Project Frontier Jorge Menéndez-Pidal

WP-001 · Working Paper · October 2026

Building or Squeezing? How Spain Absorbed Two Immigration Waves

The Incidence of Population Shocks in Local Housing Markets

Jorge Menéndez-Pidal

Abstract

When a local housing market receives a population shock, the shock is absorbed by new construction, by conversion of the existing stock, by households consuming less space and by the movement of other residents, and prices move until these margins exhaust it. I develop a spatial-equilibrium framework in which these shares have a closed form and sum to one, and I estimate it for Spain’s two immigration waves with a 2003–2024 panel of 50 provinces and a shift-share instrument based on settlement by country of birth. In 2003–2008 each unit of inflow was matched by about 0.7 units of new housing. In 2015–2024 the construction margin closed: the dwelling-stock response is zero, and administrative starts and completions respond to inflows only in provinces that came out of the 2008 bust with little unsold new housing. The current wave has been absorbed by squeezing instead. In the population register, persons per household rise by 0.84% for each 1% of population arriving, and each 1% raises rents by about 1% and house prices by about 4% cumulatively. Natives move towards receiving provinces, which amplifies the shock; with that reallocation the model matches the rent response only if space per household is about four times as elastic as standard calibrations assume. Neither topography nor vacant urban land predicts the response across provinces, so the paper reads the collapse between waves as a fall in effective supply elasticity without identifying a single cause. The rent burden falls mainly on the bottom income deciles and on households headed by people under 45.

Keywords housing supply elasticity, immigration, crowding, spatial equilibrium, incidence, housing overhang, shift-share

No.
WP-001
Date
01.10.2026
Status
Draft v2
Area
Housing Economics
Fields
Urban · Labor · Public economics
Method
Spatial equilibrium · shift-share IV
Data
50 Spanish provinces, 2003–2024
JEL
R21 · R23 · R31 · J61 · H22

01The question

Not “does immigration raise house prices?” but: when a local housing market receives a demand shock, what determines how much of it becomes prices, how much becomes construction, and how much becomes people?

Immigration is the main shock in the Spanish case, but the mechanism is general. Refugees, students, remote workers, a new university or a tech boom are all population shocks. The paper studies how the same shock produces very different outcomes depending on a market's capacity to build.

Housing supply elasticity is not merely a determinant of house prices. It is a determinant of how economies absorb population growth.

02The mechanism

In a spatial-equilibrium model, arrivals lower wages slightly (labour demand elasticity \(\sigma\)) and raise housing demand (demand elasticity \(\varepsilon\)). Residents compare their wage net of housing costs and some relocate (mobility \(\kappa\)). New supply responds with elasticity \(\eta\). The price response to a migration shock \(\tilde m\) is:

Central object \[\hat p = \beta(\eta)\,\tilde m, \qquad \beta(\eta)=\frac{1}{\eta+\varepsilon+\kappa\left(\frac{\eta+\varepsilon}{\sigma}+s\right)}\]

Every term in the denominator is an absorption valve. A more elastic supply \(\eta\), more elastic demand for space \(\varepsilon\) or greater mobility \(\kappa\) all spread the shock away from prices. The three quantity margins add up exactly to the shock:

\[\underbrace{\eta\beta}_{\text{built}}+\underbrace{\varepsilon\beta}_{\text{less space per head}}+\underbrace{\frac{\kappa\Phi}{1+\kappa\Phi}}_{\text{residents relocate}}=1, \qquad \Phi=\frac{1}{\sigma}+\frac{s}{\eta+\varepsilon}\]

Parameters: \(\varepsilon=0.5\), \(\sigma=4\), \(s=0.3\). Spain's mean long-run supply elasticity of about 0.45 is the Banco de España estimate (Annual Report 2025, p. 146). All figures are calibrations of the model, not regression results.

03Two incidences, not one

Supply elasticity governs two distinct responses to the same potential inflow \(\tilde m\):

\[\underbrace{\frac{\partial \hat p}{\partial \tilde m}=\beta(\eta)}_{\text{housing incidence}} \qquad\qquad \underbrace{\frac{\partial \hat N}{\partial \tilde m}=\frac{1}{1+\kappa\Phi}}_{\text{population absorption}}\]

As \(\eta\) rises, \(\beta\) falls and \(\Phi\) falls, so a larger share of the shock materialises as resident population rather than higher housing costs. A place that can build absorbs more people at a lower cost to existing residents.

