# Superstar Returns? Spatial Heterogeneity in Returns to Housing

Francisco Amaral, Martin Dohmen, Sebastian Kohl, Moritz Schularick

► To cite this version:

Francisco Amaral, Martin Dohmen, Sebastian Kohl, Moritz Schularick. Superstar Returns? Spatial Heterogeneity in Returns to Housing. Journal of Finance, 2025, The Journal of Finance, 80 (5), pp.3057-3094. 10.1111/jofi.13479. hal-05448313

HAL Id: hal-05448313

https://sciencespo.hal.science/hal-05448313v1

Submitted on 8 Jan 2026

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons CC BY 4.0 - Attribution - International License
<figure><img src="image_2.png" /></figure>

# Superstar Returns? Spatial Heterogeneity in Returns to Housing

FRANCISCO AMARAL, MARTIN DOHMEN, SEBASTIAN KOHL, and MORITZ SCHULARICK*

## ABSTRACT

This paper makes the first comprehensive attempt to study within-country heterogeneity of housing returns. We introduce a new city-level data set covering 15 OECD countries over 150 years and show that national housing markets are characterized by systematic spatial variation in housing returns. Total returns in large agglomerations are close to 100 basis points lower per year than in other parts of the same country. Excess returns outside the large cities can be rationalized as compensation for higher risk, especially higher covariance with income growth and lower liquidity. Real estate in diversified large agglomerations is comparatively safe.

HOUSING IS THE MOST IMPORTANT asset in household portfolios, as it is the main collateral used for bank lending, and plays a central role in current

*Francisco Amaral is with University of Zurich and Swiss Finance Institute. Martin Dohmen is with Macro Finance Lab, University of Bonn. Sebastian Kohl is with MPIfG Cologne, and FU Berlin, JFK Institute. Moritz Schularick is with Kiel Institute for the World Economy and Sciences Po Paris. This work is part of a larger project supported by the European Research Council Grant (ERC-2017-COG 772332). We are indebted to a large number of researchers who helped with the data on individual cities, especially Jacques Friggit, Matthijs Korevaar, Avner Offer, and Chihiro Shimizu. We are grateful to Andrea Balestracci, Melina Cosentino, Gregor Jost, Dimitrios Kanelis, Gerwin Kiessling, Liudmila Kiseleva, Carla Revilla, Markus Schick, and Masashi Tanigaki for their excellent research assistance. For helpful feedback, we thank Gabriel Ahlfeldt, Benjamin Born, Esther Eiling, Marco Giacoletti, Arpit Gupta, Christian Hilber, Nir Jaimovich, Christine Laudenbach, Lara Loewenstein, Ronan Lyons, Jonathan Moreno Medina, Stijn Van Nieuwerburgh, Marco Pagano, Monika Piazzesi, Joseph E. Stiglitz, Daniel Sturm, and Sofie Waltl. We wish to acknowledge support from the Deutsche Forschungsgemeinschaft (DFG) under Germany's Excellence Strategy - EXC 2126/1 - 390838866. We also thank conference participants at the "Housing in the 21st Century" Conference and the 15th North American Meeting of the Urban Economics Association and workshop participants of the "Advances in Research on Housing Markets" workshop and of the "Financial History Workshop 2021" in Antwerp, as well as seminar participants at the Harvard Joint Center for Housing Studies, the LSE Urban and Regional Economics Seminar, and the Bonn Finance and Insurance ECONtribute Seminar, for valuable comments. Francisco Amaral, Martin Dohmen, Sebastian Kohl, and Moritz Schularick have no conflicts of interest to disclose for this paper. All remaining errors are our own.

Correspondence: Moritz Schularick, Kiel Institute for the World Economy and Sciences Po Paris; e-mail: moritz.schularick@sciencespo.fr

This is an open access article under the terms of the [Creative Commons Attribution License](https://creativecommons.org/licenses/by/4.0/), which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

DOI: 10.1111/jofi.13479

© 2025 The Author(s). *The Journal of Finance* published by Wiley Periodicals LLC on behalf of American Finance Association.
macroeconomic models of aggregate fluctuations Kaplan, Moll, and Violante (2018); Berger et al. (2018). Housing is not easily diversifiable, however, meaning that households are typically highly exposed to fluctuations in the value of their houses Piazzesi and Schneider (2016). In this paper, we show that there are significant differences in returns within the residential real estate asset class, and these differences are driven by the location of the asset. Using newly compiled long-run data for 15 economies, we show that there are systematic differences in risk profiles and asset returns between housing in metropolitan areas and other parts of the same country.

The “housing market” is a collection of markets that differ along many attributes Glaeser et al. (2014); Piazzesi, Schneider, and Stroebel (2020). Households typically do not hold geographically diversified housing portfolios, but rather individual properties in specific locations Levy (2021). The local nature of housing markets suggests that studying their geographic heterogeneity is key to better understanding their impact on macroeconomic fluctuations Piazzesi and Schneider (2016). To date, however, we know very little about the spatial distribution of housing market risk and return.

Due to the lack of high-quality data sets, research on housing markets has developed slowly Piazzesi (2018). We therefore constructed a comprehensive city-level data set covering cities in 15 Organization for Economic Co-operation and Development (OECD) countries and their hinterlands over the last 150 years. The data set is the result of a multiyear effort, during which we systematically assembled, cleaned, and harmonized historical data across countries and time periods. In constructing the data set, we were able to draw to some extent on existing historical research. In most cases, however, we had to manually collect house price and rent data from yearbooks or primary sources such as newspapers, tax records, and notary archives. We complement these data with three granular data sets covering returns for the cross-section of cities in the United States and Germany. For the United States, we update the data covering the entire cross-section of Metropolitan Standard Areas (MSAs) constructed by Gyourko, Mayer, and Sinai (2013) with more recent data from the American Community Survey (ACS). We also merge new housing price series covering 30 U.S. cities over the last 120 years provided by Agorastos et al. (2024) with rental return data from Demers and Eisfeldt (2022) to construct long-run city-level housing return series. For Germany, we hand-collected a data set of housing returns covering 127 small and large German cities.

These new data sets allow us to establish a new and robust stylized fact: In the long run, there are systematic differences in total returns on residential real estate between metropolitan areas and other parts of the same country. In particular, large metropolitan areas have experienced lower total returns on housing than other parts of the same country. An investment in large cities is associated with a negative return premium of about 100 basis points (bps) per year. These return differences are a robust feature of the data across countries and time periods and are highly statistically significant. An annual negative return premium of about 1 percentage point accumulates to substantial return differentials over the long run.
While in many cases house prices in large cities have grown faster than in the rest of the country Gyourko, Mayer, and Sinai (2013), rental returns have typically been consistently lower, so that taking rental returns into account reverses the spatial distribution of house returns. The negative spatial correlation between capital gains and rental returns has also been recently documented by Demers and Eisfeldt (2022), but we can show for the first time that differences in rental returns are larger and more persistent than differences in capital gains, leading to higher long-run returns.<fnref n="1" /> This key finding is consistent with recent studies showing that more expensive neighborhoods within a city have seen lower total returns than cheaper neighborhoods over the past decade Demers and Eisfeldt (2022); Morawakage et al. (2022).

In the second part of the paper, we show that the spatial distribution of returns is consistent with the spatial distribution of risk and liquidity in housing markets. In particular, we show that the covariance of income growth with returns, idiosyncratic price risk, and liquidity risk are positively correlated with returns across space. Our core finding of lower returns in large agglomerations can thus be rationalized in a parsimonious rational-expectations equilibrium of the housing market: Higher returns outside cities are compensation for higher risk. Suppose that everything that makes large cities special—their diversified economies, large markets, amenities, and international linkages—also makes them safer places to invest. The present value of future housing services is subject to less risk, so buyers are willing to pay a higher price and accept a lower return on housing investments. For remote locations to attract capital, they must offer higher returns.

Our analysis in the second part of the paper supports this risk-based interpretation of the (negative) premium on large-city real estate. On the one hand, the covariance between housing returns and income growth is lower in large cities. Between 1950 and 2018, the covariance between U.S. MSA-level income growth and MSA-level housing returns was significantly larger in smaller MSAs. On the other hand, households typically do not hold diversified housing portfolios and therefore are also exposed to idiosyncratic risk. We show that idiosyncratic housing risk is considerably higher outside the large cities. Using U.S. transaction-level data from Corelogic, we find that the idiosyncratic component of housing risk decreases with MSA size. Because liquidity is low, homeowners in thinner markets face a greater risk of not realizing the local market return at the time of sale. Data from real estate search engines confirm a significant increase in housing market liquidity with city size. Recent work by Giacoletti (2021) and Sagi (2021) also suggests a strong relationship between idiosyncratic risk and housing market liquidity. In contrast to idiosyncratic volatility, systematic or index price volatility is relatively low and largely uniform across MSAs. As such, our findings are consistent

<footnote n="1">¹ As Demers and Eisfeldt (2022) point out, this result overturns the conventional wisdom that real estate in coastal areas of the United States is a better investment than in fly-over cities.</footnote>
with the existing literature Demers and Eisfeldt (2022), which has focused exclusively on the latter component of housing price volatility and, therefore has not identified substantial differences across MSAs.

We perform several robustness checks of our main results. Importantly, we show that all of our results continue to hold when we extend the city-level returns from Demers and Eisfeldt (2022) back to the beginning of the 20th century using the long-run hedonic price and rent series from Agorastos et al. (2024).

We also use different rental yield benchmarks, examine subperiods and the effects of rent regulation, and vary the definition of metropolitan areas. First, since our main result is driven by differences in rental yields, we rebuild our main data set using independent, country-specific, contemporary rental yield benchmarks. The overall results are very similar. Due to data constraints, our historical series do not explicitly account for the segmentation between owner-occupied and rental housing. However, our results hold in both high- and low-homeownership cities, where the issue of market segmentation should be less pronounced or even nonexistent. Moreover, recent research using high-quality granular data shows that the prices of renter- and owner-occupied housing comove strongly over time Begley and Willen (2021).

Second, although we are interested in long-run returns, we want to ensure that they are not driven by specific time periods. We separate the early historical parts of the sample, and also split the sample period in 1990. The same patterns are found in the historical period as well as in the last three decades. Third, we divide our data set into different rent regulation and tax regimes. It turns out that our results are not driven by periods with strict rent controls or with different taxation of capital gains or rents. Finally, we explore different definitions of cities and experiment with different size cutoffs in different periods. Once more, none of these changes alter the new stylized fact that this paper uncovers: lower long-run returns in large agglomerations.

*Previous literature.* Our work contributes to a number of distinct research fields. The paper builds on and extends research on asset returns in housing markets Lustig and Van Nieuwerburgh (2005); Piazzesi, Schneider, and Tuzel (2007); Piazzesi (2018). In addition, it adds a new disaggregated perspective to research on returns to national housing portfolios Jordà et al. (2019) and brings an international comparative perspective to papers on housing returns in individual regions Eichholtz et al. (2021); Demers and Eisfeldt (2022).

Our paper also speaks to the urban economics literature by bringing together housing price data with rental yields, housing returns, and measures of local housing market risk. While the existing literature has focused on the spatial distribution of economic activity Glaeser (2010) and its impact on house prices Saiz (2010); Gyourko, Mayer, and Sinai (2013); Hilber and Vermeulen (2016), we highlight another consequence of agglomeration: In addition to having higher productivity and wage levels Ahlfeldt and Pietrostefani (2019), less concentrated labor markets Desmet and Rossi-Hansberg (2013), higher elasticities of urban costs Combes, Duranton, and Gobillon (2019), and more
diversified industry compositions Duranton and Puga (2000), large cities also
have lower housing risk.

This paper is also part of, and contributes further to, a nascent literature
on the risk-return relationship in housing markets Case, Cotter, and Gabriel
(2011); Han (2013); Sagi (2021); Giacoletti (2021); Demers and Eisfeldt (2022),
and complements recent work by Hilber and Mense (2021) as it points to per-
sistent differences in price-rent ratios between cities.

We further contribute to the literature on the role of housing in portfolio
choice Cocco (2005); Chetty, Sándor, and Szeidl (2017); Gomes, Haliassos, and
Ramadorai (2021) by quantifying how households' exposure to housing risk
changes with the location of their residential property. Finally, we speak to
the rapidly growing literature on the drivers of return heterogeneity across
the wealth distribution Gabaix et al. (2016); Benhabib and Bisin (2018);
Bach, Calvet, and Sodini (2020); Kuhn, Schularick, and Steins (2020) by
showing that expensive, high-income locations provide lower total returns on
housing.

The paper is organized as follows. Section I describes our new long-run
data set and provides an overview of the series that we construct (see also
the detailed documentation in the Data Appendix<fnref n="2" />). In Section II, we describe
the novel stylized facts emerging from our data set and compare city-level
and national-level housing returns. We establish our key finding that total
returns are lower in large cities. Section III introduces three granular data
sets for the United States and Germany and studies housing returns over the
entire city-size distribution in both countries. In Section IV, we turn to the
differences in housing risk as an explanation for the return differences. We
show that housing risk is lower in large cities, due to covariance risk between
excess returns and local income as well as smaller idiosyncratic shocks in
more liquid markets. Finally, Section V concludes.

