# Shift in house price estimates during COVID-19
reveals effect of crisis on collective speculation

Alexander Michael Petersen  Department of Management of Complex Systems,
Ernest and Julio Gallo Management Program, School of Engineering, University
of California, Merced, California 95343, USA

11footnotetext:  Send correspondence to<EMAIL_ADDRESS>
We exploit a timely city-level panel of individual house price estimates for
both small and big real-estate markets in California USA to estimate the
impact of COVID-19 on the housing market. Descriptive analysis of spot house
price estimates, including contemporaneous price uncertainty and 30-day price
change for individual properties listed on the online real-estate platform
Zillow.com, together facilitate quantifying both the excess valuation and
valuation confidence attributable to this global socio-economic shock. Our
quasi-experimental pre-/post-COVID-19 design spans several years around 2020
and leverages contemporaneous price estimates of rental properties – i.e.,
real estate entering the habitation market, just not for purchase and hence
free of speculation – as an appropriate counterfactual to properties listed
for sale. Combining unit-level matching and difference-in-difference
approaches, we estimate that properties listed for sale after the pandemic
featured an excess monthly price growth of roughly 1 percentage points,
corresponding to an excess annual price growth of roughly 12.7 percentage
points, which accounts for more than half of the annual growth observed across
those regions in 2021. Simultaneously, uncertainty in price estimates
decreased, signaling the irrational confidence characteristic of prior asset
bubbles. We explore how these two trends are related to market size, local
market supply and borrowing costs, which altogether lend support for the
counter-intuitive roles of uncertainty and interruptions in decision-making.

Real Estate $|$ Price Dynamics $|$ IT Services $|$ Asset Bubble $|$ COVID-19
Quasi-experiment $|$ Unit-level Matching

One of the many perplexing outcomes of the COVID-19 pandemic was the emergence
of exuberant markets in the United States (US) after the dust settled from the
first wave of global shock. This was particularly evident in the US housing
market, as illustrated in Fig. 1(A), which shows official government house
price indices from 2010-2022 for several regions in California (CA) that grew
by up to 23% in 2021. While there is a significant body of literature focusing
on the short-term market decline in real estate markets immediately following
the onset of the pandemic in spring 2020 balemi2021covid ; liu2021impact ;
ramani2021donut ; d2022covid , here we analyze the overwhelming reversal that
followed in the medium term. The common explanations for increased home prices
in response to the various dimensions of the socio-economic shock
bonaccorsi2020economic ; bunn2021covid ; meyer2022pandemic ;
aleta2022quantifying  are increased demand paired with reduced housing supply
deriving from stay-at-home orders and subsequent shifts to work-from-home
accommodation.

Yet few studies account for the widespread uncertainty regarding the scope and
duration of the global pandemic, and wether or not the shock and sudden
interruption to normal daily life affected human decision-making – namely,
buying a house, one of the most impactful financial life-course events
individuals may encounter. Importantly, in the US this decision is
increasingly facilitated by online real-estate platforms such as Zillow.com,
Trulia.com, Redfin.com and the like, which aggregate home seller information
into virtual marketplaces that facilitate comparing individual candidate
houses, calculating a purchase budget, and assessing the overall real-estate
market – by professional investors, traditional homeowners and casual browsers
alike ZillowPorn . Consequently, this inflow of high-frequency market
information that is aggregated by online real-estate platforms informs
potential buyer and seller speculation, defined as near-term expectations of
price and price movements malpezzi2005role , which is invariably conditioned
by individuals varying and sensitive perceptions of uncertainty.

To explore the impact of pandemic uncertainty on financial decision-making
within this context, we constructed a 10-region panel over a nearly 4-year
time period (2018-2021) by taking monthly snapshots of Zillow Inc. listings
(www.zilllow.com) for properties featured in two categories: “For Sale” and
“Rent” (see Methods for details). Figure 1(B) shows the location of the 10
regions, which are also official administrative units in CA. The largest
principal city by population within each region is San Jose ($\sim$1 million
inhabitants in 2021); and by area is Fresno (116 square miles); the smallest
city by population is Mariposa ($\sim$1500 inhabitants) and by area is
Livingston (3.7 square miles). Despite a wide variation in size, location and
socio-economic backdrop, these 10 regions all feature shortages in affordable
housing, a common problem plaguing California and various other metropolitan
areas in the United States loftus2011tent ; raetz2020hard . Seven of the
principal cities are located along a major industrial and commuter
transportation highway (CA 99), and are within the 3-hour super-commuter
travel-time from the greater Bay Area, thereby qualifying as bedroom
communities. Conversely, two regions (Mariposa and Oakhurst) are oriented
around recreational tourism in and around Yosemite National Park. All
together, these municipalities span a wide range of house prices, market size
and turnover to support within and across-city analysis at high geo-temporal
resolution.

Figure 1:  Schematic of data sampling and before- and after-2020 matching
design. (A) All-Transactions House Price Index data by region, obtained from
the Federal Reserve Bank of St. Louis (www.fred.stlouisfed.org). Annual
percent increase from Oct. 2020-2021 are listed in the legend (2021 data not
yet available for Mariposa; for more details see Fig. S1). (B) Longitudinal
panel of Zillow Inc. house listings across 10 regions in northern California,
USA constructed over 4-year time period 2018-2021 (see Fig. S2 for sample size
information). Shown are the locations and names of the 10 principal cities –
separated into Big (magenta) and Small market (green) based upon 2021
population sizes (proportional to circle radius). (C) Spatial distribution of
mean house price estimate calculated for properties listed for sale in San
Jose before 2020; each grid is color-coded according to its corresponding
distribution quintile. (D) Mean 30-day price changes, color scale corresponds
to distribution quintiles. (E) Mean price estimate after 2020 using values
deflated to 1/1/2018 US$. (F) Percent difference between grid values in panels
B and D. (G,H) Schematic of house matching design. For each After-2020 house
listing (indexed by $h$), we identified two sets of matched houses
$\\{m_{h}\\}$ based upon multiple criteria: the matched house was listed for
sale in the same time period, in the same price strata, and within a 1/2 mile
radius of the central house. (G) Candidate matches before 2020 (10 matches
indicated by orange dots); and (H) after 2020 (8 matches). Candidate houses
within the same period not meeting these criteria are indicated by blue dots.

We exploit 3 overall features of this unique dataset to understand the
implications of COVID-19 as a socio-economic shock. First, we leverage a
hierarchical approach to analyzing house listings, which are the fundamental
units of observation. Bestowed with precise longitude and latitude information
for each listing, we perform unit-level matching to estimate the magnitude of
house valuation increases attributable to market uncertainty associated with
COVID-19. We also compare results for data grouped by both city and by market
size, the latter proxied by principal city population, resulting in two market
size categories: big (San Jose, Modesto, Fresno) and small (7 other cities).

Second, as the top real-estate website in the U.S. in 2021 with roughly 36
million visits per month ZillowPopularityRank1 , Zillow updates their listing
valuation estimates continuously. As such, data obtained from the Zillow API
is algorithmically consistent and thereby facilitate constructing near
simultaneous snapshots of entire regional housing markets. Given the
relatively rapid onset of the COVID-19 pandemic and subsequent health and
socio-economic policy across CA, we separate observations into two periods:
before 2020 and after 2020. We also control for the data sampling month in our
matching procedure to account for well-known intra-annual housing market
activity cycles FirstTueCAMarket .

