Project Frontier Jorge Menéndez-Pidal

WP-001 · Working Paper · October 2026

The Incidence of Population Shocks
in Local Housing Markets

Housing Supply Elasticity, Migration and Spatial Adjustment

Jorge Menéndez-Pidal

Abstract

When a local housing market receives a population shock, the shock is absorbed through new construction, conversion of the existing stock, households consuming less space and the relocation of existing 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 in which housing supply elasticity governs both the price incidence of a shock and the share of it a place can absorb as population. I estimate the framework for Spain’s two immigration waves using a 2003–2024 panel of 50 provinces and a shift-share instrument based on settlement patterns by country of birth. In the current wave, each 1% of population arriving raises rents by about 1% and house prices by about 4% cumulatively. Prices outrun rents, which points to capitalised expectations. The construction response, which absorbed about 0.7 of each unit of inflow in 2003–2008, has fallen to zero, and the implied short-run supply elasticity is indistinguishable from zero. The current wave has instead been absorbed by more residents per dwelling. Inflows do not displace natives: Spain-born adults move towards receiving provinces, which amplifies rather than offsets the shock. The results identify supply elasticity as the state variable that separates the two waves. They also show that, when supply does not respond, population growth is accommodated by crowding rather than by building.

Keywords housing supply elasticity, immigration, spatial equilibrium, incidence, rent control, remote work, shift-share

No.
WP-001
Date
01.10.2026
Status
Draft v1
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. 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. Calibration.

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 nationality:

\[Z_{it}=\frac{\sum_n \lambda_{ni}\,\Delta M^{(-i)}_{n,t}}{N_{i,t-1}}\]
  • 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 crowding, 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−0.041.82
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 supply response has collapsed. The construction share fell from about 0.7 to zero; the implied short-run supply elasticity is indistinguishable from zero.
  • Natives move towards receiving provinces, so relocation amplifies the shock rather than absorbing it.
  • 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).

09Status: 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 v1.

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). “The Incidence of Population Shocks in Local Housing Markets: Housing Supply Elasticity, Migration and Spatial Adjustment.” Project Frontier Working Paper No. 001, Madrid.

BibTeX 
@techreport{menendezpidal2026incidence,
  author      = {Men{\'e}ndez-Pidal, Jorge},
  title       = {The Incidence of Population Shocks in Local Housing Markets: Housing Supply Elasticity, Migration and Spatial Adjustment},
  institution = {Project Frontier},
  type        = {Working Paper},
  number      = {001},
  address     = {Madrid},
  year        = {2026},
  month       = {oct}
}

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