# I. Spatial Heterogeneity in Housing Returns: A New Long-Run Data Set

This section introduces our new historical city-level data set. The data
cover 27 cities over the long run: London, New York, Paris, Berlin, Tokyo,
Hamburg, Naples, Barcelona, Madrid, Amsterdam, Milan, Melbourne, Sydney,
Copenhagen, Rome, Cologne, Frankfurt, Turin, Stockholm, Oslo, Toronto,
Zurich, Gothenburg, Basel, Bern, Helsinki, and Vancouver. The city-level data
set contains house prices and rents as well as rental yields for every city.
Below, we briefly discuss the criteria we employed for the choice of cities and
the methods used to construct these series. Details on the sources for each city,
as well as a comprehensive list of all the new data series in this paper, can be
found in the Data Appendix.

<footnote n="2">² The Data Appendix and the Internet Appendix may be found in the online version of the article on The Journal of Finance website.</footnote>
## A. City Sample

We focused our data collection on the largest cities in 15 developed countries. For each country, we define the largest cities in terms of population in 1900 and include cities with a population share of more than 1% in 1900. Wherever possible, we also aim to cover at least 10% of the country's population in 1900 in order to analyze a relevant share of the country's housing markets. Selecting cities based on the population in 1900, rather than the current population, circumvents the problem of survivorship bias. A detailed discussion of the selection of cities by country is provided in the Internet Appendix. Urban systems evolve over time, as do city boundaries. Over time, all cities and local housing markets grow, through either the incorporation of more suburbs or the creation of metropolitan regions. We follow the administrative definitions in our sources, which makes our definitions of cities consistent across countries. The city definitions are mostly identical for the rental and ownership markets.

Table I summarizes the sample. The coverage of price and rent data is reported in columns (5) and (6). The sample starts in 1870, but there are some gaps. We have seven decades of data for all cities and a balanced panel for the period after 1950. Column (3) shows the share of cities in the national population in 1900, and column (4) shows the aggregate share of the national population in 1900 covered by our sample cities.

## B. Sources and Methodology

This section briefly describes the data sources and construction of the total return series. For all cities in our sample, we construct annual house price indices and rent indices, and we then compute total housing return series.

### B.1. House Price and Rent Indices

Whenever possible and of sufficient quality, we use house price and rent indices from existing research. An example is the return series for Amsterdam described in Eichholtz et al. (2021). In most cases, however, house price and rent indices are not readily available or of insufficient quality. To construct these series, we first used data from a wide range of secondary sources such as city yearbooks, but in many cases, we had to collect data by hand from various primary sources, including newspapers, tax records, notaries, real estate agent archives, and various other archival data. About half of the series are newly constructed.

The criteria for selecting appropriate sources depended primarily on the representativeness and availability of the data. When we had multiple sources to choose from, we used the source that provided the best coverage and the most detail. In the case of London, for example, we could rely in-part on data from previous research, but we had to fill a large gap after World War II. The existing house price series cover the years before 1946 and after 1969. To link the series, we hand-collected asking prices from newpaper's real estate
<table><caption>Table I
City Choice and Data Coverage</caption><thead><tr><th>City<br>(1)</th><th>Pop1900<br>(2)</th><th>Share pop<br>(3)</th><th>Country<br>(4)</th><th>House Prices<br>(5)</th><th>Rents<br>(6)</th></tr></thead><tbody><tr><td>London</td><td>6,480</td><td>0.157</td><td>0.157</td><td>1895-2018</td><td>1870-2018</td></tr><tr><td>New York</td><td>4,242</td><td>0.056</td><td>0.056</td><td>1920-2018</td><td>1914-2018</td></tr><tr><td>Paris</td><td>3,330</td><td>0.082</td><td>0.082</td><td>1870-2018</td><td>1870-2018</td></tr><tr><td>Berlin</td><td>2,707</td><td>0.048</td><td>0.078</td><td>1870-2018</td><td>1870-2018</td></tr><tr><td>Tokyo</td><td>1,497</td><td>0.034</td><td>0.034</td><td>1950-2018</td><td>1950-2018</td></tr><tr><td>Hamburg</td><td>895</td><td>0.016</td><td>0.078</td><td>1870-2018</td><td>1870-2018</td></tr><tr><td>Naples</td><td>563</td><td>0.017</td><td>0.054</td><td>1950-2018</td><td>1950-2018</td></tr><tr><td>Barcelona</td><td>552</td><td>0.030</td><td>0.059</td><td>1950-2018</td><td>1947-2018</td></tr><tr><td>Madrid</td><td>539</td><td>0.029</td><td>0.059</td><td>1950-2018</td><td>1947-2018</td></tr><tr><td>Amsterdam</td><td>510</td><td>0.099</td><td>0.099</td><td>1870-2018</td><td>1870-2018</td></tr><tr><td>Milan</td><td>491</td><td>0.015</td><td>0.054</td><td>1950-2018</td><td>1950-2018</td></tr><tr><td>Melbourne</td><td>485</td><td>0.130</td><td>0.257</td><td>1880-2018</td><td>1901-2018</td></tr><tr><td>Sydney</td><td>478</td><td>0.128</td><td>0.257</td><td>1880-2018</td><td>1901-2018</td></tr><tr><td>Copenhagen</td><td>462</td><td>0.180</td><td>0.180</td><td>1938-2018</td><td>1885-2018</td></tr><tr><td>Rome</td><td>438</td><td>0.013</td><td>0.054</td><td>1950-2018</td><td>1950-2018</td></tr><tr><td>Cologne</td><td>437</td><td>0.008</td><td>0.078</td><td>1902-2018</td><td>1890-2018</td></tr><tr><td>Frankfurt</td><td>350</td><td>0.006</td><td>0.078</td><td>1897-2018</td><td>1895-2018</td></tr><tr><td>Turin</td><td>330</td><td>0.010</td><td>0.054</td><td>1950-2018</td><td>1950-2018</td></tr><tr><td>Stockholm</td><td>300</td><td>0.059</td><td>0.084</td><td>1875-2018</td><td>1894-2018</td></tr><tr><td>Oslo</td><td>227</td><td>0.102</td><td>0.102</td><td>1870-2018</td><td>1892-2018</td></tr><tr><td>Toronto</td><td>205</td><td>0.038</td><td>0.050</td><td>1900-2018</td><td>1921-2018</td></tr><tr><td>Zurich</td><td>150</td><td>0.045</td><td>0.098</td><td>1905-2018</td><td>1890-2018</td></tr><tr><td>Gothenburg</td><td>130</td><td>0.025</td><td>0.084</td><td>1875-2018</td><td>1914-2018</td></tr><tr><td>Basel</td><td>109</td><td>0.033</td><td>0.098</td><td>1912-2018</td><td>1889-2018</td></tr><tr><td>Helsinki</td><td>97</td><td>0.037</td><td>0.037</td><td>1946-2018</td><td>1946-2018</td></tr><tr><td>Vancouver</td><td>69</td><td>0.013</td><td>0.050</td><td>1950-2018</td><td>1950-2018</td></tr><tr><td>Bern</td><td>64</td><td>0.019</td><td>0.098</td><td>1912-2018</td><td>1890-2018</td></tr></tbody></table>

Cities are ordered by population level in 1900. Column (2) shows city-level population in 1900 per 1,000 inhabitants. Column (3) describes the share of each city's population of total country population in 1900. Column (4) reports the cumulative share from all cities in a respective country in our data set. Columns (5) and (6) describe data coverage from earliest to latest year of price and rent indices. For some cities there are gaps in data coverage because of missing data, for example, during periods of war and hyperinflation. City-level population data come from Reba, Reitsma, and Seto (2016) and country-level population data from Jordà, Schularick, and Taylor (2017). For Cologne and Frankfurt, city-level population was below 1% of country population in 1900. However, in 1900, the German Empire had a considerably different area compared to Germany today. In 1950, the population of both Frankfurt and Cologne was above 1% of Germany's total population. The estimate for Vancouver is taken as the sum of Burrard and Vancouver city from the Canadian population census from 1901. Burrard officially became part of Vancouver in 1904.

classified sections. We focused on sales ads that provided enough information to construct quality-adjusted indices.

Whenever microdata were available, we relied on repeat sales or hedonic regression methods. For example, for Frankfurt, we constructed a hedonic house price index from 1960 to 2018 using transaction-level data from public sources and their archives. When micro-level data were not available, we used data
disaggregated by housing type and location within a city to construct stratification indices.

In constructing rent indices, we relied primarily on rent indices from statistical agencies. Examples are rent indices constructed by city statistical offices for (city-level) Consumer Price Index (CPI) data. These mainly use the repeated rent method. In other cases, where we were able to collect micro-level data, we relied on hedonic methods. For example, for the city of Oslo, we constructed a hedonic rent index for the period between 1950 and 1970 from newspaper rental advertisements. In other cases, we constructed stratification indices whenever possible, relying mainly on statistical publications. For example, in the case of Stockholm, we used average rent by dwelling size to construct a chained stratification rent index. We benchmark our rent indices to rents recorded in housing censuses. Historically, such censuses have been conducted approximately every 10 years and typically cover all rental units, providing an accurate picture of the general level of rents in a city.

We deflate all price and rent indices are deflated using country-level CPI data from Jordà, Schularick, and Taylor (2017), with a general national CPI that includes housing costs. Normalization allows us to compute real log returns at the city and country level, following the convention in the literature (e.g., Giacoletti, 2021). We also report undeflated results, which not only preserves, but also enhances, within-country differences, since the largest and increasing component of the deflator is housing costs.<fnref n="3" /> Ultimately, there is no harmonized CPI excluding housing costs at the national level, let alone at the local level, that we could use. An alternative would be to use city-level CPIs, but these are available only for a subsample of our cities. The differences between these city-level CPIs and between the city-level and national CPIs are negligible, with almost perfect co-movement and correlation (see Internet Appendix II). Deflating by the total national CPI is thus a reasonable but conservative choice, and the only available option for the full sample.<fnref n="4" />

The resulting series cover a representative city-level housing portfolio that approximates the behavior of the value-weighted housing market within a city.<fnref n="5" />

## B.2. Housing Return Series

We use house price and rent indices to construct housing return series. As is well known, a house generates two types of returns. First, the price of a house can change, generating a capital gain (or loss). Second, a house provides a consumption stream in the form of housing services. The consumption stream can be sold to generate a cash flow by renting out the house. Alternatively, they

<footnote n="3">³ The technical definition of this component, in particular, owner-occupied costs and weighting, has been the subject of much debate within countries Gordon and van Goethem (2007).</footnote>

<footnote n="4">⁴ See the Data Appendix for details on data sources and index construction by city.</footnote>

<footnote n="5">⁵ In Internet Appendix, we compare hedonic house price indices for different market segments for large German cities. We show that over a 30-year period, the trends for all housing market segments were similar.</footnote>
can be consumed, in which case the owner receives the replication value as a cash flow. Total returns on housing can be computed as

$$Total\ return_{t} = \frac{P_{t} - P_{t-1}}{\underbrace{P_{t-1}}_{\text{Capitalgain}}} + \frac{R_{t}(1-c)}{\underbrace{P_{t-1}}_{\text{Netrentreturn}}}, \quad (1)$$

where $P_t$ is the house price at time t, $R_t$ is the gross rent payment at time t, and c are the total net operating costs as a share of $R_t$, which we describe in more detail below.<fnref n="6" /> Following this equation, the construction of city-wide (real) capital gains is straightforward using our house price indices. To construct rental return series, we estimated rent-price ratios, which we adjust for nominal house price growth as follows: Rent return = $\frac{R_t}{P_t} * \frac{HPI_{t}^{nom}}{HPI_{t-1}^{nom}}$.

Rent-price ratio estimates are constructed following the rent-price approach used in Jordà et al. (2019) and Brounen et al. (2013). To do so, we first use benchmark rent-price ratios for the end of our sample period in 2018. We again follow Jordà et al. (2019) and use benchmarks calculated from realized net operating income yields of real estate investors. These benchmarks were provided by MSCI, which collects data from a variety of real estate investors for large cities around the world.