And third, we exploit a novel data resource for quantifying speculation and
uncertainty within the real-estate asset class, for which little is known. As
a leading IT service provider, Zillow collects, integrates and calculates
real-time house price estimates based upon a proprietary in-house algorithm
that estimates individual house prices based upon a massive and near
comprehensive historical database extending back to the mid 2000s, including
ask prices elected by the owners and subsequent actual sale prices. These
source data are readily available to the public and have fostered data science
education and research by way of open competitions ZillowAPI ; ZillowKaggle .
Note that house estimates are not just available at the point of market entry,
but are interpolated between these on-market events in real time. As such,
even if Zillow price estimates are algorithmically biased relative to real
listing and sales prices, estimates are consistent and robust, integrating
macroeconomic, regional, neighborhood and house-specific factors – as opposed
to non-centralized data sources such as realtor listing prices, which vary
across realtor and owners’ propensity for speculation and other idiosyncratic
factors.

Another key dimension of Zillow data is the consistent property value
estimation for properties listed for sale and for rent. Within the context of
the pandemic, this latter class of real estate entering the habitation market
played an important role in accommodating individuals’ opportunities to work
remotely. Importantly, Zillow data obtained for rental listings through the
API are not monthly rent estimates, but rather, consistent property
valuations, and thus directly comparable in estimation procedure and price
magnitude to those that are for sale. Hence, because rental properties were
simultaneously available – just not for sale, and hence free of speculation
pressure – they provide an invaluable counterfactual baseline leveraged in a
difference-in-difference estimation that yields a consistency check for
estimates based upon unit-level matching of houses listed after 2020 with
neighboring houses listed prior to 2020.

Accordingly, in what follows we address the three research questions. First,
what are the characteristics of high-frequency real estate price dynamics
(1-month resolution), and did they shift after the onset of the COVID-19
pandemic? Second, to what degree did the pandemic shock to market uncertainty
affect collective speculation – namely, in house price estimates and certainty
in those estimates? And third, how did shifts in speculation depend on market
size, supply, and benchmark borrowing rates? To summarize our findings, we
show that the market response to COVID-19 uncertainty counterintuitively
featured excessive over-valuation that exacerbated an already ‘hot’ housing
market in CA, combined with decreased levels of uncertainty. These two
hallmarks of a speculative bubble were stronger in the smaller housing markets
which were more susceptible to the sudden supply contraction. These insights
are supported by behavioral theory regarding the persuasive power of
uncertainty tormala2016role  and sudden unexpected interruptions
kupor2015persuasion . In response to this severe and unanticipated magnitude
of shock, the collective response to COVID-19 uncertainty and daily life
interruptions combined with the real-time inflow of market information
collected by online real-estate platforms may have contributed to herding
behavior that is central to speculative bubble formation in complex socio-
economic systems roehner2002patterns ; hong2008advisors ; glaeser2008housing ;
shiller2015irrational .

## Results

House-level data. We obtained housing market data for 10 proximal CA regions
illustrated in Fig. 1(B) on a monthly basis from March 2018 to September 2021
using the open Zillow API; see Fig. S2(A-C) showing monthly sample sizes by
period and property type (for sale and rent). For elaboration on the data
collection procedure see Methods – Data Collection along with the official
Zillow API page describing available house-level data ZillowAPI . In summary,
Zillow assigns each property a unique identifier (ZPID) that facilitates
listing disambiguation. For each listing $h$ sampled in month $m$ we obtained
the official address; zip-code; longitude and latitude; the Zillow price
estimate (ZEstimate${}^{\mbox{\scriptsize\textregistered}}$, denoted by
$P_{h,m}$); a high and low range for the ZEst. ($P^{+}_{h,m}$ and
$P^{-}_{h,m}$, respectively); and the change in $P_{h,m}$ over the previous
30-day period ($\delta P_{h,m}$). Note that $P_{h,m}$ implicitly incorporates
other features unavailable through their basic API, such as housing unit size,
construction date and materials, and other house-level information (e.g. yard
dimensions, garage capacity, pool, school district, neighborhood amenities,
etc). All price values were obtained in nominal US$ relative to the sampling
date; in what follows, we deflated all price values to 1/1/2018 US$. We also
computed the price change as a percent of the initial price, $\Delta
P_{h,m}=100\times\delta P_{h,m}/(P_{h,m}-\delta P_{h,m})$. See Fig. S2(E,F)
for the mean and standard deviation of $\Delta P_{h,m}$, by period and
property type. We calculated the spot price uncertainty,
$U_{h,m}=100\times(P^{+}_{h,m}-P^{-}_{h,m})/P_{h,m}$; see Fig. S2(G,H) for the
mean and std. dev. of $U_{h,m}$, by period and property type.

We then estimated the housing market activity around a particular house $h$ by
counting the number of houses $A_{h}$ within a 0.5 mile (0.8 km) radius,
corresponding to 10 New York City blocks, for example. To complement this
spatial proximity criteria, we also only considered properties listed within
the three-month period prior to and including the data census month $m_{h}$
for each house $h$. As a macro-economic indicator of borrowing costs, we
collected weekly data compiled by Freddie
Mac${}^{\mbox{\scriptsize\textregistered}}$ on the average US 30-year fixed
rate mortgage.

Figure 2:  Systematic increase in property valuation and confidence in the
post-2020 housing market. Kernel density estimate of the probability density
function (PDF) calculated for (A) 30-day price change, $\Delta P_{h,m}$,
including the best-fit Cauchy PDF calculated using both the big and small
market data combined; and (B) PDF calculated for price uncertainty, $U_{h,m}$.
Data shown are calculated using properties listed “For Sale”; see Fig. S4 for
PDF conditioned on market size, period and property type. (C-F) Mean
($\langle\cdot\rangle$) and standard deviation (STD, $\sigma[\cdot]$)
calculated for $\Delta P_{h,m}$ and $U_{h,m}$ conditional on spot price
$P_{h,m}$. Together, these two variables show how the post-2020 CA housing
market features excess valuation growth and increasing valuation confidence
(i.e., decreased uncertainty), patterns that are common to both the big and
small markets – and surprisingly, even stronger for the small market. These
effects manifest as systematic shifts in the first and second moments – i.e.,
the characteristic location (C,D) and characteristic fluctuation scale (E,F) –
of the underlying data distributions, and are robust across the entire range
of house listing price estimates.

Housing market descriptive statistics – by region and period. The distribution
of house prices $P_{h,m}$ is approximately log-normal – see Fig. S3. This
feature is common to other asset classes such as stock prices, firm and
university sizes, and human productivity, and is consistent with the Gibrat
proportional growth model mantegna1999introduction ; plerou1999similarities ;
petersen2012persistence ; buldyrev2020rise .

Figure 2(A,B) show the distributions of $\Delta P_{h}$ and $U_{h}$,
respectively. 30-day price-change fluctuations ($\Delta P_{h}$) feature high
levels of variance around the roughly 1-2% average price growth levels
observed during the sample period. The distribution $P(\Delta P_{h})$ is
asymmetric and leptokurtic, being wider in the bulk than the Laplace (double-
exponential) tent-shaped growth distributions observed for organizations
stanley1996scaling ; plerou1999similarities ; buldyrev2020rise ;
petersen2012persistence . Both the positive and negative tails of $P(\Delta
P_{h})$ are heavy, extending well beyond the values of $\pm 40\%$ used to
truncate our data sample so that parameter estimates in our regression model
are not biased by extreme outliers. The best model for the $P(\Delta P_{h})$
distribution is a Cauchy-Lorentz probability density function (PDF), of the
general form $P(x)\sim 1/x^{2}$ for $|x-x_{0}|\gg 1$. The bulk of the data are
captured by $|\Delta P_{h}|\leq 10$; the Cauch-Lorentz parameters estimated
maximum likelihood for big and small market data pooled are $x_{0}$ = 0.2 and
scale $\gamma$ = 2.0. This data distribution indicates that fluctuations in
this real estate asset class are more similar to the heavy-tailed price
fluctuation distributions observed for equity asset class mantegna1995scaling
. One explanation for this is the large scale of real estate depreciation that
can occur over the lifetime of ownership, balanced on the other side by
relatively sudden appreciation of real estate following renovations. In other
words, when a property enters the real-estate market, the update in asset
valuation incorporates a wide range of information that has accrued over a
variable time-scale.

