Location Sorting and Endogenous Amenities: Almagro & Dominguez-Iino (2025)

What this is. The paper’s core results, the structural equilibrium model (endogenous amenities + dynamic location choice), and the estimation equations: enough to understand what was found and how, without reading all 41 pages. To replicate or extend, read the full source at the original.

TL;DR

The paper builds and estimates a dynamic spatial equilibrium model of Amsterdam in which heterogeneous households make forward-looking residential choices and firms endogenously supply consumption amenities (restaurants, bars, nurseries, touristic venues, food and non-food stores) in response to the neighborhood’s demographic composition. Using restricted Dutch administrative microdata (CBS) linked to neighborhood amenity counts (ACD BBGA) and short-term rental listings (Inside Airbnb), and exploiting tourist inflows as a demand shifter via a shift-share instrument, the paper shows: (1) short-term rental (STR) penetration raises rents 0.09-0.21% per 1% growth in listings (IV); (2) tourist presence increases touristic amenities and restaurants but leaves nurseries unchanged; (3) preference heterogeneity across household types increases residential sorting but reduces welfare inequality relative to the homogeneous-preference benchmark, because neighborhoods become horizontally differentiated; and (4) STR entry produces winner-loser welfare splits by household type once amenity adjustment is allowed: the highest-income group (Older Families) loses 4% of income while lower-income Singles and Younger Families gain 1-2%. The paper extends prior work by Guerrieri, Hartley, and Hurst (2013) and Diamond (2016) by microfounding how different amenity types respond to demographic heterogeneity.

Core results

Magnitudes and significance are as reported; \* = 5%, \*\* = 1%. Locators point into the source PDF.

#	Result	Locator	Magnitude
R1	STR penetration raises neighborhood rents (IV); OLS is downward-biased, consistent with tourist-attractive areas becoming locally less attractive to residents	Table I, p.1038	IV (full controls + district-year FE): coeff = 0.205 (SE 0.093), F = 69.66; OLS = 0.109 (SE 0.018); range across specs: 0.091-0.205
R2	STR penetration raises house sale prices (IV); OLS severely underestimates the price effect	Table I, p.1038	IV (full controls + district-year FE): coeff = 0.326 (SE 0.102), F = 65.9; OLS = 0.037 (SE 0.022); range: 0.149-0.326
R3	Tourist presence drives supply of touristic amenities but not nurseries; supply responses are sectorally differentiated by the demographic type driving demand	Table III, p.1054; text p.1053	10% more tourists: +2.3% touristic amenities, +0.5% restaurants, +2.3% bars, +0.9% food stores, +2.9% non-food stores, 0% nurseries
R4	Heterogeneous preferences increase residential sorting but reduce welfare inequality relative to the homogeneous benchmark; horizontal neighborhood differentiation is the mechanism	Figure 9, p.1064; Table VII, p.1065	Entropy index: 0.8 (heterogeneous) vs 0.4 (homogeneous); welfare gap (max/min consumer surplus): ~1 vs ~10; Gini indices rise for 5 of 6 amenity sectors under heterogeneous preferences
R5	STR entry produces welfare gains for younger/lower-income households and losses for older/higher-income households once amenity endogeneity is accounted for; direction reverses vs the exogenous-amenity benchmark	Figure 10, p.1066	Older Families: -4% income CE loss; Singles: +1-2% CE gain; Younger Families: +1-2% CE gain; under exogenous amenities all lose 1-2% (dark bars in Figure 10)

Overall (paper’s conclusion). Two-way heterogeneity, in household preferences and in amenity supply responses, determines both the degree of horizontal differentiation across neighborhoods and the distributional incidence of urban policies. Low-income households may gain rather than lose from STR entry if the amenities tourists bring align with their preferences, reversing naive predictions based on rent effects alone. The amenity channel matters for incidence qualitatively, not just quantitatively.

Theory / model

The model has three blocks: endogenous amenity determination, housing supply, and household/tourist location demand. There are $J+1$ locations ($J$ inside the city plus an outside option) and $K+1$ household types ($K$ local types and a tourist type $T$). The population composition of location $j$ at time $t$ (equation 1, p.1042) is:

$$M_{jt} \equiv [M^1_{jt}, \ldots, M^K_{jt}, M^T_{jt}]', \tag{1}$$

and the amenity vector (equation 2, p.1042) is:

$$a_{jt} \equiv [N_{1jt}, \ldots, N_{Sjt}]', \tag{2}$$

where $N_{sjt}$ is the number of varieties in amenity sector $s$ at location $j$.

