Location Sorting and Endogenous Amenities: Evidence From Amsterdam

Related Literature

Spatial equilibrium models date back to Rosen (1979) and Roback (1982) and are a benchmark to study spatial inequality across and within cities (Moretti (2013), Diamond (2016), Couture and Handbury (2020)). A subset of the literature focuses on the within-city margin, but typically remains silent on the exact mechanisms through which specific amenities are provided (Bayer, Ferreira, and McMillan (2007), Guerrieri, Hartley, and Hurst (2013), Ahlfeldt, Redding, Sturm, and Wolf (2015), Davis, Hartley, and Gregory (2019), Su (2022)). Recent studies impose structure on amenity provision, but often lack heterogeneity in residents' preferences over amenities or collapse amenities into a single quality index (Couture, Gaubert, Handbury, and Hurst (2024), Hoelzlein (2020), Miyauchi, Nakajima, and Redding (2021)). We contribute by allowing for preference heterogeneity over multiple and differentiated amenities, whose supply is microfounded through a market mechanism. We build upon the notion of “preference externalities”: demand-side preference heterogeneity can translate into differences in the variety of products supplied (George and Waldfogel (2003), Handbury (2021)). Similarly, we interpret neighborhoods as differentiated products where amenities play the role of endogenous product attributes, and highlight the implications for residential sorting and inequality.

Our paper also contributes to the literature on the STR industry, as well as tourism more broadly. There is extensive work on the effects of STR entry on the housing market (Sheppard and Udell (2016), Koster, Van Ommeren, and Volkhausen (2021), Garcia-López, Jofre-Monseny, Martínez-Mazza, and Segú (2020), Barron, Kung, and Proserpio (2021)) and hotel revenue (Zervas, Proserpio, and Byers (2017)). Farronato and Fradkin (2022) studied the effect of STR entry on competing hotel sector. Calder-Wang (2021) studied the distributional effects on the New York City rental market, focusing on rent effects but abstracting from amenity effects. Faber and Gaubert (2019) showed the importance of tourism in the economic development of the Mexican coastline. Finally, Allen, Fuchs, Ganapati, Graziano, Madera, and Montoriol-Garriga (2021) studied the effects of seasonal tourism on prices of goods and amenities borne by residents of Barcelona. We complement their work by simultaneously studying the effects of tourism on both residential and amenity markets, showing how they interact to shape urban inequality.

In terms of methods, we use discrete choice tools from the empirical industrial organization literature and show how they can be applied to urban residential markets (McFadden (1974), Berry (1994), Berry, Levinsohn, and Pakes (1995), Rust (1987)). Specifically, our dynamic estimation uses the Euler Equation in Conditional Choice Probabilities (ECCP) estimator (Hotz and Miller (1993), Arcidiacono and Miller (2011), Aguirregabiria and Magesan (2013), Scott (2013), Kalouptsidi, Scott, and Souza-Rodrigues (2021b)). The method has been applied to several contexts where dynamics are first order: agricultural markets (Scott (2013), Hsiao (2021)), occupational choice (Traiberman (2019), Humlum (2021)), and residential choice (Diamond, McQuade, and Qian (2019), Davis, Hartley, and Gregory (2019), Davis, Gregory, Hartley, and Tan (2021)).

Individual-Level Data: Residential Histories and Socioeconomic Characteristics

Our individual-level microdata are from the statistical bureau of the Netherlands, Centraal Bureau voor de Statistiek (CBS). The key data set for our dynamic model is the residential cadaster, from which we construct a panel of residential history for the universe of individuals in the Netherlands. We also observe household-level demographics from tax return data: income, educational attainment, employment status, household composition, and ethnic background. We classify households as low-, medium-, or high-skill using educational attainment bins. Because we do not observe workplace nor occupations, our analysis focuses on residential market, rather than labor market outcomes. Further details are in Supplemental Appendix A.2.1 (Almagro and Domínguez-Iino (2025)).