Yields are defined net of total operating costs, which consist of maintenance and property taxes as well as other costs. Other costs included are management costs as well as the cost of vacancies, letting and rent review fees, ground rents, and bad debt write-offs. Finally, we use our rent and price indices to calculate rent-price ratios over time:

$$\frac{RI_{t+1}}{HPI_{t+1}} = \left( \frac{RI_{t+1}/RI_t}{HPI_{t+1}/HPI_t} \right) \frac{RI_t}{HPI_t}. \quad (2)$$

The disadvantage of this methodology is that possible measurement errors accumulate over time due to extrapolation. There are three main sources of potential measurement error. First, the price and rent series that we use to extrapolate the 2018 benchmark correspond to two different market segments: renter-occupied and owner-occupied housing. If these two market segments have different price trends in the same city over time, then our rental return series will be biased Glaeser and Gyourko (2010). However, recent evidence based on micro-level United States data shows that house prices in both segments exhibit very similar trends over time Begley and Willen (2021). In addition, using transaction-level data for large German cities, we show that price trends in the owner-occupied and rental markets are very strongly

<footnote n="6">⁶ Throughout the paper, we follow existing literature and measure housing returns in log points instead of percentage points. The main reason is that log returns are time-compoundable, whereas percentage returns are not. Moreover, log returns have preferable distributional features and are approximately equal to percentage returns for small numbers. For a full rationalization, please refer to the Data Appendix.</footnote>
correlated over the long run.<fnref n="7" /> Second, our rental yield benchmarks for 2018 may be off, automatically distorting the level of our rental return series. To account for this, we collect alternative estimates from independent sources. We do so not only for 2018, but also for historical periods. We obtain the independent estimates from the literature or real estate websites (e.g., Numbeo), or we construct our own estimates using transaction or listing microdata on the price and rental income of the same properties. Table II provides a summary of the sources we use for rental yield estimates, with more details in the Data Appendix. When the rent-price approach estimates deviate from these historical sources, we adjust the estimates to the historical measures, as detailed in the Data Appendix. Third, the ratio of net to gross rental income may change over time, biasing our estimates. However, the evidence in section III.C of Jordà et al. (2019) and figure 3 of Demers and Eisfeldt (2022) shows that the ratio of net to gross income has remained relatively constant over time, with very little variation across regions over the past 30 years. In addition, we find no systematic differences in the ratio of net to gross income across 22 U.S. cities for both 2007 and 2020 using MSCI data.<fnref n="8" />

## II. Returns in Large Cities

In this section, we first establish the main stylized facts on long-run housing returns in large cities. We then analyze trends in capital gains and rental returns, as well as their contributions to total returns, and compare large cities to the rest of the country.

We begin with summary statistics on log real housing returns and its components for our new data set. Panel A of Figure 1 shows average log housing returns for the full time period and Panel B for the post-1950 period.<fnref n="9" /> Total city-level housing returns were in the range of 4 to 6 log points per year, with some variation across the cities in our sample. Toronto, Amsterdam, Gothenburg, Tokyo, and Sydney observe the highest long-term returns. Panel B shows that housing returns were higher in the post-1950 period, reaching about 6 log points.

Figure 2 plots the distribution of annual log real housing returns for the pre- and post-1950 periods. While housing returns were lower on average in the pre-1950 period, they had a higher standard deviation than in the post-1950 period, as evidenced by a thicker left tail in the pre-1950 period. This is not surprising given that this period included two world wars, the Great Depression, and large fluctuations in housing policy. After 1950, large-city returns were almost 2 percentage points higher with a lower standard deviation.

<footnote n="7">⁷ We construct hedonic price indices for rental and owner-occupied housing for the last 60 years for large German cities and show that the trends are very similar across market segments. The results can be found in Section I of the Internet Appendix</footnote>

<footnote n="8">⁸ The figure can be found in Section II of the Data Appendix.</footnote>

<footnote n="9">⁹ A table with summary statistics by city in log points, including standard deviations, can be found in the Data Appendix. We also include a table of average percentage point (simple) returns for comparison with other literature.</footnote>
<table><caption>Table II
Overview of the Rental Yield Benchmark Sources</caption><thead><tr><th>City</th><th>Main 2018<br>Benchmark</th><th>Alternative 2018<br>Benchmark</th><th>Historical<br>Benchmarks</th><th>Homeownership<br>Rate 2011 (in %)</th></tr></thead><tbody><tr><td>London</td><td>MSCI</td><td>Numbeo</td><td>MSCI</td><td>49.5</td></tr><tr><td>New York</td><td>MSCI</td><td>Demers and Eisfeldt<br>(2021)</td><td>Demers and Eisfeldt<br>(2021)</td><td>30.8</td></tr><tr><td>Paris</td><td>MSCI</td><td>Numbeo</td><td>Newspaper ads<sup>a</sup></td><td>33.1</td></tr><tr><td>Berlin</td><td>MSCI</td><td>Transaction registry<sup>a</sup></td><td>Transaction registry<sup>a</sup></td><td>14.8</td></tr><tr><td>Tokyo</td><td>MSCI</td><td>Numbeo</td><td>Newspaper ads<sup>a</sup></td><td>45.8</td></tr><tr><td>Hamburg</td><td>MSCI</td><td>Transaction registry<sup>*</sup></td><td>Transaction registry<sup>a</sup></td><td>23.3</td></tr><tr><td>Naples</td><td>MSCI</td><td>Numbeo</td><td>Not adjusted</td><td>55.5</td></tr><tr><td>Barcelona</td><td>MSCI</td><td>Numbeo</td><td>Newspaper ads<sup>a</sup></td><td>64.0</td></tr><tr><td>Madrid</td><td>MSCI</td><td>Numbeo</td><td>Newspaper ads<sup>a</sup></td><td>73.2</td></tr><tr><td>Amsterdam</td><td>MSCI</td><td>Numbeo</td><td>Eichholtz (2020),<br>newspaper ads<sup>a</sup></td><td>27.2</td></tr><tr><td>Milan</td><td>MSCI</td><td>Numbeo</td><td>Not adjusted</td><td>68.0</td></tr><tr><td>Melbourne</td><td>Corelogic</td><td>Numbeo</td><td>Newspaper ads<sup>a</sup></td><td>72.8</td></tr><tr><td>Sydney</td><td>Corelogic</td><td>Numbeo</td><td>Stapleton (2007)</td><td>65.2</td></tr><tr><td>Copenhagen</td><td>MSCI</td><td>Numbeo</td><td>Tax survey, Statistics<br>Denmark</td><td>50.6</td></tr><tr><td>Rome</td><td>MSCI</td><td>Numbeo</td><td>Not adjusted</td><td>70.6</td></tr><tr><td>Cologne</td><td>MSCI</td><td>Transaction registry<sup>a</sup></td><td>Transaction registry<sup>a</sup></td><td>26.0</td></tr><tr><td>Frankfurt</td><td>MSCI</td><td>Transaction registry<sup>a</sup></td><td>Transaction registry<sup>a</sup></td><td>19.2</td></tr><tr><td>Turin</td><td>MSCI</td><td>Numbeo</td><td>Not adjusted</td><td>65.7</td></tr><tr><td>Stockholm</td><td>MSCI</td><td>Real estate agency</td><td>Kalbro and Mattson<br>(1995)</td><td>62.2</td></tr><tr><td>Oslo</td><td>Numbeo</td><td>Real estate agency</td><td>Not adjusted</td><td>75.5</td></tr><tr><td>Toronto</td><td>MSCI</td><td>Numbeo</td><td>Census estimates<sup>a</sup></td><td>54.6</td></tr><tr><td>Zurich</td><td>MSCI</td><td>Real estate agency</td><td>Real estate agency</td><td>9.0</td></tr><tr><td>Gothenburg</td><td>MSCI</td><td>Real estate agency</td><td>Kalbro and Mattson<br>(1995)</td><td>55.7</td></tr><tr><td>Basel</td><td>MSCI</td><td>Real estate agency</td><td>Newspaper ads<sup>a</sup> real<br>estate agency</td><td>13.7</td></tr><tr><td>Helsinki</td><td>Numbeo</td><td>Real estate agency</td><td>Not adjusted</td><td>48.0</td></tr><tr><td>Vancouver</td><td>MSCI</td><td>Numbeo</td><td>Census estimates<sup>a</sup></td><td>48.5</td></tr><tr><td>Bern</td><td>MSCI</td><td>Real estate agency</td><td>Newspaper ads<sup>a</sup> real<br>estate agency</td><td>16.6</td></tr></tbody></table>

This table lists all of the main and alternative sources that we use to construct reliable rental yield benchmarks. The table additionally provides information on the homeownership rate in the respective city for 2011. More details about the sources and methods used to construct these series, and about all other series from various authors that we use, can be found in the Data Appendix.

ªOwn estimate using microdata from the above-mentioned source.

Rental returns account for about 67% of total housing returns over the past 150 years. Panel A of Figure 3 shows that while the relative share of rental returns has been quite volatile over time, it has remained the largest contributor to total housing returns. In fact, for all cities in our sample except Milan, rental returns account for more than 50% of total housing returns in the long run. This result is consistent with the findings in Jordà et al. (2019) and Demers and Eisfeldt (2022).
<figure><img src="image_3.png" /></figure>

**Figure 1. City-level real average total housing returns (log points).** Cities are ordered by population level in 1900. The figure shows average total real housing returns in log points for all cities in our main sample. The series have been deflated using the national CPI series from Jordà, Schularick, and Taylor (2017). Panel A covers the full sample of return data in our main data set, which is the subset of years for which rent and house price data (minus one year) exist; compare with Table I. Panel B shows average housing return data by city starting in 1950. (Color figure can be viewed at wileyonlinelibrary.com)

<figure><img src="image_4.png" /></figure>

**Figure 2. Distribution of annual real housing returns (log points)** The figure shows the distribution of annual total housing returns in log points for all cities in our main sample. The series have been deflated using the national CPI series from Jordà, Schularick, and Taylor (2017). Panel A covers the full sample of cities until 1950; compare with I. Panel B covers the full sample of cities after 1950. (Color figure can be viewed at wileyonlinelibrary.com)

A. *Large Agglomerations versus National Housing Markets*

In the next step, we merge our city-level data set with national housing returns from Jordà et al. (2019) to compare returns in large cities with those in the rest of the country. Jordà et al. (2019) compiled data on capital gains, rental returns, and total housing returns for nationally diversified housing portfolios that represent the weighted sum of housing markets within a given country. We extend their data to 2018 using country-level house price and rent
<figure><img src="image_5.png" /><figcaption>**Figure 3.** Share of total log returns, 1870–2018. Panel A: The displayed series are 10-year lagged moving averages; for example, the share of capital gains for 2010 is the average share of capital gains between 2000 and 2010. All cities receive an equal weight. This panel shows the share of log capital gains and log rental returns in the sum of both. In the few cases in which the moving average log capital gains are negative, we take the absolute value of the moving average log capital gains instead. Panel B: Average share of log real capital gains and log rental returns by city for the entire period for which we have data for the city. (Color figure can be viewed at wileyonlinelibrary.com)</figcaption></figure>

indices from national statistical offices and substitute house price series for Japan after 2008 and for Sweden after 1952, as series with better methodology and coverage became available. See the Data Appendix for details.

The national housing portfolios include the metropolitan areas in our sample. For the sake of transparency and comparability, we continue to compare the metropolitan returns to the national series from that study. However, we also calculate the returns of a “rest of the country” portfolio as the weighted average of the housing returns in the other locations in the country. National returns can be expressed as

$$National \ return_t = w_{t-1} * Large\ cityreturn_t + (1 - w_{t-1}) * RoCreturn_t, \quad (3)$$

where *w* is the relative weight of the large city in the respective national housing series.<fnref n="10" /> Using equation (3) and our large-city return series, we can approximate housing returns in the rest of the country (*RoC return*) by subtracting large cities in our data set from the national series. In the absence of market capitalization data, we use population shares as portfolio weights to construct return series for the rest of the country (excluding the large cities). All city-level and national population data for this calculation come from the United

<footnote n="10">¹⁰ To confirm our rest-of-the-country calculation, we use the MSA-level data set of Gyourko, Mayer, and Sinai (2013) to calculate the average combined total housing return for all American MSAs except New York. Notwithstanding the differences in data source and methodology, we obtain a very similar result as our estimate for the rest of the country, with the difference in the average annual log total return between 1950 and 2018 ranging from 0.4 to 0.6 percentage points, depending on the weighting scheme for the rest of the country.</footnote>
Nations (2018). Due to higher housing prices in the large cities, using a popula-
tion weight gives the large cities a smaller weight than a market cap-weighted
index. As such, the returns for the rest of the country that we remove from the
national series are likely to represent a lower bound.

In some cases, the geographical coverage of the national house price series in
the pre-war period is too narrow to allow for a meaningful comparison between
the major cities and the rest of the country. In the Data Appendix, we include
a table detailing the geographic coverage of the national house price series by
country. Thus, for the comparison between metropolitan returns and the rest of
the country, we focus on the 70-year period between 1950 and 2018, for which
the national house price series have sufficiently broad geographical coverage.
Nevertheless, the overall results are very similar when we look at returns over
the full sample period (see Section III.B of the Internet Appendix).

To guide the reader through the results, we start with Paris as an example.
Our data show that an investor who bought an apartment in Paris in 1950 re-
alized an average annual capital gain of 4.85 log points over the period to 2018.
The average annual rental return in Paris was 3.66 log points, resulting in a
healthy total annual return of 8.33 log points. This means, for example, that
investments in Paris residential real estate have significantly outperformed
investments in the French stock market, even on an unleveraged basis.

How does this return compare to the rest of France? An investment in the French national housing portfolio over the same 70-year period had an annual return of 4.48 log points, which is somewhat lower than Paris. Since Paris is a substantial part of the French national portfolio, the difference must be driven by other regions of France, where house prices rose about half a percentage point less per year than in Paris. However, the picture changes when we include rental yields, which were much higher in the rest of the country (5.06 versus 3.66), more than offsetting Paris' capital gains advantage. Total housing returns were 9.15% per annum in the rest of France, some 85 bps per annum higher than in Paris. Thus, despite higher capital gains, Paris underperformed the rest of France in terms of total housing returns.