Endogenous amenities. Households have Cobb-Douglas preferences over housing and a composite amenity good, with $\phi^k$ the expenditure share on amenities for type $k$. Within each amenity sector, firms supply differentiated varieties under CES preferences (substitution elasticity $\sigma_s > 1$). Individual demand for variety $i$ in sector $s$ at location $j$ (equation 3, p.1042) is:

$$q^k_{isjt} = \frac{\alpha^k_s \phi^k w^k_t}{p_{isjt}} \left(\frac{p_{isjt}}{P_{sjt}}\right)^{1-\sigma_s}, \tag{3}$$

where $\alpha^k_s$ is type $k$‘s sectoral budget share and $P_{sjt}$ is the sector-location price index. Firms engage in monopolistic competition with free entry, equating variable profits to a fixed cost $F_{sjt}(N_{jt})$ increasing in total firm count $N_{jt}$. The zero-profit condition yields equilibrium varieties (equation 7, p.1043):

$$N_{sjt} = \frac{1}{\sigma_s F_{sjt}} \sum_k \alpha^k_s \phi^k w^k_t M^k_{jt}. \tag{7}$$

This delivers a mapping $a_{jt} = \mathcal{A}(M_{jt})$ (equation 8, p.1043): equilibrium amenities are a function of population composition alone, encoding the preference-externality mechanism.

Housing supply. Absentee landlords choose between the long-term (LT) rental market (income $r_{jt}$ per floor-space unit) and the short-term (ST) market (income $p_{jt}$) subject to an operating cost wedge $\kappa_{jt}$. Under Type I EV shocks, long-term supply (equation 9, p.1044) and short-term supply (equation 10) are:

$$\mathcal{H}^{LT,S}_{jt}(r_{jt}, p_{jt}) = \frac{\exp(\alpha r_{jt})}{\exp(\alpha r_{jt}) + \exp(\alpha p_{jt} - \kappa_{jt})} \mathcal{H}_{jt}, \tag{9}$$ $$\mathcal{H}^{ST,S}_{jt}(r_{jt}, p_{jt}) = \mathcal{H}_{jt} - \mathcal{H}^{LT,S}_{jt}(r_{jt}, p_{jt}). \tag{10}$$

Local household location choice. At each period $t$, household $i$ of type $k$ chooses location $j_{it}$ to maximize discounted expected utility. The flow utility inside the city (p.1044-1045) is:

$$u^k_t(j, x_{it}) = \bar{u}^k_t(j) + \delta^k_\tau \log \tau_{it} - MC^k(j_{it}, j_{it-1}), \tag{11}$$

where $\tau_{it}$ is location tenure, $MC^k$ is a moving cost that combines a bilateral distance-adjusted component and a fixed component, and $\bar{u}^k_t(j)$ collects aggregate state-dependent payoffs. Under Type I EV preference shocks, location choice probabilities (equation 12, p.1045) are:

$$\mathbb{P}^k_t(j|x_{it}) = \frac{\exp\!\left(u^k_t(j,x_{it}) + \beta \mathbb{E}_t[V^k_{t+1}(x_{it+1},\varepsilon_{it+1})|j,x_{it},\varepsilon_{it}]\right)}{\sum_{j'} \exp\!\left(u^k_t(j',x_{it}) + \beta \mathbb{E}_t[V^k_{t+1}(x_{it+1},\varepsilon_{it+1})|j',x_{it},\varepsilon_{it}]\right)}. \tag{12}$$

Stationary equilibrium. A stationary equilibrium (Definition, p.1048) is a vector of long-term rental prices $\mathbf{r}$, short-term rental prices $\mathbf{p}$, amenities $\mathbf{a}$, and stationary population distributions $\pi^k(\mathbf{r}, \mathbf{a})$ for each type $k$, such that the long-term and short-term rental markets clear for every location and $a_j = \mathcal{A}(M_j)$ for every $j$. Population and amenities are thus jointly determined in equilibrium.

Method

Estimation proceeds in three independent blocks.

