The Impact of Urban Population on Housing Cost: The Case of Australia

Abstract


Introduction
Population expansions contribute to urban agglomeration and productivity growth, but they also come with the potential drawback of increasing social cost, such as the cost of housing.
Balancing the benefits and costs of urban agglomeration is a crucial objective for policymakers in population planning.While the economic advantages of larger cities, including population size and density, have been extensively studied (Ciccone and Hall, 1996;Ciccone, 2002), there is a scarcity of quantified evidence regarding the specific costs associated with population growth, particularly in relation to housing.For policymakers, having such evidence on the costs and benefits of population growth is important for managing the expansion of city population.
As such, estimating the effects of city population on urban costs has garnered significant interest over the years.However, obtaining such estimates is far from straightforward -besides the usual concerns like omitted variable bias, the presence of measurement error could lead to attenuation bias.Moreover, the high cost of living in urban areas may discourage population growth (Cannari, Nucci and Sestito, 2000), leading to a reverse effect.To address these concerns, we propose a new approach to estimate the elasticity of housing cost with respect to city population using Australian panel data.Our work employs fixed effects model to eliminate the confounding effects of unobserved heterogeneity, known as fixed effects, such as unobserved location attributes that might jointly influence population growth and housing cost.To address the confounding issues of reverse causality and measurement error, we propose a new instrumental variable (IV) for city population to identify its effect on housing cost.
For our IV to be applicable within a panel fixed effects framework, it must contain both cross-sectional and time variations.To this end, we construct a Bartik-style IV by interacting data on city climate and visa issuance.A Bartik-style IV is one that is created by taking the interaction between a time-varying variable common across all cross-sectional units and a time-invariant variable that varies cross-sectionally.This interaction term will create an IV that exhibits variations across both time and space, ensuring that its effect on the endogenous variable (i.e.city population) will not be washed out by the inclusion of fixed effects into the regression model.
In our case, our time-varying variable is related to overseas immigration, which directly contributes to population growth.Immigration has been a significant driver of Australia's population expansion since 1995, and visa issuance, decided by the Australian federal government in response to the country's labor market and economic conditions (Productivity Commission, 2016), determines the annual number of new overseas migrants entering Australia.For our work, it is important to emphasize that Australian cities do not have the authority to influence visa issuance levels, which implies that visa issuance from a city planner's perspective is taken as given.Our cross-sectional variable is city climate, which influences people's location choices and, consequently, city population levels (see, e.g., Roos, 2005;Jordan, 2007).Like visa issuance, it is reasonable to assume that climate is exogenous (Dell, Jones and Olken, 2014).Thus, our IV for city population, which is constructed by interacting climate and visa issuance, should be plausibly exogenous.
We implement two-stage least squares (2SLS) regression using our climate-visas IV as an instrument for city population.In the first stage, we find a positive relationship between the number of visas issued and population, particularly in cities with favorable climates.This result aligns with the hypothesis that attractive climates draw in more migrants, leading to more population growth (Combes, Duranton and Gobillon, 2019).Our second-stage estimates indicate that a 1% increase in city population is associated with an average increase in home prices ranging from 1.16% to 1.59%, and an average increase in rental prices ranging from 1.84% to 1.97%.These elasticities suggest that housing costs tend to increase at a faster rate than population growth.
Overall, our study highlights the concerning trend that housing costs, especially rental costs, tend to rise more quickly than population growth.As individuals and households with lower incomes tend to allocate a larger proportion of their earnings to housing expenses, an increase in housing cost induced by population growth can significantly exacerbate the inequality of income net of housing expenditure.Therefore, proactive measures are needed to address the challenges posed by population growth on housing affordability.

Results
In this section, we present the estimation results from the OLS, reduced form, and 2SLS regressions.Details on the data and statistical models are provided under Methods.Further results from our robustness checks are provided under Supplementary Information.

OLS estimates
Table 1 presents the OLS estimates of the elasticities of home and rental prices with respect to current (population ist ) and lagged (population ist−1 ) city population based on Eq. ( 1).The results indicate that the elasticities of home prices are 0.461 and 0.412, respectively, while the elasticities of rental prices are 0.384 and 0.297, respectively.All the OLS estimates show that city population is statistically significant for housing cost at the 1% level.Interestingly, although the log of housing supply and employment rate show the expected signs, they are statistically insignificant, suggesting that population growth plays a more significant role in driving home and rental prices in Australia than housing supply and employment.(3).In Columns (1) and (2), the estimated effects of our instrument on home prices are 0.578 and 0.772, respectively.This indicates that, on average, a 1% increase in visa issuance in the previous year (t − 1) or previous two years (t − 2) would lead to an additional 0.578% or 0.772% increase in home prices in cities with a favourable climate compared to those without.