In Figure 4, we expand the perspective to all 27 large cities in the sam-
ple and compare them to their national housing markets. Figure 4 shows the
differences in capital gains (left), rental returns (middle), and total housing
returns (right) between 1950 and 2018 for each city relative to national re-
turns.<fnref n="11" /> A general pattern is easy to discern. As in the French case, capital
gains are higher in almost all large cities. The only major exception is Tokyo—
a city that experienced a severe housing crisis in the early 1990s. Real house
prices in Tokyo in 2018 were still only a third of their 1990 level, while house
prices in other parts of the country are 65% of their 1990 level. Rental returns
are generally much lower in the major metropolitan areas, and total returns
are lower.<fnref n="12" />

<footnote n="11">¹¹ Internet Appendix Table IA.I presents the numbers with standard errors from paired *t*-tests.</footnote>

<footnote n="12">¹² The main exception is (West) Berlin. Since there are no data for East Berlin between 1945 and 1990, the Berlin portfolio covers only West Berlin after World War II. The higher housing return</footnote>
<figure><img src="image_6.png" /><figcaption>**Figure 4.** Average differences in city-level and national returns (log points), 1950–2018. This graph shows the mean difference in log capital gains (Panel A), log rental returns (Panel B), and log total returns (Panel C) between the city level and the respective national portfolio by city. The period covered is 1950 to 2018, except for German cities, Tokyo, and Toronto, where the national data start in 1963, 1960, and 1957, respectively. (Color figure can be viewed at wileyon-linelibrary.com)</figcaption></figure>

Table III formalizes the analysis of different large city/national housing portfolio definitions, along with paired *t*-tests for equality of means between city and national housing portfolios. The table shows capital gains, rental returns, and total returns at the large-city level (column (1)) and for national housing portfolios as defined in Jordà et al. (2019) (column (2)). Column (4) shows the population-weighted return for the rest of the country (excluding large cities) as defined above. Panel B narrows the definition of large city to the single largest city in each country (New York, London, Paris, etc.), which provides an even stronger comparison between large cities and the rest of the country.<fnref n="13" />

At 2.25 log points, capital gains in the 27 largest cities were about 43 bps higher than in the national portfolio and 61 bps higher than in the rest of the country. Rental returns, in contrast, were lower in the metropolitan areas, with a difference of 1.39 or 1.65 log points, depending on the comparison portfolio. The higher rental returns outside the metropolitan areas more than compensate for the lower rate of capital appreciation. Our overall benchmark estimate

in West Berlin may not be surprising given the city's unique history. Prior to the fall of the Berlin Wall and the reunification of Germany in 1990, Berlin was not only highly supply-constrained, but also a potentially very risky place to invest, given the political tensions between the Soviet Union and the West. In addition, the reunification of Germany itself could be seen as a very large positive shock to (West) Berlin, potentially pushing housing returns away from their equilibrium path for several years. The other outliers are much smaller and tend to be characterized by exceptionally high capital gains relative to the respective national index. These, in turn, could be driven by large positive shocks to urban development. The main example is Basel, which has experienced rapid economic growth since World War II and is now the region with the highest GDP per capita in Switzerland. Within Switzerland, the canton of Basel-Stadt (Nuts-2 region) had by far the highest GDP per capita in 2018, almost double that of the canton of Zurich (Source: Swiss Federal Statistical Office, table je-e-04.02.06.03, published on January 21, 2021).

<footnote n="13">¹³ We use the largest city per country in our data set. This means that Toronto is included even though Montreal was the largest city in 1950 because housing data for Montreal are missing.</footnote>
<table><caption>Table III
City-Level and National Yearly Housing Returns (Log Points),
1950–2018</caption><thead><tr><th></th><th colspan="5">Panel A. 27 large cities</th></tr><tr><th></th><th>Cities</th><th>National</th><th>Difference</th><th>RoC</th><th>Cities – RoC</th></tr></thead><tbody><tr><td>Capital gain</td><td>2.25</td><td>1.82</td><td>0.43* (0.23)</td><td>1.64</td><td>0.61** (0.26)</td></tr><tr><td>Rent return</td><td>3.55</td><td>4.94</td><td>-1.39*** (0.04)</td><td>5.21</td><td>-1.65*** (0.05)</td></tr><tr><td>Total return</td><td>5.72</td><td>6.68</td><td>-0.95*** (0.23)</td><td>6.76</td><td>-1.04*** (0.26)</td></tr><tr><td>N</td><td colspan="5">1,767</td></tr></tbody><tbody><tr><th></th><th colspan="5">Panel B. Only largest city/country</th></tr><tr><th></th><th>Cities</th><th>National</th><th>Difference</th><th>RoC</th><th>Cities – RoC</th></tr><tr><td>Capital gain</td><td>2.45</td><td>2.12</td><td>0.33 (0.30)</td><td>1.99</td><td>0.46 (0.34)</td></tr><tr><td>Rent return</td><td>3.53</td><td>5.17</td><td>-1.63*** (0.06)</td><td>5.41</td><td>-1.88*** (0.07)</td></tr><tr><td>Total return</td><td>5.89</td><td>7.18</td><td>-1.29*** (0.30)</td><td>7.30</td><td>-1.41*** (0.34)</td></tr><tr><td>N</td><td colspan="5">1,061</td></tr></tbody></table>

The table shows averages of city-level and national log capital gains, log rental returns, and log housing returns as well as the difference. National return averages are weighted by the number of cities in the respective country in the sample. Standard errors of differences (in parentheses) and significance are calculated using paired *t*-tests to test equal means of city-level and national return variables. Rest of country (RoC) returns are calculated as national housing portfolio return share after taking out the returns of the 27 national large cities. We use previous-year population shares as weights of the portfolio share of our cities, and thus the estimate should be interpreted as a lower bound. Panel A shows the results averaged over all 27 cities in our main data set. Panel B shows the results only for the cities, with the largest population in their respective countries in 1950 in our data. \* : *p* < 0.1; \*\* : *p* < 0.05; \*\*\* : *p* < 0.01.

is that, over the long run, total returns in the large cities were 95 to 100 bps per year lower than in the national portfolio and the rest of the country.

Panel B of Table III focuses only on the largest city within each country (measured by 1950 population). For this sample, the average difference between the city level and the rest of the country rises to 1.41 log points per year. The average total return on the national housing portfolio is about 7% per year, which means that the returns in large cities are about 15% lower.

While Demers and Eisfeldt (2022) also show that cities with higher capital gains have lower rental returns and that less expensive cities have higher total returns than more expensive cities, the differences they find are not statistically significant. This can be explained by the fact that their sample consists only of large cities and their analysis period is relatively short.<fnref n="14" />

<footnote n="14">¹⁴ Demers and Eisfeldt (2022) also find that more expensive cities underperform less expensive cities by about 1 percentage point per year. We show in Internet Appendix Section X that city size and price levels are very strongly positively correlated. Demers and Eisfeldt (2022), however, do not find this difference to be statistically significant. The source used by the authors, the American Housing Survey, has historically focused on relatively large cities. In addition, the sample period</footnote>
Finally, our results are also consistent with existing evidence that more expensive neighborhoods have experienced lower total housing returns than cheaper neighborhoods over the past decade Demers and Eisfeldt (2022); Morawakage et al. (2022).

## B. Further Tests

Capital gains are higher in large cities, but they are more than offset by lower rental returns, resulting in lower total returns. In what follows, we subject this core finding to a number of additional tests. First, we use alternative rental yield benchmarks. Second, we show that our results hold in the older historical period as well as in more recent decades. Finally, we examine the potential role of rent regulation. A discussion of the effect of taxation can be found in Section IV of the Internet Appendix, where we show that differences in real estate taxation do not affect our results. In addition, in Section III.A of the Internet Appendix, we show that our main results hold when using the nominal series, that is, the return series not adjusted for CPI.

*Alternative rental yield benchmarks.* The data used to calculate rental yields are compiled by professional real estate investors and are based on rental yield benchmarks net of maintenance, management, and other costs. As our core finding is based on the differences in rental yields between major cities and the rest of the economy, we recalculate yields using alternative rental yield benchmarks taken from country-specific sources or from the user-driven online database Numbeo.com. More detailed information on the sources can be found in Table II and in the Data Appendix.

The alternative estimates potentially provide broader coverage of the housing market but might be less precise.

Panel A of Table IV reports results using alternative rental return data. If anything, the alternative data accentuate the differences in rental yields, suggesting that differences between market segments within cities do not play a major role. In the Data Appendix, we report summary statistics of our main data set and the individual city returns based on the alternative rental return benchmarks. The differences are small.

*Subperiods.* Because of limited data availability, most of the recent literature on housing returns focuses on developments over the past two or three decades. A natural question that arises is whether our results also hold for the most recent period, which has seen a particularly pronounced rise in house prices Knoll, Schularick, and Steger (2017) and the emergence of global superstar cities.

As a first test, we split our sample period in 1990. Panel B of Table IV shows the results for the 27 largest cities relative to the national index. Our main

analyzed starting in 1986 does not include the 1970s, a decade characterized by relatively low house price appreciation and higher rental yields Jordà et al. (2019); Eichholtz et al. (2021). This omission limits the consideration of a period in which rental yields had a more significant impact on total returns.
<table><caption>Table IV
City-Level and National Yearly Housing Returns (Log Points),
1950–2018</caption><thead><tr><th rowspan="3"></th><th colspan="6">Panel A. Alternative benchmarks</th></tr><tr><th colspan="3">27 Large Cities</th><th colspan="3">Only Largest City/Country</th></tr><tr><th>Cities</th><th>National</th><th>Difference</th><th>Cities</th><th>National</th><th>Difference</th></tr></thead><tbody><tr><td>Capital gain</td><td>2.25</td><td>1.82</td><td>0.43* (0.23)</td><td>2.57</td><td>2.13</td><td>0.45 (0.29)</td></tr><tr><td>Rent return</td><td>3.32</td><td>4.94</td><td>-1.62*** (0.04)</td><td>3.42</td><td>5.20</td><td>-1.78*** (0.06)</td></tr><tr><td>Total return</td><td>5.50</td><td>6.68</td><td>-1.18*** (0.23)</td><td>5.90</td><td>7.22</td><td>-1.32*** (0.29)</td></tr><tr><td>N</td><td colspan="3">1,767</td><td colspan="3">1004</td></tr></tbody></table><table><thead><tr><th rowspan="3"></th><th colspan="6">Panel B. Standard benchmarks</th></tr><tr><th colspan="3">Until 1990</th><th colspan="3">Post 1990</th></tr><tr><th>Cities</th><th>National</th><th>Difference</th><th>Cities</th><th>National</th><th>Difference</th></tr></thead><tbody><tr><td>Capital gain</td><td>2.67</td><td>2.21</td><td>0.46 (0.37)</td><td>1.69</td><td>1.31</td><td>0.38* (0.22)</td></tr><tr><td>Rent return</td><td>3.73</td><td>5.37</td><td>-1.63*** (0.07)</td><td>3.31</td><td>4.36</td><td>-1.06*** (0.04)</td></tr><tr><td>Total return</td><td>6.31</td><td>7.47</td><td>-1.16*** (0.37)</td><td>4.94</td><td>5.62</td><td>-0.68*** (0.22)</td></tr><tr><td>N</td><td colspan="3">1,011</td><td colspan="3">756</td></tr></tbody></table>

The table shows averages of city-level and national log capital gains, log rental returns, and log housing returns as well as the difference. National return averages are weighted by the number of cities in the respective country in the sample. Standard errors of differences (in parentheses) and significance are calculated using paired *t*-tests to test equal means of city-level and national return variables. Panel A shows the results averaged using alternative rental yield benchmarks from country-specific sources. The left-hand side shows the results averaged over all cities in our main data set. The right-hand side shows the results for the cities that had the largest population in their respective countries in 1950. Panel B reports the results using the standard benchmarks from MSCI for the years from 1950 to 1990 and from 1991 to 2018. * : *p* < 0.1; ** : *p* < 0.05; *** : *p* < 0.01.

results also hold for the most recent period: Large city returns were also significantly lower in the post-1990 period. The same is true for the largest city in each country. Internet Appendix Table III.C presents moving averages over the entire period.

*Rent regulations.* Could stricter rent regulations in large cities explain the lower rental returns compared to the rest of the country? First, from an asset pricing perspective, rent regulations themselves should not affect housing returns because they only regulate the cash flow received from the asset. Since the price of an asset is determined by the discounted value of expected future cash flows, we would expect house prices to adjust to different cash flows, leaving rent-price ratios unaffected. However, rent controls could affect expectations about future rents, which could affect house prices and current returns.

As an empirical test of the effect of rent control on returns, we use the rent control index from the *Rental Market Index (ReMaIn) Database*. The database, compiled by Kholodilin (2020), uses rent legislation since 1914 in 64 countries
to create standardized indices that measure the presence and intensity of rent control, tenant protection, and housing rationing.

The results in Table IA.V in Internet Appendix Section III.D confirm that, regardless of the rent control regime, capital gains are higher and rental returns are lower in large cities compared to the national average. The absolute difference between large cities and national returns is even slightly higher in stricter rent control regimes.