Amenity supply (GMM). Taking logs of equation (7) and parameterizing the fixed cost as $F_{sjt}(N_{jt}) = \Lambda_j \Lambda_t R(N_{jt}) \Omega_{sjt}$ with $R(N_{jt}) = N^\eta_{jt}$, the estimating equation (equation 24, p.1051) is:

$$\log N_{sjt} = \lambda_j + \lambda_t - \eta \log N_{jt} + \log\!\left(\sum_k \beta^k_s X^k_{jt}\right) + \omega_{sjt}, \tag{24}$$

where $X^k_{jt} \equiv \phi^k w^k_t M^k_{jt}$ is total amenity expenditure by type $k$ in location $j$, $\beta^k_s \equiv \alpha^k_s / \sigma^s$ captures how type $k$‘s expenditure converts to amenity supply in sector $s$, and $\omega_{sjt}$ is an unobservable supply shock. The key endogeneity concern is that $\omega_{sjt}$ shifts firm costs and thus residential composition $M^k_{jt}$ simultaneously. The instrument is $Z^k_{jt} = w^k_t S^{\gamma(k)}_{jt}$, the interaction of type $k$‘s wages with the housing stock of its modal tenancy status $\gamma(k)$, exploiting the idea that neighborhoods composed primarily of social housing attract households qualifying for social housing assistance. GMM is implemented on a three-way panel of 22 districts for 2008-2018. The housing supply inverse elasticity $\eta = 1.52$ is calibrated from Saiz (2010).

Housing demand from locals (ECCP). The method builds on eccp-estimator (Aguirregabiria and Mira (2010), Scott (2013), Kalouptsidi, Scott, and Souza-Rodrigues (2021b)). The parametric flow utility (equation 27, p.1056) for type $k$ in location $j \neq 0$ is:

$$\bar{u}^k_t(j) = \delta^k_j + \delta^k_t + \delta^k_r \log r_{jt} + \delta^k_a \log a_{jt} + \delta^k_b \log b_{jt} + \xi^k_{jt}, \tag{27}$$

where $\delta^k_a = [\delta^k_1, \ldots, \delta^k_s, \ldots, \delta^k_S]$ is the vector of amenity preference parameters (one per sector). Exploiting renewal actions (household pairs who at $t+1$ choose the same new location $\tilde{j}$, so their continuation values cancel), the estimating equation (equation 29, p.1057) is:

$$Y^k_{t,j,\tilde{j},x_{it}} = \delta^k_j + \delta^k_t + \delta^k_r \log r_{jt} + \delta^k_a \log a_{jt} + \delta^k_b \log b_{jt} + \delta^k_\tau \Delta\tau_{it} - \Delta MC^k_{it} + \tilde{\xi}^k_{t,j,\tilde{j},x_{it}}, \tag{29}$$

where $Y^k$ is the log ratio of path likelihoods for the two paths diverging from state $x_t$ and converging at $\tilde{j}$ in period $t+1$, and $\Delta\tau_{it}$ is the change in location capital (tenure). The left-hand side is formed from conditional choice probabilities estimated via multinomial logit. Seven instruments are used to address endogeneity of rents and amenities: three post-2011 rental-market policy dummies (social-housing reclassification 2011, rent deregulation 2015, STR regulation 2017) interacted with lagged tenancy stock, plus removal of housing units inside and outside the precinct. First-stage F-stat = 169.8.

Housing supply. From equation (9)-(10), the log ratio of long- to short-term supply shares gives (p.1061):

$$\log \mathcal{H}^{LT,S}_{jt} - \log \mathcal{H}^{ST,S}_{jt} = \alpha(r_{jt} - p_{jt}) + \kappa_j + \kappa_t + \nu_{jt}.$$

The instrument for the relative price $r_{jt} - p_{jt}$ is predicted tourist demand from a shift-share following Barron, Kung, and Proserpio (2021): the “shift” is Airbnb worldwide search volume; the “share” is neighborhood-level exposure from the historic spatial distribution of touristic attractions. IV estimate (two-way FE preferred spec): $\hat{\alpha} = 0.385$ (Table VI, p.1062), implying a 1 SD increase in the STR-LT price gap (29%) raises the short-term market share by 13.6%.

Household type classification. Six types are identified using k-means-clustering on income, skill, household composition, and ethnicity from CBS tax returns (Table II, p.1050): Older Families, Singles, Younger Families (market-determined types used in structural estimation) and Students, Immigrant Families, Dutch Low Income (treated as exogenous allocation in social-housing/university assignment). Discount factor $$\beta = 0.85$.

Empirical specifications

Reduced-form STR rent effects (R1, R2). The estimating equation for Table I (p.1038) is:

$$\ln Y_{jt} = \beta \ln(\text{Commercial Airbnb listings}_{jt}) + \gamma X_{jt} + \mu_{dt} + \varepsilon_{jt},$$

where $Y_{jt}$ is either rent/m² or house sale price, $X_{jt}$ includes housing stock, average income, and high-skill population share, and $\mu_{dt}$ are district-year fixed effects. Standard errors are clustered at the wijk (neighborhood) level. The shift-share IV for Airbnb listings uses worldwide Airbnb search volume as the shift and the spatial density of historic monuments as the neighborhood share. First-stage F-stats exceed 65 in all IV specifications.