The price uncertainty, another valuable feature of the Zillow Inc. pricing
algorithm, also shows considerable variation, is narrowly centered around the
10% level, but with significant right-skew. Whereas for $P(\Delta P_{h})$
calculated using houses for sale we observe a systematic shift towards excess
frequency of $\Delta P_{h}>0$ values after 2020 relative to before; for
$P(U_{h})$ we observe the opposite trend. Interestingly, in the case of rental
properties, we observe no shift in $P(\Delta P_{h})$ comparing before and
after, whereas the frequency of larger $U_{h}$ values post-2020 increases
dramatically, possibly reflecting COVID-19 eviction moratorium policy rapidly
implemented in the US national2021rental ; benfer2021eviction ;
gromis2022estimating . see Fig. S4 for complementary distributions conditioned
on market size, period and property type.

Prominent shifts in real-estate speculation during COVID-19. Using the CA real
estate market before 2020 as a comparative baseline, Fig. 2 shows that the
post-2020 market feature hallmarks of a speculative bubble – namely (a)
accelerated valuation growth net of change in fundamentals and (b) increased
confidence in excess valuation. Somewhat ironically, these characteristics may
have emerged by way of contagious spreading of ‘irrational exuberance’ among
market agents roehner2002patterns ; glaeser2008housing ; shiller2015irrational
. We argue that enhanced real-estate speculation derives from the global
COVID-19 uncertainty shock, which muddled global expectations for investment
returns; yielded a confounding and non-uniform impact on the public, as
indicated by a diverging “$K$-shaped” recovery in the US population
dalton2021k ; induced drastic policy interventions, such as the sudden
reduction of the US federal funds target rate taking the form of a long-
lasting financial-quake petersen2010quantitative ; petersen2010market , which
among other immediate effects promoted aggressive household borrowing that
boosted home-purchasing and home-improvement activity; and triggered a sudden
housing supply-demand imbalance exacerbated by the rapid expansion of remote
work-from-home policy liu2021impact ; mondragon2022housing , in particular in
the IT sector that is concentrated in the Bay Area mega-region. While these
factors primarily affect the house purchase market, they also augmented
uncertainty and speculation levels in the rental market, given the coincident
increased demand for rent combined with sudden rent protection policy that
together shifted risk-levels for both tenants and rental property owners
benfer2021eviction .

Combined, these factors are reflected by drastic systematic shifts in the
characteristic levels of speculation ($\Delta P_{h,m}$) and uncertainty
($U_{h,m}$) across the entire range of $P_{h,m}$ – for both small and big
markets. Notably, we observe higher average $\Delta P_{h,m}$ in small markets
than in big markets, consistent with nationwide analysis of the impact of
state-level shutdowns on price changes in the months before and after their
implementation, which were found to be mediated by differences in population
and structural density between urban and rural markets d2022covid . See
Methods – Housing market descriptive statistics for additional analysis of the
price and price-change distributions, with the latter best explained by the
“fat-tailed” Cauchy-Lorentz distribution.

Compared with recent work analyzing the real estate market in southern CA that
finds a negative relation between price growth and price landvoigt2015housing
, consistent with other asset classes such as firms and stocks
buldyrev2020rise , we instead observe an increasing trend in $\langle\Delta
P_{h,m\rangle}\rangle$ with $P_{h,m}$ after 2020, indicative of accelerated
speculation – see Fig. 2(A). This shift is also readily apparent in the higher
levels of price-growth variation ($\sigma[\Delta P_{h,m\rangle}]$) observed
after 2020 – see Fig. 2(B). Again, this pattern deviates from the well-
established decreasing size-variance relationship found for other asset
classes mantegna1995scaling ; stanley1996scaling ; plerou1999similarities ;
mantegna1999introduction ; buldyrev2020rise . Contrariwise, Fig. 2(C,D)
indicate a reduction in mean and standard deviation of price uncertainty after
2020, also consistent with the conditions of a speculative bubble.

Quantifying the effect of COVID-19 on collective speculation in the CA real-
estate market. We implement two complementary quasi-experimental methods –
unit-level matching and difference-in-difference (DiD) regression – that
leverage the COVID-19 pandemic as an instrument conley2021past  for
identifying the impact of a shock to market uncertainty, in combination with
housing under-supply and reduced demand for housing and amenity density
liu2021impact , further exacerbating stress in the CA real-estate market
balemi2021covid , in particular the regulatory environment for affordable
housing construction d2022covid . In this regard, our results contribute to
prior empirical and theoretical work on how inelastic supply and speculation
support the emergence of bubbles malpezzi2005role ; glaeser2008housing .

Unit-level matching: Our quasi-experimental matching design does not conform
to a traditional treated-control setting stuart2010matching , as the pandemic
was perniciously pervasive and so their is no untreated group. Yet our
approach still incorporates notable advantages of matching designs. Foremost,
this approach accounts for unobserved covariates that are nonetheless
correlated with the available matching variables. That is, while we do not
explicitly incorporate house-specific features – such as vicinity to shopping
and schools, backyard area and other physical amenities such as a pool, along
with other price factors – these variables are implicitly incorporated into
$P_{h,m}$ deriving from seller-elected ask prices. Moreover, by virtue of its
design as a leading e-platform parker2016platform  that derives value by
aggregating comprehensive and contemporaneous local and national house
listings, $P_{h,m}$ values are believed to be consistent and thus well-suited
for the purpose of unit-level matching.

Our matching design also exploits the high geo-temporal resolution of the
listing data to match properties listed after 2020 with similar properties
listed before 2020, thereby optimizing measurement precision in the evaluation
of market shifts due to pandemic uncertainty. An advantage of this approach is
addressing the high degree of price and price change variation that exists
even within a single region, as illustrated in Fig. 1(C). To be specific, we
account for unobserved unit-level features stuart2010matching  by strictly
matching houses according to three listing features: (a) price strata, (b)
calendar month, and (c) geographic location – variables that are only weakly
related to the variables central to our analysis, $\Delta P_{h,m}$ and
$U_{h,m}$. We match on price strata by first calculating an intensive variable
$Q_{c}(P_{h,m})\in 1,2...10$, with 1 (respectively, 10) representing the
lowest (highest) price decile that is a specific to a particular city $c$ and
before/after period. Assuming that potential buyers would be open to a range
of house prices in excess of a single decile, we then allow for matches within
$\pm 1$ decile group from $Q_{c}(P_{h,m})$. We constrained matches temporally
by requiring matched houses from the same calendar month or 1 calendar month
prior of the central house, which accounts for intra-year housing market
cycles. And we constrained matches geographically by requiring matched houses
to be within a 0.5 mile (0.8 km) radius of the central house.