Housing Unit Data: Tax Valuations, Tenancy Status, Physical Characteristics, Rental Prices, and Transaction Values

First, we obtain property values from a CBS tax appraisal panel for the universe of residential housing units for 2006–2020, which also includes geo-coordinates, quality measures, and the occupant's tenancy status (owner-occupied, rental, social housing). For the subset of these properties that are transacted, we can confirm that their tax appraisals are highly correlated with transaction prices (we observe all housing sale transactions in the Netherlands). Second, we obtain rental prices from a CBS national rent survey for 2006–2019. Since the survey does not cover the universe of tenants, we impute rental prices by linking it to the universe of tax appraisal valuations and employing a random forest, which outperforms traditional linear hedonic models (Mullainathan and Spiess (2017)). Imputation details are in Supplemental Appendix A.2.4.

Neighborhood-Level Data: Amenities, Demographic Changes, Tourist Inflows

We use two levels of geographic units based on Amsterdam's administrative divisions: 99 “wijk” (neighborhoods) that belong to 25 larger “gebied” (districts). An average wijk had roughly 8540 inhabitants as of 2018. After dropping unpopulated or industrial-use-only neighborhoods, we end up with 95 neighborhoods and 22 districts. We observe annual neighborhood-level outcomes from Amsterdam City Data (ACD) from 2008 to 2018. These outcomes include demographics (e.g., ethnic, income, and skill composition) and a rich set of consumption amenities. We also obtain city-level tourist inflows from ACD. The ACD wijk-level and Tourism data are publicly available at ACD BBGA (https://onderzoek.amsterdam.nl/dataset/basisbestand-gebieden-amsterdam-bbga) and ACD Tourism (https://data.amsterdam.nl/dossiers/dossier/toerisme/fdcc54a1-5aa7-4ddf-af16-1c28a99b8c5f/?term=toerisme).

For our estimation procedure and counterfactuals, we narrow down the set of amenities to six: restaurants, bars, food stores, non-food stores, nurseries, and “touristic amenities.” First, we chose these categories because they are available at a granular spatial unit for the whole time period in our sample (many categories are not reported every year nor at every administrative subdivision). Second, these categories likely vary in the extent to which they cater to tourists versus different types of locals. “Touristic amenities” is a category defined by ACD that includes tourist-oriented business such as travel agencies, cultural/recreational establishments, and lodging. We remove lodging from the original ACD definition because we treat hotels separately in our analysis—we consider them solely as accommodation for tourists rather than as a consumption amenity that could potentially be valued by both tourists and locals. Thus, our final measure of touristic amenities consists of consumption services that some locals may value, such as cultural/recreational establishments. Bars includes pub-style establishments that serve only alcohol, as well as cafe-style establishments that serve both coffee and alcoholic drinks, without being full-fledged restaurants. Food stores refers to establishments that sell food without service, such as a grocery or convenience store. Non-food stores refers to non-food commercial retail, such as clothing stores. Restaurants and nurseries are self-explanatory.

Short-Term Rental Listings

Airbnb holds over 80% of the STR market share in Amsterdam. Hence, throughout the paper, we use Airbnb and STR interchangeably. Our Airbnb data are from Inside Airbnb (http://insideairbnb.com/), an independent website providing monthly web-scraped listings data for many cities. Our data consist of listing-level observations with information such as geo-coordinates, prices per night, calendar availability, and reviews. We use this information to separately identify “active” from “dormant” STR listings, and to flag commercially-operated listings—those likely to be permanently rented to tourists, thus reducing housing supply for locals. We define commercial listings as entire-home listings with booking activity above a threshold. Classification details are in Supplemental Appendix A.2.7.

Final Sample: Time Period and Geographic Unit of Analysis

We construct an annual panel of location choices and characteristics for 2008–2018. For our dynamic model of locals' residential choices, we aggregate 95 neighborhoods (wijk) into 22 districts (gebied). Using larger geographical units allows us to estimate more precise conditional choice probabilities that feed into the estimation of the dynamic model. Because demand is at the district level, we also use districts in the estimation of amenity supply. Our estimation of housing supply and tourist demand only requires unconditional choice probabilities. Thus, for those cases, we use the smaller neighborhoods as spatial units, allowing us to obtain more precise estimates.