*Extreme returns:* In Figure 2, we plot the distribution of annual log total returns for our sample of 27 cities. It is clear from the figure that there is a non-negligible number of outliers. In particular, in the post-1950 period, the period over which our main results hold, we have 15 cases of annual total returns exceeding 40%. These outliers are due entirely to capital gains, that is, periods in which there are substantial jumps in our house price series for specific cities.

To ensure that our results are not driven by these outliers, we exclude these outliers and rerun the main analysis. As shown in Table IA.VI in Internet Appendix, all of our main results hold when the outliers are excluded. As an additional robustness test, we collect information on each of these 15 outliers to confirm that they are not noise. In the Data Appendix, we provide both qualitative and quantitative evidence to support our findings. For example, the house price series for Sydney and Melbourne increased by more than 50% in 1950, which can be explained by the fact that the strict house price controls introduced in Australia in 1942 were lifted at the end of 1949 Stapleton (2007).

To account for the effect of negative outliers, we replicated the main analysis excluding all city-level total housing returns that fell within both the top 5% and the bottom 5% of the distribution. The detailed results are presented in Table IA.VII of the Internet Appendix. Notably, the key findings of the paper remain highly robust and retain their statistical significance.

### III. Housing Returns over the City-Size Distribution

In this section, we examine housing returns across the entire cross-section of cities in two countries: the United States and Germany. This choice of countries allows us to analyze two national real estate markets that belong to two different “housing regimes” Kohl (2017). U.S. cities are dominated by owner-occupied single-family homes with light rent regulation but comparatively strong homeownership subsidies. The German housing market is characterized by tenant-occupied, multistory buildings and a soft rent control regime without much homeownership support Kholodilin and Kohl (2021). In typologies of housing regimes Schwartz and Seabrooke (2008), these two countries often end up on opposite sides and are seen as representative of different approaches to housing policy Kemeny (1995).

We use two different data sets covering the full size distribution of cities. The approach and methodology are the same within the data sets. The central question is whether the findings from the long-run comparison of large
cities with other parts of the country hold more broadly across the entire city-size distribution.

## A. U.S. Superstars Redux

For the United States, we rely on the data set compiled by Gyourko, Mayer, and Sinai (2013), to which we add two additional observations for 2010 and 2018 from the ACS.<fnref n="15" /> Their original data cover the near universe of MSAs from 1950 to 2000 at a decadal frequency from the *Census on Housing and Population*. Gyourko, Mayer, and Sinai (2013) find large differences in house price appreciation across metropolitan areas over a 50-year period.

Due to the decadal frequency of the data, we calculate total housing returns as averages of capital gains and rental yields over 10-year periods. We also use rental yields instead of rental returns because the decadal data do not allow us to calculate rental returns accurately. Rental yields are the inverse of the price-rent ratios calculated by Gyourko, Mayer, and Sinai (2013), which are then adjusted downward for maintenance costs and depreciation. We assume that one-third of gross rents are spent on these costs across all locations.<fnref n="16" />

We define the largest cities as the largest 5% of the sample MSAs in terms of 1950 population. Choosing the largest 5% as a cutoff allows us to focus on exceptionally large and economically important cities. The size of these cities will be far from the mass point of cities, since the distribution of city sizes is approximately a Pareto distribution.<fnref n="17" /> Below, we compare these top 5% of cities with all other MSAs in the data set and with the smallest 5% of MSAs. Our overall results do not depend on these cutoffs.<fnref n="18" />

Table V reports now-familiar patterns. Rental yields are significantly lower in large cities than in all other cities or in small cities. The absolute difference in total returns is estimated to be between 50 and 80 bps per year, slightly lower than in the international sample. This is to be expected as we include more large cities.

The third row shows the comparison of the “superstar” cities as defined by Gyourko, Mayer, and Sinai (2013) with the rest of the city distribution<fnref n="19" /> extended to 2018. Using this sample of cities, the difference in capital gains

<footnote n="15">¹⁵ To make the data comparable, we construct MSA-level aggregates using official 1990 boundaries, as Gyourko, Mayer, and Sinai (2013) do. All of our results remain virtually the same when we restrict our analysis to the original data set covering only the years up to 2000, and, if anything, become stronger when we restrict the sample to only MSAs with full county coverage in 2010 and 2018. Results are available upon request. All data are at the MSA level, but for simplicity we refer to them as “cities” here. For details on data construction, see the *Internet Appendix* and Gyourko, Mayer, and Sinai (2013).</footnote>

<footnote n="16">¹⁶ This correction is in line with Demers and Eisfeldt (2022) and MSCI estimates.</footnote>

<footnote n="17">¹⁷ See, for example, Eeckhout (2004) or Duranton (2007).</footnote>

<footnote n="18">¹⁸ For a detailed description of which cities are included in the top 5%, see Section V of the *Internet Appendix*.</footnote>

<footnote n="19">¹⁹ We use the *everetiuperstar* variable from the original data set extended to 1960, 2010, and 2018. The authors exclude MSAs that do not meet the 50,000 population threshold in 1950.</footnote>
<table><caption>Table V
Difference in Housing Returns (Log Points) for 316 U.S. MSAs, 1950–2018</caption><thead><tr><th>Sample</th><th>Capital Gain</th><th>Rental Yield</th><th>Total Return</th><th>N</th></tr></thead><tbody><tr><td>Large vs. rest</td><td>0.13 (0.21)</td><td>-0.67*** (0.16)</td><td>-0.52*** (0.15)</td><td>2,184</td></tr><tr><td>Large vs. small</td><td>-0.20 (0.25)</td><td>-0.63*** (0.20)</td><td>-0.80*** (0.20)</td><td>217</td></tr><tr><td>GMS superst. vs. rest</td><td>0.53*** (0.13)</td><td>-0.68*** (0.11)</td><td>-0.17* (0.10)</td><td>1,936</td></tr><tr><td>GMS superst. vs. small</td><td>0.44** (0.19)</td><td>-0.55*** (0.18)</td><td>-0.13 (0.18)</td><td>347</td></tr></tbody></table>

The table reports averages of city-level and national log capital gains, log rental returns, and log housing returns as well as the difference. National return averages are weighted by the number of cities in the respective country in the sample. Standard errors of differences (in parentheses) and significance are calculated using paired *t*-tests to test equal means of city-level and national return variables.

is significantly positive. This is not surprising since the authors sample their superstar cities based on exceptionally high house price growth. For these cities, the difference in rental yields is significantly negative and larger in absolute terms than the difference in capital gains.

Thanks to the detailed data, we can also sort the cities into size deciles from smallest to largest MSA. We split the first and last deciles again to get a more accurate picture of the tails of the distribution.

The average total log returns within each bin are plotted in Figure 5, which shows that total real estate returns decrease with city size. The relationship is not perfectly monotonic across all size bins, but it is clearly visible overall.<fnref n="20" /> The results in Table V are based on a comparison between the largest 5% of MSAs, which includes 15 MSAs, and the rest of the country. To ensure that our results are not affected by low statistical power, we run the regression, in the first row of Table V, 10,000 times, randomly selecting 15 MSAs from the original sample in each run. In Section VI of the Internet Appendix, we present the distribution of the coefficients for total returns, rental returns, and capital gains, along with their respective *p*-values. For both total returns and rental returns, the results show that the coefficients for the top 15 MSAs are significantly different from the distribution of random MSAs, and the *p*-values are uniformly distributed between zero and one. This confirms the statistical robustness of our results. For capital gains, the results are different. The coefficient for the largest 15 MSAs falls within the distribution of coefficients for the randomly selected MSAs, indicating that higher capital gains may not be a statistically robust result.

*Cross-sectional differences in vacancy rates.* If lower quality properties in smaller cities are not rented, this could potentially lead to an upward bias in our rental yield estimates. This is because the rental yield calculations would

<footnote n="20">²⁰ The results for stock markets are similar. The “big vs. small” factor is also not linear across all size bins and is much stronger for the tails of the distribution. See Fama and French (1993).</footnote>
<figure><img src="image_7.png" /><figcaption>**Figure 5.** Total returns for 316 MSAs (log points) by population size, 1950–2018. All returns are log returns. Cities are divided into bins based on the size of the MSA population in 1950. The middle eight bins cover size deciles 2 to 9. The four extreme bins split the smallest and largest deciles in half. As the data for American MSAs only exist at decadal intervals, we are not able to construct rental returns. Rental yields, however, are used as a decent approximation of rental returns. (Color figure can be viewed at wileyonlinelibrary.com)</figcaption></figure>

be limited to higher quality housing, leading to an incomplete representation of the rental market. The rental yield differences we observe between small and large cities could then be explained by the fact that in larger cities, houses are rented across the entire quality distribution.

To test this hypothesis, we collected data on rental vacancy rates at the census tract level for all 384 MSAs in the United States from the ACS for the years 2010 and 2020.<fnref n="21" /> To approximate the quality of the housing stock, we ranked the census tracts in each MSA based on their housing value. With these data in hand, we analyzed vacancy rates along the housing value distribution for large and small MSAs.

We find that the least expensive housing tends to have lower vacancy rates in the smallest MSAs than in the largest MSAs. In the least expensive census tracts in the smallest MSAs, the highest rental vacancy rate was 17.3%, while in the largest MSAs, the least expensive census tracts in some cases had

<footnote n="21">²¹ Census tracts are statistical subdivisions of counties that have an average population of 4,000.</footnote>
vacancy rates of more than 30% in 2010. Moreover, as we show in Section IX of the Internet Appendix, vacancy rates actually rise slightly with home value in small MSAs. It is only in the largest MSAs that vacancy rates appear to decline with home value. To ensure that our results are not driven by census tracts that are predominantly owner-occupied and thus have highly volatile rental vacancy rates, we conducted a similar analysis using rental value as a measure of housing stock quality and find the same results.

*Long-run U.S. hedonic indices.* The results presented above are based on decennial census data. For a subset of these cities, high-quality annual hedonic indices of house prices and rents are available from Agorastos et al. (2024) going back to the early 20th century. The authors digitized millions of housing listings from local newspapers and used them to construct hedonic price indices that are comparable across cities and over time, making them the best available series for studying long-run U.S. housing prices.

We use the available city-level net rental yield estimates from Demers and Eisfeldt (2022) for the years 1985 to 2006 and then extrapolate back to 1920 using the hedonic price and rent indices from Agorastos et al. (2024), following the method outlined in equation (2). This approach allows us to construct annual total returns for 21 U.S. cities over the period from 1920 to 2006. The sample includes very large cities, such as New York or Los Angeles, as well as medium-sized cities, Washington D.C., and smaller cities, such as Tampa Bay, thus covering a heterogeneous set of cities in terms of size.<fnref n="22" /> This allows, for the first time, the study of the long-run evolution of city-level housing returns for individual U.S. cities at an annual frequency.<fnref n="23" />

As can be seen in Table VI, we are able to replicate our main results using this independent data set that became available only recently. In Panel A, we compare the returns in New York and Los Angeles to the rest of the sample and to the smallest cities in the sample. In both cases, we find a large and highly significant negative large city premium. Consistent with our baseline results, this negative premium is driven by lower rental returns in the large cities that outweigh stronger capital gains performance. In Panel B, we repeat the analysis by expanding the list of large cities to include Chicago and Philadelphia. We are again able to replicate all of our baseline results, but now the magnitude of the negative large-city premium is very close to our baseline results of 100 bps on an annual basis.<fnref n="24" /> This result makes sense because the set of large cities is now closer to our baseline analysis for the United States. In Section VIII of the Internet Appendix, we show that these results hold for the post-1950 period as well.

<footnote n="22">²² In Section VIII of the Internet Appendix, we describe how we construct the series in more detail.</footnote>

<footnote n="23">²³ Existing data sets extend back in time but only at a decadal frequency Gyourko, Mayer, and Sinai (2013) or focus only on the last 30 years Demers and Eisfeldt (2022).</footnote>

<footnote n="24">²⁴ The results in Panel B of Table VI are only borderline significant, which can be explained by the fact that we only use 21 cities for this analysis.</footnote>
<table><caption>Table VI
Difference in Yearly Housing Returns from Agorastos et al. (2024), 1920–2006</caption><thead><tr><th colspan="5">Panel A. New York and Los Angeles</th></tr><tr><th>Sample</th><th>Capital Gain</th><th>Rental Yield</th><th>Total Return</th><th>N</th></tr></thead><tbody><tr><td>Large vs. rest</td><td>0.45* (0.26)</td><td>-2.70*** (0.58)</td><td>-2.22*** (0.49)</td><td>1,825</td></tr><tr><td>Large vs. small</td><td>0.48* (0.27)</td><td>-2.74*** (0.71)</td><td>-2.23*** (0.54)</td><td>522</td></tr></tbody><tbody><tr><th colspan="5">Panel B. New York, Los Angeles, Chicago, and Philadelphia</th></tr><tr><th>Sample</th><th>Capital Gain</th><th>Rental Yield</th><th>Total Return</th><th>N</th></tr><tr><td>Large vs. rest</td><td>0.24 (0.27)</td><td>-1.44* (0.78)</td><td>-1.18* (0.71)</td><td>1,825</td></tr><tr><td>Large vs. small</td><td>0.27 (0.25)</td><td>-1.46* (0.88)</td><td>-1.17 (0.74)</td><td>696</td></tr></tbody></table>

The table reports differences in housing returns between large cities and the rest of the sample or small cities. It covers 21 cities at a yearly frequency between 1920 and 2006. The data are from Agorastos et al. (2024) and Demers and Eisfeldt (2022). Differences are measured as coefficients in a random effects panel regression of the dependent variable (log capital gain, log rental yield, and log total housing return) on a large-city dummy and year fixed effects. Standard errors (in parentheses) are clustered at the city-level. Large cities are defined as New York and Los Angeles in Panel A and as New York, Los Angeles, Chicago, and Philadelphia in Panel B. The second row of each panel shows the same but compares large cities only to small cities, which are defined as at or below the 15th percentile of the city population distribution in 1950. * : p < 0.1; ** : p < 0.05; *** : p < 0.01.