Figure 3:  Estimation of housing market valuation shifts attributable to
COVID-19. (A-C) $\overline{\Delta}_{Y}$ is the distribution average of the
unit-level difference $\Delta_{Y,h}=Y_{h}-\langle Y\rangle_{\\{m_{h}\\}}$ in
the variable $Y$, calculated across the set of all houses listed after 2020;
the counterfactual baseline $\langle Y\rangle_{\\{m_{h}\\}}$ is calculated
across the set of matched houses $\\{m_{h}\\}$ listed before 2020. In this
way, matching facilitates a more precise estimation of the impact of COVID-19
on the housing market. Error bars indicate the standard error of the mean and
stars indicate the significance level of a T-Test for the likelihood of the
null hypothesis $\overline{\Delta}_{Y}=0$. See Fig. S6 for average match
differences sizes by city, $\overline{\Delta}_{Y,c}$. (A) The difference in
price estimate ($Y=P_{h,m}$; all values deflated to 1/2018 US$) shows the
average price change for listings after 2020. (B) The difference in price
change ($Y=\Delta P_{h,m}$) measures shifts in price valuations at high
temporal resolution (30-day), and shows that properties listed for sale had
excess price valuation relative to those listed for rent. (C) The difference
in price uncertainty ($Y=U_{h,m}$) is inversely related to valuation
confidence. In the case of properties listed for sale, we observe a
1-percentage point reduction in price-uncertainty, i.e. higher valuation
confidence; conversely, we observe drastic price uncertainty increases for
rental properties. (D) Summary of the COVID-19 treatment effect on properties
listed for sale, based upon a two-period difference-in-difference model
implemented for three regions for which sufficient rental property data are
available, wherein rental properties serve as the control group for before and
after 2020. To summarize, average $\Delta P_{h,m}$ values increased between
0.85 and 1.21 percentage points, and price uncertainties declined between 3
and 9 percentage points – from the levels they plausibly would have maintained
in the absence of the pandemic. Note that in both cases, this treatment effect
corresponding to properties listed for sale. Error bars represent the 95%
confidence interval in each point estimate; full table of parameter estimates
are reported in Tables S1-S2. Significance levels indicated by the asterisks:
* $p<0.05$, ** $p<0.01$, *** $p<0.001$.

By way of example, Fig. 1(G,H) illustrates the matching procedure using an
property from San Jose listed after 2020, which also highlights the reduction
in market supply after 2020 relative to before. Note that not all houses
within the specified radius of pre-2020 listings are candidate matches because
of the price variation spanning several $Q_{c}(P_{h,m})$ strata. We denote the
set of matched houses for a given central house $h$ by $\\{m_{h}\\}$, which is
by construction a subset of the houses counted by $A_{h}$.

Figure 3(A-C) shows the average difference between properties listed after
2020 and their most similar matched properties listed before 2020. The null
hypothesis associated with no COVID-19 impact on the housing market
corresponds to $\overline{\Delta}_{Y}=0$, which we test using a one-sample
Student T-test. Regarding absolute price change, for both big and small
markets the difference in $\overline{\Delta}_{Y}$ between houses for sale and
rent within the same market is roughly 8,000 US$ – see Fig. 3(A). Similar
juxtapositions between $\overline{\Delta}_{Y}$ values in Fig. 3(B,C) can be
made between the average values between property types within the same market
– namely, excess percent price change in the case of properties for sale, and
excess price uncertainty changes for properties listed for rent. For this
reason, properties listed for rent serve as a control group in the next
section. In terms of the magnitude of this effect on properties listed for
sale, the increase in $\Delta P_{h,m}$ is more than double the characteristic
levels observed prior to the pandemic – see Fig. 2(A); and for the price
uncertainty, the reduction is roughly 4% of the pre-2020 average uncertainty
levels – see Fig. 2(B).

Figure 4:  Marginal effects of local market supply and mortgage rate on price
change and uncertainty. (A,B) Predictions of the relationship between the
supply of alternative houses (defined as the number of matched houses within
the same period as the central house listing, $A_{h,m}$) and price change
$\Delta{P}_{h}$. Positive shift in $\Delta{P}_{h}$ of roughly 0.5 percent
after 2020 relative to before, which diminishes at higher levels of market
supply – for both small and big markets. (C,D) Predictions of the relationship
between the average 30-year US Mortgage rate (Fixed rate, shown as percentage)
and $\Delta{P}_{h}$. Positive shift on the order of 0.4 percent for both small
and big markets. (E-H) Similar to panels (A-D) but showing the OLS model
predictions for price uncertainty. As expected, the uncertainty associated
with COVID-19 is more clearly manifest in the market valuation uncertainty
than the price dynamics. Counter-intuitively, however, the increased levels of
uncertainty associated with the pandemic appear to have reduced uncertainty in
price estimations, which points to the amplification of market speculation
during this period of global stress. Shaded areas indicate 95% confidence
interval around the predicted margins of response indicated by the dashed
line; predictions calculated using all other covariates at their mean values.

Difference-in-Difference regression: We ran a two-period difference-in-
difference (DiD) model for three regions (San Jose, Fresno, Merced) for which
sufficient rental property data is available to serve as the before and after
2020 control group. This approach leverages differences in the Zillow
valuation estimates for off-market (rental) properties, which thereby provides
a critical market counterfactual – homes that are available for habitation,
just not for sale, and hence free of speculation. See the Methods – Regression
model specification for a list of control variables and other implementation
details. In a nutshell, we apply ordinary least squares (OLS) regression to
estimate the model $Y_{h,m}=\delta_{TE}(I_{h,\text{ForSale}}\times
T_{m})+\vec{\beta}\cdot\vec{X}+\vec{\gamma}\cdot\vec{I}+\epsilon$ for each
specified city, where $\vec{X}$ (respectively, $\vec{I}$) represents a battery
of continuous (respectively, factor) controls, and the DiD interaction
$\delta_{TE}(I_{h,\text{ForSale}}\times T_{m})$ captures the difference
between the two property types (specified by the indicator variable
$I_{h,\text{ForSale}}$) across the two periods (specified by the indicator
$T_{m}$). See ref. liu2021impact , which analyzes repeated-transaction home
price data within and across 25 largest metropolitan statistical areas over
the period in question, and shows that the conditions of the DiD parallel
trend assumption are sufficiently satisfied.

Fig. 3(D) shows the estimated treatment effect $\delta_{TE}$ for each model
and city. Full model estimates are elaborated in Tables S1 for the dependent
variable $Y\equiv\Delta P_{h,m}$ and S2 for $Y\equiv U_{h,m}$. Thirty-day
price changes increased on average between $\delta_{TE,P}=0.85$ (Fresno) and
1.2 (San Jose) percentage points above what they likely would have been in the
absence of COVID-19 market shock, including but not limited to construction
supply constraints yagi2021global ; raetz2020hard , remote-work-induced
migration liu2021impact ; baum2019microgeography  and speculation
malpezzi2005role ; glaeser2008housing . And price uncertainties declined
between $\delta_{TE,U}$ = -3 (San Jose) and -9 (Merced) percentage points. As
a robustness check, we confirm that each OLS regression point estimate is
consistent with the difference $\overline{\Delta}_{Y,\text{For
Sale}}-\overline{\Delta}_{Y,\text{Rent}}$ using the matching analysis results
shown in Fig. 3(B,C).

To further convey the relative impact on price change and uncertainty, Fig. 4
shows the margins associated with (a) neighborhood market activity $A_{h,m}$,
a micro-level indicator of housing supply measured as the number of
potentially competing listings in the immediate vicinity of each listing; and
(b) inverse homeowner borrowing power $M_{m}$, measured according to the
average 30-year fixed-rate mortgage. Panels (A-D) can be used to approximate
the semi-elasticity of price with supply, and are consistent with standard
economic theory. For example, an additional 10 local listings (i.e. $A_{h,m}$
shifting from 10 to 20) corresponded to a reduction in price change of roughly
0.6 (resp. 0.7) percentage points for the small (resp. big) market before
2020; however, after 2020 this reduction increased in magnitude by roughly 0.1
percentage points for both markets as indicated by the increasingly steep
slope after 2020. This shift in the semi-elasticity is net of the baseline
shift captured by $\delta_{TE,P}$.