PrecisionThis concerns the local absorption of a shock that has already arrived, not the decision to migrate to Spain. The claim is “higher supply elasticity increases the share of a migration shock absorbed through population rather than prices,” not “building more attracts more immigration.”

04Two waves as a natural laboratory

Spain received two large immigration waves under very different supply regimes. The model predicts that the difference in supply elasticity alone can produce very different price incidence:

Regimeηβ, priceη·β, construction
1998–2008 (elastic supply)≈ 20.340.68
2015–2026 (current)≈ 0.450.820.37
Rigid supply01.400

Today's price pass-through is about 2.4 times the elastic-supply regime, with half the construction response. This is a prediction of the model. The estimates below support it: the construction response fell from about 0.7 to zero between the two waves.

Rents and prices are treated as separate outcomes. Since \(p=r/c\) and the user cost \(c\) embeds expected growth, the gap between the price and rent responses measures a capitalisation and expectations component, which matters especially in booms.

05Spatial heterogeneity and the absorption index

A 1% population shock has no single effect across Spain. Its incidence depends systematically on each market's capacity to expand supply, \(\beta_i=\beta(\eta_i)\). Combining the price and construction responses yields a provincial supply elasticity, which has not been directly estimated for Spain:

\[\hat\eta_i=\frac{\hat\theta_i}{\hat\beta_i}\]

The paper proposes a Housing Absorption Index, \(HAI_i=f(\eta_i,\kappa_i,\varepsilon,\sigma,s)\), measuring a market's capacity to absorb population without passing the shock mainly into prices. A map of it would show Madrid, Barcelona, Málaga or the Balearics as markets with different capacities to absorb demand, not just different price levels.

Mobility adds a second axis. Low or high \(\eta\) combined with low or high \(\kappa\) gives four kinds of market, and turns a housing-supply paper into a genuine spatial-equilibrium paper. Native responses are modelled as endogenous population reallocation, which can be an outflow, an inflow or neither, rather than assumed displacement.

06Institutions and technology

Rent control redistributes pressure. With a regulated segment R and a free segment F, the key parameter is \(\lambda\), the share of regulated stock that leaves the residential rental market. With \(\lambda=0\) the cap only redistributes the shock. With \(\lambda>0\) the average rent response can rise:

Per 1% arrivalsNo controlλ = 0λ = 0.15λ = 0.3
Free-segment rent1.05%2.63%3.45%5.00%
Average rent1.05%1.05%1.38%2.00%
Units in regulated segment—−2.6%−3.4%−5.0%

ω = 0.6, ηL = 1, κ = 0. Model calculation, not an estimate (Appendix C of the paper). The empirical evidence on regulation rests on four treated provinces.

Remote work relocates demand. A remote worker brings housing demand without local labour supply, so their price impact exceeds an immigrant's by a factor \(\psi(1+\kappa/\sigma)\). The empirical question is where that demand goes. The exposure measure \(\tilde T_m=\Delta T\,\theta_m\) is preferred to the resident share of teleworkers.

Extension: immigration as construction labour. Arrivals raise housing demand but can also expand the construction workforce and so raise \(\eta\). That feedback is currently omitted and is the natural extension.

07Identification

The empirical design uses a shift-share instrument built from historical settlement patterns by country of birth:

\[Z_{it}=\frac{\sum_n \lambda_{ni}\,\Delta M^{(-i)}_{n,t}}{N_{i,t-1}}\]
  • Pre-trend tests, and 2001 base shares alongside alternative base years
  • Leave-one-out construction and Rotemberg weights
  • First-stage strength; robustness to excluding dominant origin countries
  • Shift-share-robust standard errors

08What the data say

Spain's current immigration wave is being absorbed by squeezing, not by building.

