The impact of urban population on housing cost: the case of Australia

The study investigates how city population growth affects housing costs in Australian cities. While urban agglomeration can boost productivity, it can also raise social costs like housing. Estimating the causal impact is difficult due to omitted variable bias, measurement error (which can attenuate estimates), and reverse causality (high costs may deter population growth). The authors use a panel fixed effects framework to control for unobserved time-invariant city characteristics and state-year factors, and propose a new instrumental variable to address reverse causality and measurement error when estimating the elasticity of housing costs with respect to city population.

The paper situates its contribution within housing affordability and urban amenity literatures. Prior work documents multiple drivers of affordability, including supply factors (construction costs, regulation) and demand-side forces (income inequality). The amenity perspective (e.g., Glaeser et al.; Diamond) suggests rents can rise faster than wages as cities attract skilled workers and consumption amenities matter alongside production externalities. Related research in urban inequality and sustainability shows mixed patterns: smart city features may reduce digital divides, but low-income and minority groups face higher risks of energy and transport poverty, and larger cities may exhibit higher interpersonal inequality. Earlier studies linking urban costs and population size often use associations without identification or rely on cross-sectional IVs; Combes et al. use IVs in pooled cross-sections. The present study advances this literature by providing panel IV evidence at the Australian city level and introducing a Bartik-style instrument based on climate and visa issuance.

Data: A panel of 513 Australian cities (Local Government Areas) from 2003–2016. Housing costs (average home and rental prices) and housing supply (listings) from AURIN, aggregated from monthly to yearly. City population and employment rates from ABS; employment rates available in 2001, 2006, 2011 censuses and extrapolated for intervening years. Visa issuance covers permanent and temporary skilled migrants, international students, and long-stay businessmen (over 70% of visas), excluding short-term visitor visas; data from the Department of Home Affairs. Climate zones from the Bureau of Meteorology (BoM), categorizing cities into seven zones; zones 2, 5, 6, and 7 are deemed favorable climates. Summary statistics are reported for log(population), log(visas), log prices, log supply, employment rate. Model: The main specification regresses log housing cost (home or rent) on log city population, controls (log housing supply, employment rate), with city fixed effects and state-year fixed effects. Challenges include measurement error in population, reverse causality, and omitted variables. Instrumental variable strategy: Construct a Bartik-style IV as the interaction of a city’s time-invariant climate (favorable climate dummy) and the time-varying national log visa issuance (lagged one or two years): favorable climate_i × log(visas_{t−j}), j=1,2. Climate is argued exogenous to economic outcomes and shapes residential location choices; visa issuance is determined by the federal government based on nationwide labor market needs and is plausibly exogenous to city-level housing costs. First stage: log(population_it) on the IV, controls, and fixed effects. Second stage: log(price_it) on predicted log(population_it) with the same controls and fixed effects. A reduced form relates log(price_it) directly to the instrument. Standard errors are clustered at the city level. Instrument strength is assessed via Kleibergen–Paap statistics against Stock–Yogo critical values.

- OLS with fixed effects: Elasticities of housing costs with respect to population are positive and significant at the 1% level. For home prices, elasticities are 0.461 (current population) and 0.412 (lagged). For rental prices, 0.384 (current) and 0.297 (lagged). Housing supply and employment rates are generally insignificant in OLS. - Reduced form: The interaction of favorable climate and lagged visa issuance significantly increases home and rental prices, indicating migration-driven population growth raises housing costs more in favorable-climate cities. - First stage (2SLS): The IV is strong and positive. A 1% increase in visa issuance (t−1) is associated with an additional 0.035%–0.050% population increase in favorable-climate cities; similarly, using visas (t−2) yields 0.036%–0.049%. Kleibergen–Paap F-statistics exceed the 10% critical value, indicating instrument relevance. - Second stage (2SLS): A 1% increase in city population raises home prices by 1.164%–1.589% and rental prices by 1.843%–1.972% on average. These 2SLS elasticities are about three times larger than OLS estimates, consistent with OLS attenuation bias from measurement error and reverse causality. Rental costs appear to rise faster than home prices. - Overall implication: Housing costs in Australian cities increase faster than population growth, with particularly strong effects on rents.

The results show that population expansions causally drive up both home and rental prices, with rental prices responding more elastically. This implies that population growth can worsen post-housing-expenditure income inequality, as lower-income households allocate larger income shares to housing. Compared to prior studies (e.g., Combes et al.), the estimated elasticities here are larger, likely due to the use of panel IV with city and state-year fixed effects that address reverse causality, measurement error, and unobserved heterogeneity. The findings reinforce concerns that amenities and migration-driven growth can pressure housing markets, suggesting the need for policy responses to maintain affordability and mitigate inequality.

The paper demonstrates that Australian city housing costs, especially rents, rise more than proportionally with population growth. Methodologically, it contributes a panel fixed-effects IV approach using a Bartik-style instrument (climate × visa issuance) that is feasible with publicly available data and potentially transferable to other national contexts. Policy-wise, the evidence highlights the need for proactive measures to address affordability pressures associated with population growth. Future research could apply similar instruments in other countries, explore heterogeneous effects across city types and climate zones, and examine interactions with supply constraints and regulatory environments.

Employment rates are only observed in census years (2001, 2006, 2011) and are extrapolated for missing years, which may introduce measurement uncertainty. The identification relies on the exclusion restriction that lagged national visa issuance affects local housing costs only through local population and that climate is exogenous; violations would bias estimates. Results are based on Australian LGAs and the 2003–2016 period, which may limit generalizability beyond this context.