## B. German Cities

For Germany, we constructed a novel data set for this study, covering 42 (West) German cities between 1974 and 2018 at an annual frequency. The data set covers only comparatively large cities, corresponding to urban municipalities excluding rural hinterlands.<fnref n="25" /> We extend the data to 127 (West) German cities from 1992 onwards in a data set that covers the near universe of (West) German cities. We exclude East Germany because data coverage started later in most cases and East German cities may have been fundamentally different from West German cities at the beginning of our sample period. The data set is constructed using market reports from the German Real Estate Association and one of its predecessors.<fnref n="26" /> These market reports surveyed local real estate agents and collected city-level observations for various market and quality segments. For the period from 1989 onwards, the source allows us to directly use annual estimates for rental yields, so that we only have to rely on the rent price approach discussed above for some years. We provide more information on data sources and methods in the Data Appendix.

<footnote n="25">²⁵ The average size of the cities covered is about 418,000 inhabitants in 1975, with a standard deviation of about 414,000 and a minimum of about 31,000.</footnote>

<footnote n="26">²⁶ The *Immobilienverband Deutschland (IVD)* and its predecessor *Ring deutscher Makler (RDM)*.</footnote>
<table><caption>Table VII
Difference in Housing Returns (Log Points) for 42 German Cities, 1975–2018</caption><thead><tr><th>Sample</th><th>Capital Gain</th><th>Rent Returns</th><th>Total Return</th><th>N</th></tr></thead><tbody><tr><td>Large vs. rest</td><td>0.47 (0.57)</td><td>-0.91*** (0.34)</td><td>-0.45* (0.25)</td><td>1,848</td></tr><tr><td>Large vs. small</td><td>1.03 (0.72)</td><td>-1.58*** (0.43)</td><td>-0.57* (0.35)</td><td>264</td></tr></tbody></table>

The table reports differences in annual housing returns between large cities and the rest of the sample or small cities. It covers 42 major German cities between 1975 and 2018. Differences are measured as coefficients in a random effects panel regression of the dependent variable (log capital gain, log rental return, and log total housing return) on a large-city dummy and year fixed effects. Standard errors (in parenthesis) are clustered at the city-level. Large cities are defined as being at or above the 95th percentile of the city population distribution in 1975. The second row shows the same but compares large cities only to small cities, which are defined as at or below the 5th percentile of the city population distribution in 1975. * : p < 0.1; ** : p < 0.05; *** : p < 0.01.

We begin by comparing large cities with other cities (or the smallest 5% of cities). To do so, we sort the cities by their 1975 population.<fnref n="27" /> As for the United States, we define large cities as those at or above the 5% largest of the size distribution.

Table VII confirms an identical pattern for Germany—lower total returns in the larger cities. The return gap widens when we compare large and small cities. We also examine the more comprehensive data on residential returns starting in 1992. The results are presented in the Internet Appendix.

*Rental yield comparability.* As in the United States data set, small cities outperform large cities mainly due to the significantly lower rental yields in the latter. In the previous section, we conduct several robustness checks to ensure that our rental yield measures are not biased. The German data set provides an excellent opportunity to directly compare rental yields across cities. This is possible because we have a time series of rental yields for each city in the post-1989 sample, eliminating the need to estimate rental yields using rent and price series, as is done in the main analysis. Moreover, the rental yield series are derived using the same method for all cities in the sample, making them highly comparable.

In Figure 6, we present two bin scatter plots illustrating net rental yields based on city population in 1989. These plots show a strong and significant negative relationship between yield and population for both samples, one starting in 1973 and the other in 1989. The difference between Panels A and B is due to the fact that the 1973 sample contains a smaller number of cities and consists entirely of large cities, resulting in a stronger negative correlation in Panel B.

Using data for the cross-section of cities in both the United States and Germany, we confirm that the largest cities tend to have lower total housing

<footnote n="27">²⁷ Source: Federal Statistical Office of Germany: Gemeindeverzeichnis, Gebietsstand: 31.12.1975, Statistisches Bundesamt.</footnote>
<figure><img src="image_8.png" /><figcaption>**Figure 6.** Net rental yield and population size. The figure shows a bin scatter of city-level net rental yields from IVD by population in 1989 for 42 West German cities (Panel A and 127 West German cities (Panel B). The net rental yields are residualized for year effects. Population data come from the “Gemeindeverzeichnis” of the German Statistical Office. (Color figure can be viewed at wileyonlinelibrary.com)</figcaption></figure>

returns than other housing markets in the same country. In the next section, we discuss a framework that rationalizes these findings with differences in risk and present supporting empirical evidence.

## IV. Housing Risk and Return

Both in the long-run historical data and across the distribution of cities in the United States and Germany, we find that in large metropolitan areas: (i) capital gains tend to be higher, (ii) rental returns tend to be lower, and (iii) the difference in rental returns is greater than the difference in capital gains, so that total returns are lower in large cities. In this section, we show that differences in housing risk between large and small cities can explain these findings. While an extensive literature documents differences in capital gains and elucidates their driving forces, comparatively less attention has been paid to understanding the spatial distribution of total returns. In this section, we first review the existing literature and show how it explains the spatial pattern of capital gains. We then focus on housing risk as a potential factor that can explain the observed empirical distribution of total returns across regions.

Population growth and tighter housing supply constraints have led to substantial increases in house prices in the superstar cities Gyourko, Mayer, and Sinai (2013).<fnref n="28" /> There has also been a large increase in the share of college

<footnote n="28">²⁸ Empirical evidence presented by Hilber and Vermeulen (2016) shows that more inelastic housing supply leads to more pronounced house price growth in response to increasing demand. In Section VII of the Internet Appendix, we present additional evidence that housing supply is particularly inelastic in large cities.</footnote>
graduates and higher income households in the largest cities over the past
two decades Couture and Handbury (2020), exacerbating regional income
disparities.<fnref n="29" /> This process of income sorting Diamond and Gaubert (2022)
has been shown to significantly widen the gap in regional housing prices Van
Nieuwerburgh and Weill (2010). Sinai and Souleles (2005) posit that housing
prices should be higher in areas with more volatile rents, as greater rent
volatility increases the demand for the hedging benefits of homeownership.
Complementing this literature, Amaral et al. (2024) show that the secular de-
cline in interest rates increased house prices disproportionately more in large
cities.

Overall, these mechanisms have very precise predictions for the spatial distribution of capital gains, but they make no clear predictions for rental returns, mainly because they typically assume that the value of housing services, or rents, also increases more in larger cities. The net effect on total returns, specifically, whether large cities outperform or underperform the rest of the country, therefore remains uncertain.

In an asset market equilibrium with rational expectations and risk-averse housing investors, risk-adjusted returns should be equal across space, such that investors are indifferent between buying in different locations. It follows from this equilibrium condition that riskier, smaller cities must offer higher non-risk-adjusted total returns. As shown in Section XI of the Internet Appendix, another corollary of this condition is that spatial differences in rental returns will outweigh spatial differences in capital gains. For the asset market equilibrium condition to be satisfied, the effect of higher rental yields in smaller cities must be greater than the effect of higher capital gains in the largest cities. This corollary about the decomposition of returns into rental yields and capital gains aligns with the empirical observations that large cities tend to have more inelastic housing supply and, hence, higher expected rent growth and capital gains in equilibrium Gyourko, Mayer, and Sinai (2013), and the higher expected rent growth is reflected in lower rental yields in more supply-constrained areas Plazzi, Torous, and Valkanov (2010).

While the spatial division between rental yields and capital gains can
be accounted for by the documented differences in expected rent growth
Gyourko, Mayer, and Sinai (2013), the distribution of total returns appears
to be explained primarily by spatial differences in risk. To assess whether
differences in risk can account for our main findings, we quantify various
measures of housing risk at the city level in the subsequent sections of this
paper.

<footnote n="29">²⁹ While the significant influx of college graduates was concentrated in the downtown areas of large cities Couture and Handbury (2023), housing prices rose more generally in larger cities as a result of the gentrification process that affected surrounding neighborhoods Guerrieri, Hartley, and Hurst (2013).</footnote>
A. *Two Sources of Housing Risk*

In examining the difference in housing investment risk across cities, we consider two potential sources of risk. On the one hand, housing market returns in small cities could be more correlated with consumption growth, providing less consumption insurance. On the other hand, housing in more remote locations could exhibit higher idiosyncratic volatility, as it is typically traded in smaller and less liquid markets.

The two types of risk are conceptually independent. We first define the two concepts of risk and argue why they should be priced in housing markets. We then discuss how we measure both types of risk and provide empirical evidence on the spatial distribution of risk in housing markets.

In standard asset pricing, risk premia arise from the covariance between asset returns and marginal utility, the latter typically approximated by consumption growth Cochrane (2009). In housing markets, the covariance between local housing returns and consumption may differ between large and small cities. On the one hand, larger cities are expected to have more diversified economies, leading to reduced exposure to industry-specific shocks and a weaker covariance between housing returns and consumption growth. In addition, the increased exposure of these cities to foreign or nonlocal investors could moderate the covariance, as their investment decisions are influenced primarily by economic factors in their home regions.<fnref n="30" /> On the other hand, high-income households have increasingly moved to large cities with rising house prices Couture and Handbury (2020). This phenomenon implies a positive correlation between income growth and house price appreciation in these regions. The relative strength of these effects is an open question, and we empirically examine this issue in the next section.

Importantly, covariance with total housing returns matters when the marginal buyer is an investor. Indeed, Sinai and Souleles (2005) show that when the marginal buyer is a homeowner, and thus the house is also a consumption good, it serves as a hedge against future rent volatility and, thus, the net risk of owning a house decreases with the covariance in future housing costs.<fnref n="31" /> It may be the case that houses in larger cities are a better hedge against future increases in housing costs.<fnref n="32" />

A second potential source of risk is idiosyncratic housing risk. In the case of housing, there are good reasons to believe that idiosyncratic risk is priced in. This is because houses are large, indivisible, and illiquid assets, and most homebuyers are owner-occupiers who own a single house in a specific

<footnote n="30">³⁰ Recent studies suggest that foreign investors contribute to increased house prices in large international cities such as London, New York, or Paris, as their investment decisions are influenced primarily by economic factors in their home regions Badarinza and Ramadorai (2018); Cvijanović and Spaenjers (2021).</footnote>

<footnote n="31">³¹ This proposition has been empirically confirmed in Paciorek and Sinai (2012) and Sinai and Souleles (2013).</footnote>

<footnote n="32">³² Although this sounds like a realistic hypothesis, we are not aware of any data that would allow us to test it.</footnote>
location rather than a diversified housing portfolio Piazzesi and Schneider (2016). As a result, the standard assumptions of diversified portfolio models do not necessarily hold in housing markets and idiosyncratic risk is priced in, as Merton (1987) shows. Current estimates show that at least half of the price volatility of a house is idiosyncratic, that is, specific to the property Piazzesi and Schneider (2016); Giacoletti (2021). To test whether smaller cities have higher idiosyncratic risk, we calculate the idiosyncratic component of house price volatility following the approach developed by Giacoletti (2021).<fnref n="33" />

## B. Covariance Risk

The following holds for a utility-maximizing household that allocates resources between consumption and different investment opportunities:<fnref n="34" />

$$lnE[R_{t+1}] - lnR_f = \gamma Cov\left[ln\left(\frac{C_{t+1}}{C_t}\right), lnR_{t+1} - lnR_f\right], \quad (4)$$

where $R_{t+1}$ is the total return on the asset in the next period, $R_f$ is the return on the risk-free asset, $\gamma$ the risk-aversion parameter, and $\frac{C_{t+1}}{C_t}$ is consumption growth. This expression states that an asset that has greater co-movement with consumption features higher risk, and hence, risk-averse agents ($\gamma > 0$) request a higher excess return. Unfortunately, to the best of our knowledge, long-run data on consumption at the regional level does not exist. Instead, we approximate consumption growth with regional income growth.<fnref n="35" /> An asset is riskier when it has a higher correlation with future income as it cannot be used to hedge against income shocks, and can even amplify them.