Amenity supply estimation (R3). GMM on equation (24) for 6 amenity sectors simultaneously, using the district-level panel 2008-2018. Parameter $\beta^k_s$ captures how a 1% increase in type $k$‘s expenditure on location $j$ changes the number of sector-$s$ firms. The economic magnitude is translated to tourist effects in the text (p.1053): a 10% increase in city-wide tourists shifts amenity composition toward touristic and retail amenities and away from nurseries.

Preference heterogeneity and sorting/inequality counterfactual (R4). Two equilibria are compared: the baseline with heterogeneous amenity preferences (from Table IV estimates) against a homogeneous-preference counterfactual in which $\delta^k_a$ is replaced by its population-weighted average. Sorting is measured by an entropy index (Figure 9, p.1064); welfare inequality is the ratio of the highest to lowest consumer surplus in euros across household types.

STR welfare decomposition (R5). Three equilibria are compared step by step: (i) pre-STR equilibrium $(\mathbf{r}_0, \mathbf{a}_0)$; (ii) post-STR with exogenous amenities $(\mathbf{r}_1, \mathbf{a}_0)$; (iii) post-STR with endogenous amenities $(\mathbf{r}_1, \mathbf{a}_1)$. Welfare is measured in consumption equivalent (CE) terms: how much extra income a household in the pre-STR equilibrium must receive to be as well off as in the counterfactual. Positive CE values indicate welfare gains. Homeowners receive back landlord income from rent increases; renters do not (Supplemental Appendix A.5, p.1065).

Datasets used

Dataset	Role in paper	Wiki page
CBS residential cadaster (Centraal Bureau voor de Statistiek, Netherlands)	Individual-level annual residential histories for universe of Dutch residents; key panel for location choice estimation	no page yet
CBS tax return data	Household income, educational attainment, employment status, ethnic background; source for household type classification	no page yet
CBS housing unit tax appraisal panel 2006-2020	Property values, tenancy status, geo-coordinates, quality measures for universe of Dutch residential units	no page yet
CBS national rent survey 2006-2019	Rental prices per neighborhood; imputed via random forest and CBS valuations (Mullainathan and Spiess 2017)	no page yet
Amsterdam City Data BBGA (ACD)	Annual neighborhood-level demographics, amenity establishment counts, tourist inflows; 95 wijk / 22 districts, 2008-2018; publicly available at ACD BBGA	no page yet
ACD Tourism data	City-level tourist overnight stays and hotel room counts; public via ACD Tourism portal	no page yet
Inside Airbnb	Monthly web-scraped listing-level STR data for Amsterdam (prices per night, calendar availability, reviews); used to construct commercial listings time series	no page yet

Sample period: 2008-2018 (annual). Household type classification uses the CBS panel of 672,093 households. Amenity supply estimated on 22 districts. Housing demand estimated on 22 districts with 46 individual states per type per year.

When to read the full paper

Read the original if you are: (i) building a structural spatial equilibrium model with endogenous amenities and need the full equilibrium existence/uniqueness arguments (Supplemental Appendix A.4); (ii) running welfare counterfactuals for STR regulation in a city with heterogeneous amenity demand and need the CE calculation formulas (Supplemental Appendix A.5); (iii) implementing the ECCP estimator for dynamic location choice and need the finite-dependence / renewal-action derivation (Supplemental Appendix A.6); or (iv) using CBS microdata or ACD BBGA for Amsterdam and need the exact variable construction (Supplemental Appendix A.2). Tables I, III, IV, VI are the main empirical anchors; Figures 9, 10, 12 are the main counterfactual exhibits.

Attribution and rights

Source: peer-reviewed, Econometrica 93(3) (May 2025). This distillation was extracted by an LLM on 2026-06-26 and is not human-verified or independently reproduced. The CC BY-NC-ND 4.0 licence permits non-commercial use with attribution and no modifications; the verbatim PDF is not hosted here.

Attribution (CC BY-NC-ND 4.0). Almagro, Milena, and Tomás Domínguez-Iino. “Location Sorting and Endogenous Amenities: Evidence From Amsterdam.” Econometrica 93, no. 3 (May 2025): 1031-1071. DOI: 10.3982/ECTA21394. © 2025 The Authors. Licensed under CC BY-NC-ND 4.0. This page is a distillation by the Institute for Automated Research: core results extracted and re-expressed. The licence prohibits modifications and commercial use; this extract is used for non-commercial research reference only.