Fact 1: Tourists and STR Listings Have Grown Dramatically and Sprawled Across Amsterdam

Amsterdam has one of the highest tourist-to-local ratios in the world, above Florence and slightly below Venice (source: ESTA (https://www.official-esta.com/information/reports/cities-with-most-tourists)). Figure 1 shows that, between 2008 and 2017, the number of overnight stays per resident doubled, hotel capacity grew from approximately 22,000 to to 31,000 rooms, while STR listings grew from zero to over 25,000. The figure also shows the evolution of commercially-operated listings, which are available year-round and therefore comparable to hotel rooms in terms of nights-availability. By 2017, there were approximately 7000 of these listings, which is equivalent to 25% of the city's stock of hotel rooms.

Figure 2 shows commercial listings have sprawled to cover most of the city. By contrast, the spatial distribution of hotels remains mostly unchanged and clustered in the city center. This is partly due to zoning regulations that apply to hotels but not to the STR segment. At the aggregate level, commercially-operated STR listings represented 6% of the rental market in 2017, exceeding 20% in some central neighborhoods. These trends suggest the increasing presence of tourists as part of the city's population is significant enough to alter local housing and amenity markets.

Fact 2: Rents Have Increased More in Neighborhoods With More STR Entry

Table I shows the intensity of STR penetration is positively correlated with housing market outcomes. OLS regressions in the top panel show a 1% increase in a neighborhood's commercial STR listings is associated with a rent increase between 0.06–0.11%. These magnitudes are sizable given rents grew at an annualized rate of 1.02% between 2009–2019, and are also in line with recent studies estimating the effect of STR on housing market prices. For example, Barron, Kung, and Proserpio (2021) estimated an STR elasticity of rent of 0.018. The bottom panel of Table I repeats the regression exercise for sale prices, finding a 1% increase in commercial STR listings is associated with a house sale price increase between 0.04–0.11% in OLS specifications.

The main endogeneity concern from the OLS results is that time-varying neighborhood-level unobservables correlate with both STR penetration and housing market prices, leading to biases that depend on the sign of such correlations. For example, if neighborhoods that are becoming more attractive to tourists are becoming less attractive to locals, then such areas will have more STR and lower rent, leading to downward-biased OLS estimates. Beyond including controls that likely correlate with such unobservables, we address these concerns with a shift-share instrument (Goldsmith-Pinkham, Sorkin, and Swift (2020), Borusyak, Hull, and Jaravel (2022)), a common research design in the literature measuring the impact of STR on housing markets (Barron, Kung, and Proserpio (2021), Garcia-López et al. (2020)).

The “shift” part of the instrument exploits time variation in worldwide demand for STR, as proxied by online search activity for Airbnb. The “share” part constructs neighborhood-level exposure to tourism by using the spatial distribution of historic monuments. Our exclusion restriction requires both factors to be orthogonal to time-varying and neighborhood-level unobservables, conditional on the rest of the covariates. First, Airbnb's worldwide popularity is unlikely to be informative of neighborhood-specific trends. Second, the spatial distribution of monuments determined centuries ago is unlikely to be informative of current trends affecting housing prices. Our results indicate the OLS estimates are downward-biased. This is consistent with the unobservables being positively correlated with Airbnb presence and negatively correlated with housing market prices, that is, they are likely dis-amenities for local residents.

Finally, note the reduced-form results from Table I capture the total impact of STR. This is a combination of (i) less housing supply for locals, which raises rents, and (ii) changes in amenities, which can raise or lower rents depending on how locals value such amenities. This limitation of the reduced-form analysis is what motivates our model, with which we aim to disentangle these two channels.

Fact 3: Amenities Have Tilted Toward Tourists and Away From Locals

Beyond the impact of STR on the housing market, the amenities surrounding the housing units have also changed as tourists become an increasing share of the city's population.

Figure 3 shows touristic amenities have grown across nearly all neighborhoods, although at different intensities, while amenities catering exclusively to locals, such as nurseries, have declined in most locations. Figure 4 confirms touristic amenities indeed locate in neighborhoods with high tourist intensity, and that their growth is negatively correlated with amenities that are clearly targeted to locals, such as nurseries. Overall, these patterns are consistent with tourists having different preferences over amenities than locals. As for the other four amenities displayed in Figure 3, they are likely in between the two extremes of touristic amenities and nurseries in the sense they would not a priori seem to cater solely to locals or solely to tourists, but likely to both. The purpose of our amenity supply model is to estimate the extent to which amenities such as these lie in between the two extremes, given the observed trends can be explained by both an increasing number of tourists arriving to the city and specific types of local residents departing.