To calculate the covariance between MSA-level income growth and MSA-level excess housing returns, we turn to U.S. Census data, described above in Section III.A. These data provide a measure of total housing returns and of family income growth over time. It is important to note that the data are decadal. This implies that we compare the correlation of log excess housing returns and log income growth over long time periods.<fnref n="36" />

We first calculate MSA-specific covariances as: $Cov_s = Cov(R_s - R_f, y_s)$, where $R_s$ is total real log housing return for MSA $s$, $R_f$ is the risk-free rate approximated by total real log returns on short-term U.S. T-bills and $y_s$ is average

<footnote n="33">³³ Note that since idiosyncratic risk is a source of transaction risk, it plays a central role when the marginal buyer is an investor or a homeowner.</footnote>

<footnote n="34">³⁴ See Cochrane (2009).</footnote>

<footnote n="35">³⁵ Due to data limitations, we use reported income data. It could be argued that a homeowner is saving on rent and therefore imputed rent should also be considered as income. Unfortunately, we are not aware of a data set that includes imputed rent for this period.</footnote>

<footnote n="36">³⁶ By focusing on the 10-year averages, we are averaging out the cyclical evolution in consumption growth. This is in line with Parker and Julliard (2005), who show that the covariance between current asset returns and cumulative consumption growth explains the cross-section of expected returns to a much greater extent than the covariance between the asset's return and contemporaneous consumption growth.</footnote>
<table><caption>Table VIII
Differences in Covariances for different MSA Sortings, 1950–2018</caption><thead><tr><th>Sorting</th><th>Large vs. Rest</th><th>Large vs. Small</th><th>Rest vs. Small</th></tr></thead><tbody><tr><td>By MSA size</td><td>-0.55** (0.273)</td><td>-1.94*** (0.573)</td><td>-1.49*** (0.496)</td></tr><tr><td>By total returns</td><td>0.36 (0.416)</td><td>0.60 (0.448)</td><td>0.27 (0.167)</td></tr><tr><td>N</td><td>316</td><td>31</td><td>316</td></tr></tbody></table>

The first row reports differences in the covariance between income growth and log excess total returns by MSA size. For clarity, the differences in covariances are multiplied by 10,000. Large MSAs are defined as at or above the 95th percentile of the MSA population distribution in 1950. Small MSAs are defined as at or below the 5th percentile of the MSA population distribution in 1950. In column (3), we report the differences between small MSAs and the rest of the MSAs. The second row reports differences in total log housing returns between MSAs with large total housing returns and the rest of the sample or MSAs with smaller total housing returns. MSAs with large returns are defined as at or above the 95th percentile of the MSA average total log housing returns distribution between 1950 and 2018. MSAs with small returns are defined as at or below the 5th percentile of the MSA total log housing returns distribution between 1950 and 2018. In column (3), we report the differences between small MSAs and the rest. Differences are measured as coefficients in a cross-sectional regression of the dependent variable (covariance) on a large-MSA dummy (columns (1) and (2)) or on a rest MSA dummy (column (3)). Robust standard errors are in parentheses. Overall, we use estimates for 316 MSAs between 1950 and 2018. * : p < 0.1; ** : p < 0.05; *** : p < 0.01.

real log income growth in MSA *s*. Hence, $R_s - R_f$ is the excess return on housing in MSA *s*. We calculate the covariances for the period between 1950 and 2018.<fnref n="37" /> We then test whether these covariances are smaller in large MSAs. The results are depicted in the first row of Table VIII. The covariances of income and excess housing returns are significantly smaller in large MSAs compared to the rest. The difference in covariances becomes larger when we compare the largest MSAs to only the smallest ones. Section XIV in the Internet Appendix shows results for the entire distribution of MSAs as well as estimated betas from a consumption based asset pricing model (CCAPM).

In the same spirit, the data allow us to test whether high-return MSAs exhibit higher covariances between housing returns and income, as the CCAPM predicts. In the second row of Table VIII, we sort MSAs by housing returns and compare covariances for high- and low-return MSAs. We find that return covariances with income are lower in low-return cities. Statistical significance, however, is mixed: The results are borderline significant at the 10% level (*p* = 0.105) only in the last column, where we compare the lowest return MSAs (which tend to be the largest MSAs in terms of population) with all other MSAs. As can be seen in the middle column, the mean difference between covariances in high- versus low-return markets is particularly large, but it is not significant in the decadal data that we have at our disposal. Future research

<footnote n="37">³⁷ Note that given the decadal frequency of the data, in general, we have seven data points for each variable MSA combination. For summary statistics on the returns and income growth, please refer to Table IA.XIII in the Internet Appendix.</footnote>
will have to rely on new types of data sets with more granular consumption series and higher frequency return data to pin down these differences more firmly. For now, we conclude that the available long-run data for the United States suggest that housing risks are higher in small cities as income co-varies more strongly with local housing returns.

MSAs with low returns also tend to have smaller covariances between returns and income growth than others.

### C. Idiosyncratic Housing Price Risk

To test for spatial differences in idiosyncratic risk, we use a combination of transaction-level price data from the Corelogic deeds data set and county-level house price indices from the Federal Housing Finance Agency (FHFA) and Zillow.com for American MSAs over the past three decades. The focus is on the United States because, to the best of our knowledge, equally detailed and micro-level house price transaction data do not exist for other countries.

Importantly, these estimates of idiosyncratic risk build on sales data and mark a lower bound for estimates of the idiosyncratic risk differences between large and small markets. In Section XIV of the Internet Appendix, we demonstrate that in large cities, rental markets are substantially more liquid, and rental vacancy rates are lower and less volatile, which reduces the uncertainty that a landlord faces over his future income stream. Moreover, Sagi (2021) shows that for commercial real estate, including income streams does not significantly affect the volatility of property-level returns.

We estimate idiosyncratic house price risk as the unexplained variation in sales-level capital gains after controlling for market-level price changes (at the county level) and common house and transaction characteristics as follows:<fnref n="38" />

$$ \Delta p_{i,l,t} = \Delta v_{l,t} + BX_i + \sigma_{l,\text{idiosyncratic}} \varepsilon_{i,t}, \quad (5) $$

where $\Delta v_{l,t}$ is the growth in local county house prices, $BX_i$ is a vector of house and transaction characteristics, which includes zip-code and time fixed effects, and $\sigma_{l,\text{idiosyncratic}} \varepsilon_{i,t}$ is a sales-specific shock. We measure idiosyncratic risk as the standard deviation of sales-specific shocks for properties within a specific MSA. Using data from Corelogic on repeat sales of single-family homes for the 1990 to 2020 period, we can estimate annual idiosyncratic risk in 248 MSAs that cover around 86% of the U.S. population in 1990. We describe the data sources and the methods used to estimate idiosyncratic house price risk in more detail in Section XIII of the Internet Appendix.

<footnote n="38">³⁸ Giacoletti (2021) studies local-market risk at the zip-code level. Our definition of local markets relates to individual counties. However, the estimates of idiosyncratic risk that we obtain at the MSA level are very similar to those that we obtain at the zip-code level for MSAs for which we have sufficient observations to use both approaches.</footnote>
<figure><img src="image_9.png" /><figcaption>**Figure 7.** Annual idiosyncratic house price risk by MSA size, 1990–2020. The figure shows average annual idiosyncratic house price risk for different MSA size groups for the period between 1990 and 2020. MSAs are divided into bins based on the MSA’s population in 1990. The middle eight bins cover size deciles 2 to 9. The four extreme bins split the smallest and largest deciles in half. All series are real and annualized. (Color figure can be viewed at wileyonlinelibrary.com)</figcaption></figure>

### C.1. *Idiosyncratic Risk across Space*

Figure 7 plots our measure of idiosyncratic house price risk across different MSA size bins, showing that it decreases substantially with MSA size. Between 1990 and 2020, average idiosyncratic risk in the smallest MSAs was 12.34% of the house sales price, but about 25% lower in the largest MSAs at 9.28%. The measure of idiosyncratic house price risk is orthogonal to local housing market fluctuations and therefore is independent from the covariance risk that we examine above.<fnref n="39" /> In Section XIII.A of the Internet Appendix, we also look at the distribution of local-market housing price volatility in detail. In contrast to idiosyncratic volatility, local-market volatility is small and does not differ

<footnote n="39">³⁹ Note that this does not imply that city-wide factors are irrelevant for idiosyncratic housing risk. Realizations of sales-specific shocks are idiosyncratic by nature. But the distribution from which these sales-specific shocks are drawn is arguably the same for similar houses and will be determined by local housing market characteristics.</footnote>
significantly across MSAs. This result reconciles our findings with those of Demers and Eisfeldt (2022), who focus on local-market volatility and therefore do not find higher return volatility in low-priced cities. Accordingly, we focus our discussion here on idiosyncratic volatility.

## C.2. Idiosyncratic Risk and Housing Market Liquidity

The real estate finance literature establishes a strong link between idiosyncratic risk and illiquid markets. Empirical work by Amaral (2024), Giacoletti (2021), and Sagi (2021) shows that idiosyncratic risk is directly related to the ease of buying and selling a property.<fnref n="40" /> A close link between liquidity and idiosyncratic risk has also been shown for other asset classes, such as private equity.<fnref n="41" /> Accordingly, we would expect MSAs with large idiosyncratic house-price volatility to also have thinner and very illiquid housing markets.<fnref n="42" /> We now test these predictions.

We look at evidence from two liquidity measures across MSAs in the United States: time on the market (TOM) and asking price discount. TOM measures the number of days between the original sale listing of a house and its actual sale. The asking price discount measures the difference between the original asking price and the final transaction price. Intuitively, in more liquid markets, sellers will have to wait less time to sell (low TOM) and will be able to sell their properties for a price closer to the original asking price (low discount).

We use data from the online real estate marketplace Zillow.com on median time on Zillow and median price cut over 277 American MSAs for the last decade. Table IX compares both measures of liquidity in the 5% largest MSAs with the other 95% and the smallest 5% MSAs. In the largest MSAs, sellers take significantly less time to sell on average. Table IX shows that the difference between the largest and smallest MSAs is around 30 days, compared to an overall mean of 100 days. In addition, not only is mean TOM significantly lower in large cities, but it also fluctuates significantly less over time. Search behavior data from German real estate platforms corroborate these findings by showing that housing markets in larger cities are denser, with more potential buyers per listing.<fnref n="43" /> This result is consistent with evidence that larger cities

<footnote n="40">⁴⁰ More specifically, they show that idiosyncratic volatility is realized mostly at the points of sale and resale of the property.</footnote>

<footnote n="41">⁴¹ Robinson and Sensoy (2016) show that most of the variation in cash flows is idiosyncratic, and Sorensen, Wang, and Yang (2014) show that the idiosyncratic (nonsystematic) risk faced by private equity investors arises from their illiquidity. Furthermore, Mueller (2010) and Ewens, Jones, and Rhodes-Kropf (2013) provide empirical evidence that private equity funds with higher idiosyncratic risk also have higher expected returns.</footnote>

<footnote n="42">⁴² In addition, it may be the case that thicker markets in larger cities lead to better matching of buyers and sellers, thereby lowering idiosyncratic risk in larger cities. Unfortunately, we are not aware of any data sets that would allow us to test this possibility directly.</footnote>

<footnote n="43">⁴³ Detailed results can be found in Section XV of the Internet Appendix.</footnote>
<table><caption>Table IX
Differences in Mean and Standard Deviation of Housing Liquidity, United States, 2012–2020</caption><thead><tr><th rowspan="2">Sample</th><th colspan="3">Asking Price Discount (in p.p.)</th></tr><tr><th>Mean</th><th>SD across Time</th><th>N</th></tr></thead><tbody><tr><td>Large vs. rest</td><td>-0.87*** (0.096)</td><td>-0.36*** (0.016)</td><td>62,688</td></tr><tr><td>Large vs. small</td><td>-1.50*** (0.184)</td><td>-0.75*** (0.052)</td><td>6,336</td></tr></tbody></table><table><thead><tr><th rowspan="2">Sample</th><th colspan="3">Time on the Market (in days)</th></tr><tr><th>Mean</th><th>SD across Time</th><th>N</th></tr></thead><tbody><tr><td>Large vs. rest</td><td>-10.90* (6.184)</td><td>-4.34*** (0.904)</td><td>26,869</td></tr><tr><td>Large vs. small</td><td>-29.67*** (9.918)</td><td>-9.89*** (1.782)</td><td>2,716</td></tr></tbody></table>

Large MSAs are defined as at or above the 95th percentile of the MSA population distribution in 2010. Small MSAs are defined as at or below the 5th percentile of the MSA population distribution in 1950. Data are on the median number of days on Zillow and on the average discount to the asking price from Zillow.com for 277 MSAs over the 2012 to 2020 period.

*: p < 0.1; **: p < 0.05; ***: p < 0.01.

have thicker markets for other nontradable goods, such as restaurants Berry and Waldfogel (2010).