Another factor explaining price gains during this period are the lower
interest rates that directly affect buyer purchasing power and builder
construction costs HousingBoomMortgageRates . The slope of the lines shown in
Fig. 4(C,D) provide an estimate of the mortgage rate semi-elasticity,
indicating a roughly 0.7 percent price increase for a 1 point reduction in
$M_{m}$, which is on the lower side but and consistent with estimation based
upon a wide range of approaches defusco2017interest ; the discrepancy may be
attributable to the relatively low range of $M_{m}$ and monthly price change
horizon encountered in our analysis. Note that the estimation for smaller
(larger) interest rates for before (after) 2020 are extrapolations into out-
of-sample $M_{m}$ regimes, as indicated by the larger standard errors. Another
relevant analysis for comparison is one based upon the San Diego housing
market from 1997-2008, which attributes higher price gains for houses at the
lower end of the price distribution to cheaper credit landvoigt2015housing .
While we do not explicitly explore the interaction between $M_{m}$ and $\Delta
P$ conditional on $P$, we do not see evidence of the differential price gains
by price segment over this period for big vis-a-vis small markets, as also
indicated by Fig. 2(A).

Figure 4(E-H) show analog response margins associated with price uncertainty
$U_{h}$. For both big and small markets, uncertainty levels tempered after
2020 relative to before, corresponding to higher levels of valuation
confidence for the same levels of neighborhood supply. Counterintuitively,
this result indicates more efficient price discovery barkham1996price ,
despite greatly heightened socio-economic uncertainty. Interestingly, the
informational signal captured by $A_{h,m}$ diminished during the pandemic in
the small market, as indicated by the relatively flat profile in Fig. 4(F).

## Discussion

The rapid emergence of the global pandemic followed by deployment of pervasive
mitigation policy had unevenly impacts across society bonaccorsi2020economic ;
bunn2021covid ; dalton2021k ; national2021rental ; benfer2021eviction ;
gromis2022estimating ; aleta2022quantifying . Against this backdrop, we
contribute to a rich literature emerging from this global crisis
conley2021past . One pertinent analysis separated US counties according to
when and wether they featured government-mandated stay-at-home orders,
representing a significant interruption to everyday life and perceptions of
uncertainty, and found relatively higher house sale prices in the shut-down
counties d2022covid . Our results are also consistent with economic theory and
empirical analysis identifying reduced supply elasticity attributable to
COVID-19 supply constraints yagi2021global  that negatively impacted building
costs and other factors that exacerbated supply inelasticity
baum2019microgeography , two features that are central to the theory of
emergent housing bubbles malpezzi2005role ; glaeser2008housing . These supply
factors were complemented by remote-work options that expanded the effective
radius of search accompanied by a decreasing demand for amenity density
liu2021impact . California is also characterized by prominent regulation on
new home construction, which was further exacerbated by supply-chain
disruptions raetz2020hard .

A notable limitation to our study is that we do not account for two
complementary mechanisms, namely the emergence of remote work and the
coincident influx online market intermediaries or iBuyers. Regarding the
former, economists find that an increasing prevalence of remote work can
explain roughly half of the aggregate price changes over 2019-2021, deriving
from housing demand shifts associated with migration mondragon2022housing .
Another factor that merits consideration is the rise of speculation-driven
iBuyers, the profitability of which is highly impacted by valuation
uncertainty buchak2020intermediating . Coupled with now ubiquitous IT service
economy innovations parker2016platform ; maglio2019handbook , the real-estate
market has transformed since the last US housing boom and bust in 2008.

As one of the leading platform service providers in the US real-estate sector
ZillowPopularityRank1 , Zillow Inc. collects and recalculates algorithmically
consistent property valuations that are consumed in various contexts.
According to industry survey results from 2022 ZillowPorn , online real-estate
platforms facilitate a remarkable level of casual real-estate browsing a
11footnotetext:  Also known as “Zillow porn” ZillowPorn , as depicted in a
2021 Saturday Night Live skit SNLZillowPorn . – providing an imagination
outlet for 83% of the respondents, with only 17% claiming to search listings
with more serious home-purchase motivations. This statistic alone suggests
that the extreme levels of price growth during the pandemic may be
attributable – in addition to fundamental shifts in supply and demand – to
behavioral phenomena associated with collective adaptation to heightened
levels of life-course uncertainty, and an increased prevalence of naive
speculators that are theoretically linked to bubble formation hong2008advisors
. Furthermore, inasmuch as real-estate platform service providers facilitate
crowd-sourcing, browsing, and market-making, they also facilitate analyzing
the dynamics of speculation at high resolution and scale.

To this end, we analyzed the impact of the COVID-19 pandemic shock on
speculation and uncertainty in a select housing market by performing two
complementary econometric methods yielding consistent results. In the first
case we matched house listings based upon the set of available characteristics
(listing month, price strata, longitude-latitude) to optimize around precision
in the calculation of the difference in speculation attributable to the
pandemic stuart2010matching . We then implement a DiD model that exploit the
different valuation and socio-economic features of renting versus buying that
were emphasized during the pandemic. In all, the 10 regions analyzed capture a
relatively wide variation in size, location and socio-economic backdrop such
that we believe the results of our analysis are generalizable to other US
regions.

Results show that the pandemic induced robust non-incremental shifts in both
small and big markets, characterized by significantly higher prices combined
with decreased uncertainty in those valuations. To be specific, our estimates
indicate that properties listed for sale after the pandemic featured an excess
monthly price growth of roughly 1 percentage points, corresponding to roughly
12.7 percentage points when integrated across an entire year, which accounts
for more than half of the annual growth observed across these same regions in
2021, as illustrated in Fig. 1(A). Juxtaposed, these features may be
harbingers of ‘irrational exuberance’ shiller2015irrational  in response to a
sudden shock to long-term certainty that has augmented the dynamics and scale
of collective speculation.

## Methods

Data Collection. House listing data for each of the 10 select regions were
obtained from Zillow Inc. on a monthly basis between March 2018 and May 2019
(denoted as the period before 2020) and May 2020 and September 2021 (after
2020). For each month, we obtained a set of unique listing identifiers (ZPID)
by manually scanning across the entire Zillow.com directory for a given region
and property type (“For Sale” and “Rent”). This sampling frequency is
sufficient to collect data for the majority of listings made within a monthly
time window, as the average property during this period was on the market for
44 days d2022covid . We then used the open-access Zillow Inc. GetSearchResults
API to sample house data for each ZPID in accordance with daily API call
limits ZillowAPI .

Figure S2(A,B) shows the monthly size of the sampling panel for housing units
grouped by Zillow according to house property type; and Fig. S2(C,D) groups
the sample sizes into 6-month non-overlapping periods to facilitate visual
comparison to market supply before and after 2020. A listing is featured in
either of the availability catalogues at the owner’s discretion. The data
analyzed in this study are price estimates ($P_{h,m}$) that are dynamically
generated by Zillow Inc. based upon a proprietary in-house algorithm that
implicitly incorporates various data sources also available through the
Zillow.com service, including macro-economic market data such as mortgage
rates, regional and neighborhood data such as schools and similar houses, and
house-specific data (physical dimensions, material properties, other included
amenities) including web-metrics such as house-views. These price estimates
are not to be confused with the asking price set by the listing agent,
although inspection of 10-year historical price estimate data for various
properties indicates that a new ask price is rapidly incorporated by the
Zillow Inc. algorithm, and is a critical feature that gives rise to the
collective co-production of market speculation deriving from individual seller
and online platform service user activity.