Fact 4: The Composition of Residents Has Changed Heterogeneously Across Neighborhoods

Figure 5 shows how socioeconomic composition has evolved in each neighborhood by displaying changes in the population shares of various demographic groups. The top panel shows a falling share of residents with Dutch background in most neighborhoods, except those around the city center. By contrast, the share of non-European immigrants has increased in a few central neighborhoods and mostly in the periphery. In terms of income heterogeneity, the middle panel shows the share of residents in the top 20% of the national income distribution has grown in central neighborhoods but not in the outskirts, indicating a rise in income inequality between the core and periphery. The bottom panel shows heterogeneity along household composition: households with children have become increasingly outnumbered by those without in most neighborhoods.¹ To summarize, the heterogeneity in the socioeconomic make-up of neighborhoods and in their evolution over time motivates the heterogeneity in our model's demand primitives: rent elasticities, moving costs, and valuation of amenities.

Notation

We present the model in three steps. First, Section 4.1 shows how amenities $$ are endogenously determined by the population composition $$. Second, Sections 4.2 and 4.3 show the reverse mapping—how population composition adjusts to amenities through location choices. Third, Section 4.4 brings the two mappings together by providing an equilibrium definition through which population composition and amenities are jointly determined.

Demand for Amenities

Supply of Amenities

Equilibrium Amenities

Housing Supply in Each Location

Moving Costs and Location Tenure

Individual State Variables

We denote $$ as the vector of individual state variables that are observable to the econometrician: location $$ and tenure $$. Households also face a vector of unobservable idiosyncratic preference shocks for each location, $$.

Aggregate State Variables

Flow Utility and Value Function

Location Choice and Evolution of the Population

Housing Demand From Locals in Each Location

Tourists in Short-Term Rentals

Tourists in Hotels

Housing Demand From Tourists in Each Location

Results

Table II shows the six household types that result from our classification and summary statistics of their average characteristics. We give each group a label based on how prominent their characteristics are. For example, the “Students” group is characterized by being the youngest and lowest-income, while also being high-skilled and unlikely to have children. Among household types likely to have children, social housing tenants have the lowest income and are less likely to have a Dutch ethnic background. Moving up the income distribution, we have a group of middle-aged homeowners that do not have children, which we label as “Singles.” Next, we have a group of renters that are slightly older and wealthier, but have substantially more children, which we label as “Younger Families.” Finally, the highest-income group consists of older homeowners likely to have children, which we label as “Older Families.” Overall, the six types vary substantially along income, share with children, and age.

Household Types Used in Estimation and Counterfactuals

We estimate the housing demand of local residents, presented in Section 4.3.1, for the first three groups: “Older Families,” “Singles,” and “Younger Families.” The reason for excluding “Students” and the two social housing types is that their residential choices are driven by non-market forces outside the scope of our model. The location choices of “Students” are largely determined by university policy. As for social housing tenants, their units are assigned through a centralized application system.

Despite the exclusion of these three groups in the housing demand estimation, we include all six groups—along with tourists in hotels and in short-term rentals—in the estimation of the amenity supply model described in Section 4.1. The reason is that while residential choices might not be primarily determined by market mechanisms for all groups, as indicated in the prior paragraph, the decisions of firms supplying consumption amenities do take into account all groups regardless of how they make their housing choices. Throughout this Section 5, we show our procedure estimates housing demand and amenity supply in separate and independent blocks: estimating amenity supply only requires neighborhood-level data on population composition, so our sample restriction on the microdata for estimating housing demand does not affect our amenity supply estimates.

