus owning a home. These two preference parameters can be identified from the survey data because they jointly determine the level of a household's WTP and the response to a change in collateral constraints. A household with a relatively steep discount rate will have a lower WTP and respond more to a change in constraints. A steep discounter with a strong preference for owning over renting will have a high WTP and respond strongly to collateral constraints, but such households are rare in the data.

I estimate empirical models that show a household's survey responses can, to some extent, be predicted from observable household characteristics. Using only the predictable variation in survey responses to constructing housing demand curves gives similar results to the raw data. This prediction exercise shows that the systematic variation in household behaviour based on observable characteristics is an important source of heterogeneity that can drive market outcomes. Similar household characteristics are available in a variety of standard data sources, which allows me to use the experimental findings to infer the sensitivity of housing prices to financing conditions in other times and places. I validate my out-of-sample method using an independent contemporary data source for the United States and then apply the method to other datasets. Applying the model to Australian data suggests that the effect of collateral constraints is similar to in the United States, and has not changed substantially over the past 20 years. The model implies somewhat different effects in countries with much higher or lower rates of home ownership.

The marginal buyer sets the price in asset markets. This paper shows that in housing markets, collateral constraints have meaningfully different effects on average, compared with the effect on the marginal buyer. There are few empirical attempts to understand how heterogeneity in markets can lead the marginal buyer to diverge from average changes, in part due to the rarity of this kind of detailed data.[2] The method I employ may be useful in a wider range of empirical analyses, and can also help clarify divergent results in the housing modelling literature. Many housing models include heterogeneity, and show very different effects of collateral constraints on price. For collateral constraints to have a large effect on prices, constrained buyers must be marginal. My analysis gives reasons to think that this is relatively rare.

For policymakers assessing the effects of macroprudential policy, this paper shows that using average effects of collateral constraints on households is likely to overstate the effect on market prices. My results reinforce other recent literature on the importance of household heterogeneity in the transmission of macroprudential policy. Further, I show that the effects of constraint changes depend on the market structure and household characteristics that can vary over time and place.

The next section reviews the literature on the role of collateral constraints in housing markets, with a focus on heterogeneity. After that I further explain the method used to estimate the change in WTP of the marginal buyer, and apply it to the aggregate experimental data and a range of market segments. I then describe a heterogeneous user cost model that can interpret the empirical features of the data, before estimating regression models and using them to simulate the response of housing markets to changing collateral constraints using standard household survey data from other sources, including the Australian Survey of Income and Housing. Finally, I conclude with the implications for housing market models and policymakers.


If the respondent owns their current home, the question states that they sell it and discharge their mortgage before making the down payment on their new hypothetical home. [1]

The only example of a similar method I am aware of is in a real estate valuation paper that estimates the price effect of negative amenities like high-voltage power lines or environmental contamination (Colwell and Trefzger 2005). [2]