In order to focus our analysis on typical property listings, we exclude
observations from our raw sample according to various criteria. First, we
excluded property listings featuring extreme price change or price uncertainty
values by keeping only the observations for which $\Delta P_{h,m}\leq 40\%$
and $U_{h,m}\leq 40\%$, which together reduced the original dataset from
133,668 observations to 110,530 listings (17% reduction). Second, we excluded
those listings with fewer than 4 neighboring listings within a 0.5 mile radius
within a three-month window prior to and including the central house’s listing
month, and only considered listings from the active CA real-estate period
(March thru October FirstTueCAMarket ) during the years 2018-2021. These
criteria further reduced the sample size to 57,414 listings (48% reduction
from 110,530). Together, these criteria eliminated many listings corresponding
to empty lots and other under-developed properties located beyond the
principal city limits.

Regression model specification. We model the relation between the dependent
variable $Y\equiv\\{\Delta P_{h,m}$ or $U_{h,m}\\}$ and a battery of available
controls ($\vec{X}$ and $\vec{I}$) by way of ordinary least-squares (OLS)
regression (implemented using STATA 13.0 software) to estimate the
coefficients of the panel regression model which incorporates fixed effects to
account for time-independent factors associated with region, listing calendar
month (categorical variable indicated by $C_{m}$), and region-specific price
strata (categorial variable $Q_{c}(P_{h,m})$ which codes houses according to
ten region-specific price deciles).

Region-level regression estimates implementing a difference-in-difference
model in which the control group is constructed from valuations of properties
listed for rent, which represent an appropriate counterfactual to comparable
properties that were listed for sale. The treatment effect capturing the
impact of COVID-19 and associated market supply shocks along with US policy
interventions on real estate valuations are summarily reported in Fig. 3(D),
based upon an ordinary least-squared (OLS) model estimation performed for
three regions for which sufficient rental data were available.

In the case of the dependent variable being the 30-day price change, we
modeled the relationship including the DiD interaction
$I_{h,\text{ForSale}}\times T_{m}$ between the property type indicator
($I_{h,\text{ForSale}}$) and the before-after 2020 period indicator $T_{m}$ as

$\displaystyle\Delta P_{h,m}=\delta_{TE,P}(I_{h,\text{ForSale}}\times
T_{m})+\beta_{U}(U_{h,m}\times
I_{h,\text{ForSale}})+\beta_{U^{2}}(U^{2}_{h,m}\times
I_{h,\text{ForSale}})+\vec{\beta}\cdot\vec{X}+\vec{\gamma}\cdot\vec{I}+\text{const.}+\epsilon\
,$ (1)

where the covariates are represented by
$\vec{\beta}\cdot\vec{X}=\beta_{M}M_{m}+\beta_{A}(A_{h,m}\times
I_{h,\text{ForSale}})+\beta_{A^{2}}(A^{2}_{h,m}\times
I_{h,\text{ForSale}})+\beta_{P}\ln P_{h,m}+\beta_{P^{2}}\ln^{2}P_{h,m}$ and
the factor variables are represented by
$\vec{\gamma}\cdot\vec{I}=\gamma_{I}I_{h,\text{ForSale}}+\gamma_{T}T_{m}+\gamma_{Q}Q_{h}+\gamma_{C}C_{m}$.
The interaction between $I_{h,\text{ForSale}}$ and several control variables
are for differentiating responses conditional on property type. Full model
estimates are elaborated in Table S1.

Similarly, in the case of the dependent variable being the price uncertainty,

$\displaystyle U_{h,m}=\delta_{TE,U}(I_{h,\text{ForSale}}\times
T_{m})+\beta_{\Delta P}(\Delta P_{h,m}\times
I_{h,\text{ForSale}})+\beta_{\Delta^{2}P}(\Delta^{2}P_{h,m}\times
I_{h,\text{ForSale}})+\vec{\beta}\cdot\vec{X}+\vec{\gamma}\cdot\vec{I}+\text{const.}+\epsilon\
.$ (2)

Full model estimates are elaborated in Table S2.

Regression model used to estimate marginal effects reported in Fig. 4 are
derived from a nearly identical OLS model, which differs only in that it does
not include the DiD term ($I_{h,\text{ForSale}}\times T_{m}$). Instead, this
model includes an interaction $S_{h}\times A_{h,m}\times T_{m}$ in order to
quantify the marginal effect of neighborhood market activity $A_{h,m}$
associated with $Y=\\{\Delta P_{h,m}$ or $U_{h,m}\\}$, while accounting for
differences in period and market size. Full model estimates are elaborated in
Table S3.

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Supplementary Information – Figure S1-S7 & Tables S1-S3

Shift in house price estimates during COVID-19
reveals effect of crisis on collective speculation

Alexander M. Petersen1

1Department of Management of Complex Systems, Ernest and Julio Gallo
Management Program, School of Engineering, University of California, Merced,
California 95343, USA