Finally, for our counterfactuals, we include all six types of locals and tourists as part of our equilibrium definition. Because we do not have preference estimates for students and the two social renter types, we take their location choices as exogenously fixed to levels observed in the baseline data. Given we do not estimate preferences for these groups, we do not make any statements about their welfare effects in our counterfactuals. Our interpretation of keeping the locations of these groups fixed in counterfactuals is that their residential outcomes are determined by an allocation mechanism that does not respond to market forces. Therefore, our counterfactuals should be interpreted as addressing equilibrium responses from the part of the housing market that is determined through market mechanisms.

Identification

First, similarly to Couture et al. (2024), we calibrate η. We solve our fully estimated model for a range of $$, which is based on the range of supply elasticities from Saiz (2010). We choose $$ since it delivers the best model fit, corresponding to a housing supply elasticity of 0.66, the estimate for San Francisco in Saiz (2010).⁵ In Supplemental Appendix A.7.1, we show that the main takeaways from our counterfactuals are robust to the full range of $$.

The main identification problem in identifying $$ from (24) is simultaneity arising from the equilibrium conditions. The expenditures by household type for a given location, $$, are the outcome of residential choices made based on the availability of amenities $$. Hence, any unobservable firm costs $$ affecting $$ will also affect $$ (and thus $$) in equilibrium. Because $$ is an amenity supply shock, we require instruments that act as amenity demand shifters.

Implementation

Results

Our estimates for the $$ parameters are shown in Table III and broadly align with expected differences in consumption patterns across demographic groups. First, the supply of Nurseries, which is likely the amenity most targeted to locals—and specifically those with children—responds most positively to the three family groups and least to Singles and Tourists. Second, Touristic Amenities respond strongly to Tourists, as expected, but also to Students and Singles that might plausibly have similar consumption patterns to those of Tourists. Third, Restaurants respond mostly to Singles, Students, and Tourists, while Bars respond mostly to Tourists. Fourth, Food Stores estimates are the most homogeneous in that they respond to all groups in similar magnitude. This is consistent with the notion that they provide products (groceries) that are demanded homogeneously across all socioeconomic strata. In terms of magnitudes, our parameter estimates imply an exogenous increase in the number of tourists city-wide by 10% would increase the number of firms in Touristic Amenities, Restaurants, Bars, Food Stores, Non-food Stores, and Nurseries by 2.3%, 0.5%, 2.3%, 0.9%, 2.9%, and 0%, respectively.

Observe that, of the 42 $$ coefficients in Table III, we have several zeros because our constrained optimization problem places some coefficients on the lower bound of zero. Our interpretation is that if a $$ coefficient hits the lower bound, then it means the supply of sector-s amenities does not respond to the presence of type-k residents. Through the lens of our amenity demand model from Section 4.1, this non-response occurs because a coefficient of $$ implies type-k agents do not spend any of their income on sector-s amenities. Choosing a lower bound larger than zero would ensure $$ and thus guarantee positive amenity expenditure shares, but we choose not to do so because this would restrict the parameter space.

Finally, while we cannot directly test the exclusion restriction of equation (25), we can provide suggestive evidence that our instrument is uncorrelated with the unobservable component of fixed costs faced by firms. To the best of our knowledge, the main change in amenity regulations during 2008–2018 was a restriction in the operating hours of restaurant outdoor dining space in residential areas. These restrictions were imposed at the precinct level, a spatial unit larger than the districts at which we implement our estimation. Hence, we can use precinct-year fixed effects to control for the unobservable costs imposed by such regulations on the firms supplying amenities. In Supplemental Appendix A.7.2, we show that including precinct-year fixed effects does not significantly change our estimates from Table III. We interpret this as suggestive evidence that our instruments are not significantly correlated with the unobservable fixed costs faced by firms: if they were, the precinct-year fixed effects would have changed our results significantly, given we know that amenity regulations were indeed modified at the precinct level during this period.

Assumptions

We assume the state variables $$ follow a Markov process, along with the following standard assumptions:

Our ECCP estimator is a two-step estimator. First, we estimate conditional choice probabilities (CCP) directly from the data, using a multinomial logit that exploits information about the conditional state. We show in Supplemental Appendix A.6.4 that this approach reduces the finite sample bias relative to a non-parametric approach that estimates CCP using frequency estimators. Second, the CCP are plugged into a regression equation that relates differences in the likelihood of two different residential histories to differences in their flow payoffs. To derive this regression equation, we first introduce the concept of renewal actions.