Estimated on a 2003–2024 panel of 50 provinces, with inflows instrumented by settlement patterns by country of birth:

Per 1% of population arrivingWave 1, 2003–08Wave 2, 2015–24
Rents, cumulative—+1.05%***
House prices, cumulativenot causal+3.95%***
New construction (HAI)0.71***−0.12
Conversion of existing stock0.940.30
More residents per dwelling (accounting residual)−0.041.82
Persons per household, population register (direct)—+0.84%***
Spain-born adults moving in+0.24***+0.63***
  • Rents rise about 1% per 1% of arrivals, in line with the model and the best existing estimates. Prices rise about four times as much: a capitalisation premium of 1.65 points (shift-share-robust p = 0.002).
  • The construction margin closed. The construction share fell from about 0.7 to zero; the implied short-run supply elasticity is indistinguishable from zero. With the two waves estimated jointly on the same provinces, the fall is significant at 1%.
  • Crowding, measured directly. In the population register, persons per household rise 0.84% for each 1% of population arriving. That is smaller than the accounting residual but still the largest margin of the current wave.
  • Natives move towards receiving provinces, so relocation amplifies the shock rather than absorbing it. Recalibrated with that sign, the model matches the rent response only if space per household is about four times as elastic as the standard calibration assumes.
  • Prices rise more where geography constrains land (+2.3 points per s.d., significant at 10% with shift-share-robust inference), but a planning measure, vacant urban land in 2014, does not moderate the response. The case for supply elasticity rests mainly on the contrast between the two waves. Rent caps and remote work show the predicted signs, imprecisely.
CaveatThe first-wave instrument predicts price growth that preceded the inflow, so first-wave price responses are not interpreted causally. Second-wave estimates pass the pre-trend test, and the main results survive shift-share-robust inference (Adão, Kolesár and Morales, 2019).

09Why building stopped: the legacy of the bust

The 2008 bust left about half a million unsold new homes, very unevenly spread: more than 5% of the dwelling stock in Castellón, Toledo and Almería, 1% or less in Bizkaia or Málaga. Using the Ministry's annual reports, the paper asks whether that stock acted as a buffer.

Wave 2, per 1% of population arrivingLittle unsold stockMuch unsold stock
Housing starts, % of 2014 stock0.33**0.07
Completions, % of 2014 stock0.22**0.04

Building still responds to arrivals where the bust left little unsold housing, and not where it left most. The unsold homes themselves were not drawn down faster where more people arrived. The bust appears to have switched off building where it hit hardest, without leaving homes where the new demand went. The evidence identifies where construction survived, not the single channel that switched it off.

10Who pays

The rent response falls on market renters: 31% of people in the bottom income decile against 8% in the top, and half of households headed by someone under 30 against one in twenty of those over 65. The average cost of a 1% inflow is about 13 basis points of income in the bottom decile and 2 in the top. The price response is an unrealised gain to owners, who are older and richer.

11Status: three levels, never mixed

LevelWhere it stands
Modelη ↑ ⇒ β ↓, and population absorption ↑. Derived.
Calibrationη = 0.45 ⇒ β ≈ 0.82 for Spain. Done.
EstimationRent, price, construction, household and population responses by wave; geography, planning, regulation and remote-work interactions; shift-share-robust inference. Working paper v2: overhang, register-based crowding, recalibration and distributional incidence added. Data and code released as PF-DATA-001.

The paper deliberately does not claim that immigration explains Spain's housing crisis. The current inflow accounts for roughly 0.7 of 12.2 points of annual price growth in the calibration. The question is narrower and more defensible: given a migration-induced demand shock, why does its incidence differ across places and periods?

Citation

Menéndez-Pidal, J. (2026). “Building or Squeezing? How Spain Absorbed Two Immigration Waves: The Incidence of Population Shocks in Local Housing Markets.” Project Frontier Working Paper No. 001, Madrid.

BibTeX 
techreport{menendezpidal2026incidence,
  author      = {Men{\'e}ndez-Pidal, Jorge},
  title       = {Building or Squeezing? How Spain Absorbed Two Immigration Waves: The Incidence of Population Shocks in Local Housing Markets},
  institution = {Project Frontier},
  type        = {Working Paper},
  number      = {001},
  address     = {Madrid},
  year        = {2026},
  month       = {oct}
}

Preliminary draft. Comments welcome; please do not cite without permission.