Figure S1:  Quarterly price indices for several CA housing markets. Aggregate
region-level house price indices produced by the Federal Reserve Bank of St.
Louis (quantities are “Not Seasonally Adjusted” and “Estimated using sales
prices and appraisal data.”). (A) Official Price Index data available for San
Jose-Sunnyvale-Santa Clara; Modesto; Merced; Fresno; Mariposa County. (B,C)
Two-period percent change, $\Delta_{t}(\%)=100(x_{t}-x_{t-1})/x_{t-1}$,
calculated for the price indices ($x_{t}$) shown in panel A. Note that data
for Mariposa are estimated at the annual frequency, and not the quarterly
level as in the other cases, and because the range of values is substantially
higher, we separated the panel for Mariposa County.  Figure S2:  Sample size
and summary statistics – by period and property type.. Observations separated
into non-overlapping subsets according to listing period and property types
(For Sale and Rent). (A,B) Sample size by month. (C) Sample size as number of
houses by period and type. (C) Sample size as fraction of all houses belonging
to a period – by type, which shows common market size trends despite
differences in absolute numbers. (E,F) Mean and standard deviation of ZEst
house price, $P_{h}$. (G,H) Mean and standard deviation of ZEst house price
uncertainty, $U_{h}$. There is a gap in data collection for month numbers 18
(June 2019) thru 27 (March 2020) due to changes in the Zillow website, which
summarily haulted our ability to obtain the house-level identifiers (ZPIDs)
which were the principal input for the Zillow API for harvesting data; Data
collection re-commenced in Feb. 2020, and since there is a 2-month padding to
identify matched houses, this results in the data gap ending in May 2020. This
data gap does not affect our ability to perform a pre/post analysis, as it
falls principally during the housing market off-season of November thru
February, which are summarily excluded from our analysis anyhow. Critical
changes to the entire Zillow API platform in October 2021 haulted data
collection entirely.  Figure S3:  Distribution of house price estimates – by
city, period and property type. Price distributions are organized by city in
two sets of columns according to housing market size (Big and Small). For each
city we show the smooth kernel density estimate of the conditional price
distribution, $P(P_{h}|\text{period, unit\ type})$, calculated according to
four non-overlapping data samples: for two periods (Before 2020 – gray dashed
curve; After 2020 – colored solid curve) and two property types (For Sale and
Rent). To facilitate comparing $P(P_{h}|\text{period, unit\ type})$ across
period for a given property type, vertical bars indicate the mean price value
of the corresponding distribution. Note that all X-axes are shown on
logarithmic scale, visually indicating that many $P(P_{h}|\text{period, unit\
type})$ are log-normal distributed. Also note that there was only sufficient
house rental data available through the Zillow API for 4 regions, with only
one of these (Merced) belonging to the small market group.  Figure S4:
Distribution of price change $\Delta P_{h,m}$ and uncertainty $U_{h,m}$ – by
market size, period and property type. Distributions of 30-day price change,
$\Delta P_{h,m}$ (A-C) and price uncertainty, $U_{h,m}$ (D-F). For each data
distribution we calculated the smooth kernel density estimate by collecting
data into non-overlapping subsets based upon market size (Big and Small) and
sampling period (Before 2020 and After 2020). (A) Aggregate price change
distribution exhibits leptokurtic shape (i.e., broader than the benchmark
Normal distribution), with the best-fit distribution model identified as the
Cauchy-Lorentz probability density function (PDF) $P(x)\sim 1/x^{2}$ for
$|x-x_{0}|\gg 1$. Each dashed line corresponds to the distributions by market
size: For properties in big markets, the location $x_{0}$ = 0.15 and scale
$\gamma$ = 2.2; similarly, for properties in small markets, $x_{0}$ = 0.34 and
scale $\gamma$ = 1.5. The bulk of the data are captured by $|\Delta P_{h}|\leq
10$, with mean distribution values around 1.25 and 1.5% indicated by the solid
vertical lines. The inset shows the distribution on log-linear axes, with the
dashed line corresponding to the fit based upon both big and small market data
pooled: $x_{0}$ = 0.2 and scale $\gamma$ = 2.0. (Inset) The price change
distribution shown over the full range $|\Delta P_{h}|\leq 40$ %. The
empirical data distribution is asymmetric, with empirical frequencies in
excess of (less than) the best-fit Cauchy distribution for relatively large
$\Delta P_{h}>0$ values ( $\Delta P_{h}<0$ values). (B) Price change
distributions for houses listed for sale, by market and period, showing excess
frequency for $\Delta P_{h}>0$ comparing after to before 2020, but not for
$\Delta P_{h}<0$. (C) Price change distributions for houses listed for rent,
by market and period, where the main difference between the plots is
associated with market size. Comparing panels (B) and (C), the rent
distribution is less leptokurtic in the bulk and also decays faster in both
the positive and negative tails. (D-F) Distributions of price uncertainty,
$U_{h,m}$ indicate a skewed distribution closely centered around 10% with mean
values closer to 11% in panels D and E which is dominated by properties listed
for sale, and more variable in panel F which represents rental properties.
Figure S5:  Distributions of differences in matched-house price change and
price uncertainty – by market size and property type. Shown are the full
distributions of match differences to supplement the mean match difference
values ($\overline{\Delta}_{Y}$) reported in Fig. 3. For each house listed
after 2020 we calculate $\Delta_{h}$ between that house and the average value
of $Y$ calculated across the set of matched houses $\\{m_{h}\\}$ listed before
2020, i.e. $\Delta_{Y,h}=Y_{h}-\langle Y\rangle_{\\{m_{h}\\}}$, where the
second term in the difference is the average value of $Y$ calculated across
the set of matched houses that were listed before 2020.  Figure S6:
Estimation of housing market valuation shifts attributable to COVID-19 – by
city. (A-C) Average match differences calculated for properties listed for
sale. (D-F) Average match differences calculated for rental properties. Figure
S7:  Cross-correlation and Descriptive statistics for regression model
variables. Upper-diagonal elements: bivariate histogram between row and column
variables. Diagonal elements: histogram for variable indicated by the
row/column labels. Lower-diagonal elements: bivariate cross-correlation
coefficient: light-shaded squares indicate the Pearson’s correlation
coefficient between two variables that are both continuous measures; dark-
shaded squares indicate the Cramer’s V associate between two variables that
are both categorical.

Table S1:  Two-period Difference-in-Difference model with dependent variable
$\Delta P_{h,m}$. Ordinary Least Squares (OLS) model implemented separately
for the three regions with sufficient rental data, which serve as comparative
DiD group, corresponding to the $I_{h,\text{ForSale}}$ baseline: if $h$ is
listed for sale, then $I_{h,\text{ForSale}}=0$ and $=1$ otherwise.
Coefficients estimated with property type interaction are indicated by [For
Sale] and [Rent]. The coefficient $\delta_{TE,\Delta P}$ corresponds to the
COVID-19 treatment effect on 30-day percent price changes, $\Delta P_{h,m}$,
and visualized together in Fig. 3(D). Note that $T_{m}$ is the time period
variable, taking the value 1 if the listing occurred after 2020, and 0 if
before 2020. Parameter estimate $p$-values are shown in parenthesis below each
point estimate. OLS regression implemented in STATA 13 using “reg” calculated
with robust standard errors. Factor variables included but not reported in the
table below: Zest. price decile $D_{h,m}$, which ranges from 1 to 10; Dummy
variable for calendar month, $C_{m}$, which ranges from 3 (March) to 10
(October) capturing intra-annual housing market cycle. See Fig. S7 for the
cross-correlation matrix across the principal model covariates.

|  |  $Y=$ 30-day Percent Price Change (%), $\Delta P_{h,m}$ |
---|---|---|---
| San Jose | Fresno | Merced
Ave. US 30-yr. fixed mortgage rate, $\beta(M_{m})$ | -0.0736 | -0.306 | -5.706∗∗∗
| (0.766) | (0.343) | (0.000)
Log of ZEst. price, $\beta(\ln P_{h,m})$ | 22.17∗∗∗ | 4.274 | 8.461
| (0.000) | (0.312) | (0.517)
$\beta(\ln^{2}P_{h,m})$ | -0.670∗∗ | -0.113 | -0.309
| (0.005) | (0.499) | (0.563)
Percent price uncertainty, $\beta(U_{h,m})$ [For Sale] | 0.326∗∗∗ | 0.0398 | -0.0591
| (0.000) | (0.498) | (0.673)
Percent price uncertainty, $\beta(U_{h,m})$ [Rent] | -0.183∗ | 0.0520 | 0.465∗
| (0.014) | (0.729) | (0.029)
$\beta(U_{h,m}^{2})$ [For Sale] | -0.00850∗∗∗ | -0.00176 | 0.00298
| (0.000) | (0.210) | (0.383)
$\beta(U_{h,m}^{2})$ [Rent] | 0.00572∗∗ | -0.000364 | -0.0118∗
| (0.003) | (0.921) | (0.034)
Market activity (neighboring houses), $\beta(A_{h,m})$ [For Sale] | -0.0534∗ | -0.129∗∗∗ | -0.0451
| (0.011) | (0.000) | (0.303)
Market activity (neighboring houses), $\beta(A_{h,m})$ [Rent] | -0.0475 | 0.118 | -0.0366
| (0.218) | (0.471) | (0.384)
$\beta(A_{h,m}^{2})$ [For Sale] | 0.000389 | 0.00167∗∗ | -0.000515
| (0.382) | (0.004) | (0.566)
$\beta(A_{h,m}^{2})$ [Rent] | 0.00367∗∗ | -0.00807 | 0.000797
| (0.009) | (0.344) | (0.407)
Before/After 2020 indicator, $\gamma(T_{m})$ | 0.882∗ | -0.927 | -8.668∗∗∗
| (0.032) | (0.085) | (0.000)
Property type indicator, $\gamma(I_{h,\text{ForSale}})$ | -2.903∗∗ | 2.973∗ | 4.794∗
| (0.001) | (0.028) | (0.022)
Treatment effect, $\delta_{TE,\Delta P}(I_{h,\text{ForSale}}\times T_{m})$ | 1.213∗∗∗ | 0.853∗∗ | 1.126∗∗
| (0.000) | (0.004) | (0.004)
Constant | -178.2∗∗∗ | -36.77 | -32.13
| (0.000) | (0.170) | (0.690)
Fixed effect for price decile, $Q_{c(P_{h,m})}$ | Y | Y | Y
Fixed effect for calendar month, $C_{m}$ | Y | Y | Y
$N$ | 25466 | 15495 | 3674
adj. $R^{2}$ | 0.060 | 0.018 | 0.059
p-values in parentheses
∗ $p<0.05$, ∗∗ $p<0.01$, ∗∗∗ $p<0.001$