Renewal Actions

Two paths of actions are said to exhibit finite dependence if after a finite number of periods, the distribution of future states is the same (Arcidiacono and Miller (2011)). In our model, finite dependence appears whenever two households living in different initial locations, j and $$, choose to move to the same new location $$. We call such an action a renewal action, because the location tenure is reset and the distribution of future states is the same for both households. Because expectations of future payoffs are unobservable to the econometrician, a key difficulty in estimating dynamic models is disentangling variation in current payoffs from continuation values. Renewal actions separate these two components by equalizing continuation values, thus leaving differences in choice probabilities being solely a function of differences in flow payoffs.

Concretely, let $$ be the function that maps action j and state $$ to current location capital. Consider the following path represented by Figure 6: let j and $$ denote actions chosen at state $$, reaching states $$ and $$, respectively, and let $$ be a renewal action chosen at time $$.

The key observation is that at time $$, when two agents of the same type k choose the renewal action $$, they both move to the same individual state and hence their future expected payoffs are the same. Therefore, the value functions from each path cancel each other out at $$ and disappear from equation (26), which states that differences in the likelihood of path $$ relative to path $$ are explained solely by differences in flow utility.

Parametric Assumptions on Flow Utility

Implementation

In practice, the locations in our empirical application are Amsterdam's 22 districts (“gebied”) and our sample period is 2008 to 2018. We define the outside option as any location outside Amsterdam, and our market as households that have lived in Amsterdam at least once between 2008 and 2020. We set our discount value β equal to 0.85 (De Groote and Verboven (2019), Diamond, McQuade, and Qian (2019)). We discretize the location tenure space similarly to Rust (1987), defining two bins of location capital: less than three years of tenure or more than four. Supplemental Appendix A.6.2 shows the technical details of the discretization of the state space. Overall, each group has a total of 46 states per year (23 past locations times two location capital states). We focus on the first three groups—Older Families, Single Households, and Younger Families—because their location choices are primarily driven by market forces, in contrast to households living in social housing or university housing. Note our Older Families and Singles groups are homeowners. In treating their location decisions in the same way as those of renters, we are implicitly assuming they are renting to themselves.

Identification

Results

Table IV shows estimates of the preference parameters in (29) over moving costs, location capital, rent, and consumption amenities for our main three groups. All groups exhibit that moving is costly, with costs that increase with distance between past and current location. All households benefit from the accumulation of location capital. Estimates for rent are negative throughout.

Moving on to preferences over amenities, note the coefficients $$ from (29) capture the sum of (i) a positive effect from the direct consumption of the amenity, and (ii) indirect spillovers that the amenity brings along (e.g., noise from bars) which can be negative. As discussed when we analyzed equation (28), this explains why the signs of the coefficients in Table IV can be negative.

Moving beyond the interpretation of the sign of the amenity coefficients, comparing the intensity of preferences across household types requires translating the estimates from Table IV into willingness to pay (WTP) measures. Concretely, the WTP of group k for amenity sector s is computed as the ratio $$. Using our WTP measure, the coefficients from Table IV imply that the two family groups are willing to increase their rent by roughly 0.14% in exchange for a 1% increase in the number of nurseries, while the WTP of singles for nurseries is only 0.02%. Restaurants show a positive and significant coefficient for Singles, with a WTP of 0.3% more in rent for a 1% increase in the number of restaurants. For the other groups, the WTP for restaurants is closer to zero. The first two groups perceive a net negative payoff from Touristic Amenities, while the Younger Families exhibit a positive one. In terms of economic magnitude, the first two groups have a WTP of 0.1% and 0.2% more in rent to avoid a 1% increase in Touristic Amenities, respectively. Non-food stores are positively valued by all groups, with the highest WTP for Younger Families. Coefficients for bars are negative for all groups, suggesting the presence of negative spillovers associated with these amenities, such as noise, that outweigh their consumption benefits. Finally, coefficients for food stores are negative for all groups. Despite the signs being negative, the ordering is fairly intuitive: the WTP of the family groups for food stores is higher (i.e., less negative) than for singles.