## V. Conclusion

In our sample spanning 27 cities in 15 countries, we uncover a new stylized fact: Large cities have persistently underperformed smaller, less dynamic cities in terms of housing returns. This result is puzzling given the well-established evidence that large agglomerations have witnessed substantially stronger housing price appreciation than the rest of the country in recent decades. Taking rental returns into account changes our understanding of the performance of housing assets across space. This new stylized fact reveals a second, equally important fact about housing markets: housing investments are significantly less risky in the larger agglomerations than in the rest of the country. These two new stylized facts interact in accordance with the prediction of a standard asset market rational-expectations equilibrium: Smaller and more risky locations have to offer higher expected housing returns to attract new capital. Rationalizing the spatial distribution of housing markets through the lens of an asset market equilibrium represents, to the best of our knowledge, a novel approach, that could be very promising for spatial economics models more generally. Beyond the relevance for spatial economics, the large differences in housing returns across locations also emphasize the need to examine more closely within-asset-class return heterogeneity and its repercussions for wealth inequality dynamics and portfolio choice. Finally, by showing that the choice between locations is strongly associated with different exposures to housing risk and returns and, therefore is, ultimately,
a driver of wealth dynamics, this paper invites more research on the im-
portance of geography and size for the heterogeneity in returns on different
assets.

Acknowledgments

Open access funding enabled and organized by Projekt DEAL.

Initial submission: October 30, 2022; Accepted: January 26, 2025

Editors: Antoinette Schoar, Urban Jermann, Leonid Kogan, Jonathan Lewellen, and Thomas Philippon

REFERENCES

Agorastos, David, Rowena Gray, Ronan C. Lyons, and Allison Shertzer, 2024, The price of housing in the United States, 1890–2006, Working paper, Federal Bank of Philadelphia.

Ahfeldt, Gabriel M., and Elisabetta Pietrostefani, 2019, The economic effects of density: A synthesis, *Journal of Urban Economics* 111, 93–107.

Amaral, Francisco, 2024, Price uncertainty and returns to housing, Working paper, University of Bonn.

Amaral, Francisco, Martin Dohmen, Sebastian Kohl, and Moritz Schularick, 2024, Interest rates and the spatial polarization of housing markets, *American Economic Review: Insights* 6, 89–104.

Bach, Laurent, Laurent E. Calvet, and Paolo Sodini, 2020, Rich pickings? Risk, return, and skill in household wealth, *American Economic Review* 110, 2703–2747.

Badarinza, Cristian, and Tarun Ramadorai, 2018, Home away from home? Foreign demand and London house prices., *Journal of Financial Economics* 130, 532–555.

Begley, Jaclene, Lara Loewenstein, and Paul S. Willen, 2021, The rent-price ratio during the 2000s housing boom and bust: Measurement and implications, Working paper. Federal Reserve Bank of Atlanta.

Benhabib, Jess, and Alberto Bisin, 2018, Skewed wealth distributions: Theory and empirics, *Journal of Economic Literature* 56, 1261–1291.

Berger, David, Veronica Guerrieri, Guido Lorenzoni, and Joseph Vavra, 2018, House prices and consumer spending, *Review of Economic Studies* 85, 1502–1542.

Berry, Steven, and Joel Waldfogel, 2010, Product quality and market size, *Journal of Industrial Economics* 58, 1–31.

Brounen, Dirk, Piet Eichholtz, Stefan Staetmans, and Marcel Theebe, 2013, Inflation protection from homeownership: Long-run evidence, 1814–2008, *Real Estate Economics* 42, 662–689.

Case, Karl, John Cotter, and Stuart Gabriel, 2011, Housing risk and return: Evidence from a housing asset-pricing model, *Journal of Portfolio Management* 37, 89–109.

Chetty, Raj, László Sándor, and Adam Szeidl, 2017, The effect of housing on portfolio choice, *Journal of Finance* 72, 1171–1212.

Cocco, Joao F., 2005, Portfolio choice in the presence of housing, *Review of Financial Studies* 18, 535–567.

Cochrane, John, 2009, *Asset Pricing: Revised Edition* (Princeton University Press, Princeton, NJ).

Combes, Pierre-Philippe, Gilles Duranton, and Laurent Gobillon, 2019, The costs of agglomeration: House and land prices in French cities, *The Review of Economic Studies* 86, 1556–1589.

Couture, Victor, and Jessie Handbury, 2020, Urban revival in America, *Journal of Urban Economics* 119, 103267.

Couture, Victor, and Jessie Handbury, 2023, Neighborhood change, gentrification, and the urbanization of college graduates, *Journal of Economic Perspectives* 37, 29–52.

Cvijanović, Dragana, and Christophe Spaenjers, 2021, “We’ll always have Paris”: Out-of-country buyers in the housing market, *Management Science* 67, 4120–4138.
Demers, Andrew, and Andrea L. Eisfeldt, 2022, Total returns to single-family rentals, *Real Estate Economics* 50, 7–32.

Desmet, Klaus, and Esteban Rossi-Hansberg, 2013, Urban accounting and welfare, *American Economic Review* 103, 2296–2327.

Diamond, Rebecca, and Cecile Gaubert, 2022, Spatial sorting and inequality, *Annual Review of Economics* 14, 795–819.

Duranton, Gilles, 2007, Urban evolutions: The fast, the slow, and the still, *American Economic Review* 97, 197–221.

Duranton, Gilles, and Diego Puga, 2000, Diversity and specialisation in cities: Why, where and when does it matter?, *Urban Studies* 37, 533–555.

Eeckhout, Jan, 2004, Gibrat's law for (all) cities, *American Economic Review* 94, 1429–1451.

Eichholtz, Piet, Matthijs Korevaar, Thies Lindenthal, and Ronan Tallec, 2021, The total return and risk to residential real estate, *Review of Financial Studies* 34, 3608–3646.

Ewens, Michael, Charles M. Jones, and Matthew Rhodes-Kropf, 2013, The price of diversifiable risk in venture capital and private equity, *Review of Financial Studies* 26, 1854–1889.

Fama, Eugene F., and Kenneth R. French, 1993, Common risk factors in the returns on stocks and bonds, *Journal of Financial Economics* 33, 3–56.

Gabaix, Xavier, Jean-Michel Lasry, Pierre-Louis Lions, and Benjamin Moll, 2016, The dynamics of inequality, *Econometrica* 84, 2071–2111.

Giacoletti, Marco, 2021, Idiosyncratic risk in housing markets, *Review of Financial Studies* 34, 3695–3741.

Glaeser, Edward L., ed., 2010, *Agglomeration Economics* (University of Chicago Press, Chicago, IL).

Glaeser, Edward L., and Joseph Gyourko, 2010, *Arbitrage in Housing Markets* (Lincoln Land Institute of Land Policy, Cambridge, MA).

Glaeser, Edward L., Joseph Gyourko, Eduardo Morales, and Charles G. Nathanson, 2014, Housing dynamics: An urban approach, *Journal of Urban Economics* 81, 45–56.

Gomes, Francisco, Michael Haliassos, and Tarun Ramadorai, 2021, Household finance, *Journal of Economic Literature* 59, 919–1000.

Gordon, Robert J., and Todd van Goethem, 2007, Downward bias in the most important CPI component: The case of rental shelter, 1914-2003, in Ernst R. Berndt, and Charles R. Hulten, eds., *Hard-to-Measure Goods and Services: Essays in Honor of Zvi Griliches*, 153–195. (University of Chicago Press, Chicago, IL).

Guerrieri, Veronica, Daniel Hartley, and Erik Hurst, 2013, Endogenous gentrification and housing price dynamics, *Journal of Public Economics* 100, 45–60.

Gyourko, Joseph, Christopher Mayer, and Todd Sinai, 2013, Superstar cities, *American Economic Journal: Economic Policy* 5, 167–199.

Han, Lu, 2013, Understanding the puzzling risk-return relationship for housing, *Review of Financial Studies* 26, 877–928.

Hilber, Christian, and Andreas Mense, 2021, Why have house prices risen so much more than rents in superstar cities?, Working paper, Department of Geography and Environment, LSE, London, UK.

Hilber, Christian, and Wouter Vermeulen, 2016, The impact of supply constraints on house prices in England, *The Economic Journal* 126, 358–405.

Jordà, Òscar, Katharina Knoll, Dmitry Kuvshinov, Moritz Schularick, and Alan M. Taylor, 2019, The rate of return on everything, 1870-2015*, *Quarterly Journal of Economics* 134, 1225–1298.

Jordà, Òscar, Moritz Schularick, and Alan M. Taylor, 2017, Macrofinancial history and the new business cycle facts, *NBER Macroeconomics Annual* 31, 213–263.

Kaplan, Greg, Benjamin Moll, and Giovanni L. Violante, 2018, Monetary policy according to hank, *American Economic Review* 108, 697–743.

Kemeny, Jim, 1995, *From Public Housing to the Social Market: Rental Policy Strategies in Comparative Perspective* (Routledge, London).

Kholodilin, Konstantin, 2020, Long-term, multicountry perspective on rental market regulations, *Housing Policy Debate* 30, 994–1015.
Kholodilin, Konstantin, and Sebastian Kohl, 2021, Social policy or crowding-out? Tenant protection in comparative long-run perspective, *Housing Studies* 38, 1–24.

Knoll, Katharina, Moritz Schularick, and Thomas Steger, 2017, No price like home: Global house prices, 1870-2012, *American Economic Review* 107, 331–353.

Kohl, Sebastian, 2017, *Homeownership, Renting and Society: Historical and Comparative Perspectives* (Routledge, London).

Kuhn, Moritz, Moritz Schularick, and Ulrike I. Steins, 2020, Income and wealth inequality in America, 1949-2016, *Journal of Political Economy* 128, 3469–3519.

Levy, Antoine, 2021, Housing policy with home-biased landlords: Evidence from French rental markets, Working paper, Berkeley University.

Lustig, Hanno N., and Stijn Van Nieuwerburgh, 2005, Housing collateral, consumption insurance, and risk premia: An empirical perspective, *Journal of Finance* 60, 1167–1219.

Merton, Robert, 1987, A simple model of capital market equilibrium with incomplete information, *Journal of Finance* 42, 483–510.

Morawakage, Prabath S., G. Earl, B. Liu, E. Roca, and A. Omura, 2022, Housing risk and returns in submarkets with spatial dependence and heterogeneity, *Journal of Real Estate Finance and Economics* 67, 1–40.

Mueller, Elisabeth, 2010, Returns to private equity—Idiosyncratic risk does matter!, *Review of Finance* 15, 545–574.

Paciorek, Andrew, and Todd Sinai, 2012, Does home owning smooth the variability of future housing consumption?, *Journal of Urban Economics* 71, 244–257.

Parker, Jonathan A., and Christian Julliard, 2005, Consumption risk and the cross section of expected returns, *Journal of Political Economy* 113, 185–222.

Piazzesi, Monika, 2018, Asset pricing program, NBER Reporter 2018, 1.

Piazzesi, Monika, and Martin Schneider, 2016, Housing and macroeconomics, in John B. Taylor, and Harald Uhlig, eds., *Handbook of Macroeconomics*, 1547–1640 (Elsevier, The Netherlands).

Piazzesi, Monika, Martin Schneider, and Johannes Stroebel, 2020, Segmented housing search, *American Economic Review* 110, 720–759.

Piazzesi, Monika, Martin Schneider, and Selale Tuzel, 2007, Housing, consumption and asset pricing, *Journal of Financial Economics* 83, 531–569.

Plazzi, Alberto, Walter Torous, and Rossen Valkanov, 2010, Expected returns and expected growth in rents of commercial real estate, *Review of Financial Studies* 23, 3469–3519.

Reba, Meredith, Femke Reitsma, and Karen C. Seto, 2016, Spatializing 6,000 years of global urbanization from 3700 BC to AD 2000, *Scientific Data* 3, 1–16.

Robinson, David T., and Berk A. Sensoy, 2016, Cyclicality, performance measurement, and cash flow liquidity in private equity, *Journal of Financial Economics* 122, 521–543.

Sagi, Jacob S, 2021, Asset-level risk and return in real estate investments, *Review of Financial Studies* 34, 3647–3694.

Saiz, Albert, 2010, The geographic determinants of housing supply, *Quarterly Journal of Economics* 125, 1253–1296.

Schwartz, Herman M., and Leonard Seabrooke, 2008, Varieties of residential capitalism in the international political economy: Old welfare states and the new politics of housing, *Comparative European Politics* 6, 237–261.

Sinai, Todd, and Nicholas Souleles, 2013, Can owning a home hedge the risk of moving?, *American Economic Journal: Economic Policy* 5, 282–312.

Sinai, Todd, and Nicholas S. Souleles, 2005, Owner-occupied housing as a hedge against rent risk, *Quarterly Journal of Economics* 120, 763–789.

Sorensen, Morten, Neng Wang, and Jinqiang Yang, 2014, Valuing private equity, *Review of Financial Studies* 27, 1977–2021.

Stapleton, Nigel, 2007, Long-term housing prices in Australia and some economic perspectives, PhD dissertation, University of New South Wales, Sydney.

United Nations, 2018, World urbanization prospects: The 2018 revision, online edition, Department of Economic and Social Affairs, Population Division.

Van Nieuwerburgh, Stijn, and Pierre-Olivier Weill, 2010, Why has house price dispersion gone up?, *Review of Economic Studies* 77, 1567–1606.
**Supporting Information**

Additional Supporting Information may be found in the online version of this
article at the publisher's website:

**Appendix S1:** jofi13479-sup-0001-Internet-Appendix.pdf

**Appendix S2:** jofi13479-sup-0002-Internet-Data-Appendix.pdf

**Replication Code.**