Table S2:  Two-period Difference-in-Difference model with dependent variable
$U_{h,m}$. Ordinary Least Squares (OLS) model implemented separately for the
three regions with sufficient rental data, which serve as comparative DiD
group corresponding to the $I_{h,\text{ForSale}}$ baseline: if $h$ is listed
for sale, then $I_{h,\text{ForSale}}=0$ and $=1$ otherwise. Coefficients
estimated with property type interaction are indicated by [For Sale] and
[Rent]. The coefficient $\delta_{TE,U}$ corresponds to the COVID-19 treatment
effect on the percent price uncertainty, $U_{h,m}$, and visualized together in
Fig. 3(D). Note that $T_{m}$ is the time period variable, taking the value 1
if the listing occurred after 2020, and 0 if before 2020. Parameter estimate
$p$-values are shown in parenthesis below each point estimate. OLS regression
implemented in STATA 13 using “reg” calculated with robust standard errors.
Factor variables included but not reported in the table below: Zest. price
decile $D_{h,m}$, which ranges from 1 to 10; Dummy variable for calendar
month, $C_{m}$, which ranges from 3 (March) to 10 (October) capturing intra-
annual housing market cycle. See Fig. S7 for the cross-correlation matrix
across the principal model covariates.

|  |  $Y=$ % Price Uncertainty, $U_{h,m}$ |
---|---|---|---
| San Jose | Fresno | Merced
Ave. US 30-yr. fixed mortgage rate, $\beta(M_{m})$ | 1.736∗∗∗ | -1.360∗∗∗ | -3.201∗∗∗
| (0.000) | (0.000) | (0.000)
Log of ZEst. price, $\beta(\ln P_{h,m})$ | -26.95∗∗∗ | 3.414 | -33.97∗∗
| (0.000) | (0.326) | (0.004)
$\beta(\ln^{2}P_{h,m})$ | 0.961∗∗∗ | -0.109 | 1.500∗∗
| (0.000) | (0.419) | (0.003)
Percent price change, $\Delta P_{h,m}$ [For Sale] | -0.0166∗∗ | -0.0373∗∗∗ | 0.0306
| (0.009) | (0.001) | (0.090)
Percent price change, $\Delta P_{h,m}$ [Rent] | 0.0390∗∗ | 0.130 | -0.0736
| (0.005) | (0.148) | (0.411)
$\beta(\Delta^{2}P_{h,m})$ [For Sale] | 0.00212∗∗∗ | 0.00108∗ | 0.00165
| (0.000) | (0.024) | (0.060)
$\beta(\Delta^{2}P_{h,m})$ [Rent] | 0.00895∗∗∗ | 0.0186∗∗∗ | 0.0171∗∗
| (0.000) | (0.001) | (0.009)
Market activity (neighboring houses), $\beta(A_{h,m})$ [For Sale] | -0.0284∗ | -0.155∗∗∗ | -0.244∗∗∗
| (0.013) | (0.000) | (0.000)
Market activity (neighboring houses), $\beta(A_{h,m})$ [Rent] | 0.0926∗ | -0.328 | 0.123
| (0.023) | (0.213) | (0.244)
$\beta(A_{h,m}^{2})$ [For Sale] | 0.000271 | 0.00621∗∗∗ | 0.00769∗∗∗
| (0.263) | (0.000) | (0.000)
$\beta(A_{h,m}^{2})$ [Rent] | -0.00171 | 0.0133 | -0.00219
| (0.270) | (0.367) | (0.427)
Before/After 2020 indicator, $\gamma(T_{m})$ | 4.592∗∗∗ | 1.469∗ | 2.236
| (0.000) | (0.034) | (0.139)
Property type indicator, $\gamma(I_{h,\text{ForSale}})$ | 1.276∗∗∗ | -0.399 | 4.822∗∗∗
| (0.000) | (0.708) | (0.000)
Treatment effect, $\delta_{TE,\Delta P}(I_{h,\text{ForSale}}\times T_{m})$ | -3.067∗∗∗ | -3.588∗∗∗ | -8.882∗∗∗
| (0.000) | (0.000) | (0.000)
Constant | 191.8∗∗∗ | -5.040 | 215.0∗∗
| (0.000) | (0.823) | (0.002)
Fixed effect for price decile, $Q_{c(P_{h,m})}$ | Y | Y | Y
Fixed effect for calendar month, $C_{m}$ | Y | Y | Y
$N$ | 25466 | 15495 | 3674
adj. $R^{2}$ | 0.075 | 0.081 | 0.139
p-values in parentheses
∗ $p<0.05$, ∗∗ $p<0.01$, ∗∗∗ $p<0.001$

Table S3:  Aggregate model of properties listed ‘For Sale’ with city fixed
effects. Parameter estimates for the model yielding marginal effects plotted
in Fig. 4. $S_{h}$ is binary indicator variable coding the market size of each
city (big or small). Ordinary Least Squares (OLS) model implemented in STATA
13 using “areg” with city-level fixed effects, and calculated with robust
standard errors. Parameter estimate $p$-values are shown in parenthesis below
each point estimate.

|  $\Delta P_{h,m}$ (%) |  $U_{h,m}$ (%)
---|---|---
Ave. US 30-yr. fixed mortgage rate, $\beta(M_{m})$ | -0.693∗∗∗ | -0.374∗
| (0.000) | (0.012)
Log of ZEst. price, $\beta(\ln P_{h,m})$ | -10.49∗∗∗ | -1.343
| (0.000) | (0.254)
$\beta(\ln^{2}P_{h,m})$ | 0.462∗∗∗ | 0.0422
| (0.000) | (0.360)
Percent price uncertainty, $\beta(U_{h,m})$ | 0.114∗∗ |
| (0.002) |
$\beta(U_{h,m}^{2})$ | -0.00316∗∗∗ |
| (0.001) |
Percent price change, $\beta(\Delta P_{h,m})$ |  | -0.0231∗∗∗
|  | (0.000)
$\beta(\Delta^{2}P_{h,m})$ |  | 0.00152∗∗∗
|  | (0.000)
Market activity (neighboring houses), $\beta(A_{h,m})$ | -0.102∗∗∗ | -0.0180
| (0.000) | (0.273)
$\beta(A_{h,m}^{2})$ | 0.000990∗∗∗ | 0.00376∗∗∗
| (0.000) | (0.000)
Before/After 2020 indicator, $\gamma(T_{m})$ | 0.425 | 0.787∗
| (0.295) | (0.021)
$\beta(T_{m}\times A_{h,m})$ | -0.0122 | -0.145∗∗∗
| (0.430) | (0.000)
$\beta(S_{h}\times A_{h,m})$ | 0.0131 | -0.0931∗∗∗
| (0.213) | (0.000)
$\beta(S_{h}\times T_{m})$ | 0.164 | -1.043∗∗∗
| (0.598) | (0.000)
$\beta(S_{h}\times A_{h,m}\times T_{m})$ | -0.00286 | 0.0787∗∗∗
| (0.875) | (0.000)
Constant | 61.14∗∗∗ | 26.37∗∗∗
| (0.000) | (0.001)
Fixed effect for price decile, $Q_{c(P_{h,m})}$ | Y | Y
Fixed effect for calendar month, $C_{m}$ | Y | Y
$N$ | 46392 | 46392
adj. $R^{2}$ | 0.038 | 0.054
p-values in parentheses
∗ $p<0.05$, ∗∗ $p<0.01$, ∗∗∗ $p<0.001$