Instruments

OLS estimation leads to simultaneity bias from regressing quantities on prices. The solution is an instrument that shifts relative demand for short- versus long-term units. We use predicted tourist demand from a shift-share instrument: the “shift” part of the instrument exploits time variation in worldwide demand for STR as proxied by online search volume (Barron, Kung, and Proserpio (2021)), while the “share” part constructs neighborhood-level exposure to the shift from the historic spatial distribution of touristic attractions. The relevance condition is straightforward: higher predicted demand of tourists raises short- relative to long-term rental prices. The exclusion restriction holds as long as changes in the predicted tourist demand are uncorrelated with changes in the unobservable costs driving landlords' decisions. Intuitively, the exposure measure is unlikely to be correlated with changes in landlords' relative costs of renting short versus long term.

Results

For this section, we end our estimation sample in 2017 because by the end of this year the Amsterdam municipality began to restrict the number of nights that landlords could rent to tourists. We do this to estimate our housing supply elasticity during a period with a stable policy environment, thus avoiding changes in supply that are responding to regulatory changes rather than price changes. Table VI presents estimates for α, the landlord's marginal utility of income. OLS estimates are downward-biased compared to IV, as expected with simultaneity bias. Our preferred specification is the IV with two-way fixed effects, despite it being less significant than the others, which likely occurs due to little within-neighborhood variation in a short panel. Reassuringly, though, IV estimates are fairly stable across all specifications. In terms of economic significance, the results imply that an increase in the gap between STR prices and long-term rental prices of one standard deviation—which is equivalent to a 29% increase—would raise the market share of the short-term relative to the long-term segment by 13.6%.¹²

Amenity Quality

We do not consider quality differences within an amenity sector because we do not have the firm-level data required to incorporate this dimension. Hence, in our model, amenities are only differentiated horizontally. If we had quality data, then the nature of differentiation across amenities would be a mix of horizontal and vertical dimensions. How would this affect our takeaways? Note our counterfactual in Section 6.1 speaks to this because it shows how the degree of horizontal differentiation (measured as the degree of preference heterogeneity) matters for sorting and inequality. To the extent adding amenity quality is a way of dampening horizontal in favor of vertical differentiation, because quality is desired by all groups, we would expect our results to qualitatively change in the direction of the case of homogeneous preferences—there would be less scope to reduce inequality through sorting and the horizontal differentiation of neighborhoods.

Non-Stationarity and Transitional Dynamics

The role of our model's dynamic elements is to estimate unbiased preference parameters (Bayer et al. (2016), Traiberman (2019)). To highlight economic mechanisms, our counterfactuals focus on stationary equilibria. The reason is that we are interested in long-run changes that result from the interaction between preference heterogeneity and endogeneity of amenities. It is the cross-sectional correlation between preferences over amenities and supply responses of amenities to demographics that is at the core of our economic mechanisms. It is unclear a priori that introducing transitional dynamics would significantly change the qualitative nature of our mechanisms, beyond separately quantifying short- versus long-run impacts. Given the stationary analysis already imposes substantial technical complexity, as well as conceptual complexity in understanding how each model ingredient contributes to economic mechanisms, we leave transitional dynamics as an interesting avenue for future research.

Consuming Amenities Outside the Residential Location

We assume consumers only access amenities in their residential location. An empirical application that relaxes this assumption requires data on consumption trips across neighborhoods, which we do not have for Amsterdam. Note that our mechanisms are driven by the positive correlation between residential location and amenity consumption. Under our assumption of no commuting to consume, the correlation is perfect. Allowing for commuting would weaken this relationship, but part of the correlation would survive as long as commuting costs depend on distance from home. While we cannot quantify such costs in our setting due to data limitations, smartphone-based evidence from other cities suggests urban residents tend to consume amenities located near their home (Miyauchi, Nakajima, and Redding (2021), Allen et al. (2021)). To the extent this positive correlation between residential location and amenity consumption is also valid in our setting, we expect our main qualitative insights to hold. Finally, abstracting away from the commuting-to-consume margin is likely to be less problematic for the fairly large spatial units used in our analysis, although it is worth noting the use of larger units may reduce the scope for horizontal differentiation.