Reduced form estimates
In Columns (3) and (4), the estimated effects of our instrument on rental prices are 0.611 and 0.678, respectively.This indicates that, on average, a 1% increase in visa issuance in the previous year or two years would lead to an additional increase in rental prices by 0.611% to 0.678% in cities with a favourable climate compared to those without.These estimates are statistically significant at the 1% level, which suggests that population growth through immigration is a significant driver of housing cost especially in cities with favorable climates.3) of the lower panel in Table 3).Similarly, an increase of 1% in visa issuance in year t − 2 results in an additional increase of 0.036 to 0.049% in population in cities with a favourable climate.Furthermore, the Kleibergen-Paap first-stage F-statistics are all greater than the critical value at the 10% level, indicating that our IV is a powerful instrument for city population.
The second-stage estimation results in Table 3 confirm that city population expansions would drive up both home and rental prices.For example, a 1% increase in city population would, on average, lead to a 1.164% to 1.589% increase in home prices (see Columns (1) and (2) of Table 3).Similarly, a 1% increase in city population would result in a 1.843% to 1.972% increase in rental prices on average (see Columns (3) and (4) of Table 3).Comparing the OLS estimates of the effects of city population reported in Table 1 with the 2SLS estimates reported here, we observe that the latter are about three times larger than the former.This discrepancy highlights the downward bias in the OLS estimates if confounding effects such as reverse causality and measurement error are not accounted for.The 2SLS results therefore underscore the importance of addressing these issues when estimating the impact of city populations on housing costs as the impact size could be vastly understated.
Our 2SLS results are consistent with the conclusion drawn by Combes, Duranton and Gobillon (2019), namely, that city population expansions inevitably lead to increases in housing costs.However, our second-stage estimates of city population on housing costs are considerably larger than those reported by Combes, Duranton and Gobillon (2019). 1 This disparity may be attributed to the application of an instrumental variable approach within a panel data setting, which enables us to address the issues of reverse causality, measurement errors, and unobserved heterogeneity.By contrast, Combes, Duranton and Gobillon (2019) conducted their analysis using a pooled cross-sectional regression without accounting for city 1 Refer to Table A1 on page 1586 in Combes, Duranton and Gobillon (2019) for their two-stage least squares estimates.It should be emphasized that Combes, Duranton and Gobillon (2019) focused on at land prices.However, the appreciation of existing homes can be attributed mainly to the increase in land prices, which suggests that our analysis is comparable to Combes, Duranton and Gobillon (2019).
fixed effects, which could confound the impact of city population on housing costs.

Discussion
The study explores an implication of rising urban population in terms of housing costs in Australia.We find strong evidence that city populations have a significant impact on housing costs.Furthermore, our elasticity estimates suggest that housing costs, particularly rental costs, tend to increase at a faster rate than population growth.
As such, our paper underscores the potential for population growth to exacerbate the inequality of income after housing expenditure, which can be driven by rising housing costs.
Several studies have highlighted the link between population growth and housing cost.Using data from Organisation for Economic Co-operation and Development (OECD) counties, Gevorgyan (2019) found that if population growth increases by one percentage point, house price growth increases by 1.4 percentage points.Using data from Amsterdam and Paris, Francke and Korevaar (2022) found that a one percentage point increase in the current birth rate increases house prices about 25-30 years later by 4 to 5%.Our paper contributes to this literature by showing that housing costs may escalate at a faster rate than population growth in the Australian city-level context.As individuals and households with lower incomes tend to allocate a larger proportion of their earnings to housing expenses (Dustmann, Fitzenberger and Zimmermann, 2021), an upward trajectory of housing costs may dramatically widen the inequality in income net of housing expenses.
Methodologically, our paper contributes to the existing literature in the following ways.
Firstly, to the best of our knowledge, our study is among the first to estimate the effect of city population on housing costs by implementing an instrumental variable panel data approach.Previous studies by Thomas (1980), Richardson (1987), and Henderson (2002) have examined the association between urban costs and population expansion.These studies have found a positive relationship between population size and the cost of living (Thomas, 1980), and have documented that infrastructure spending, commuting time, and rental prices may increase due to urbanization (Richardson, 1987;Henderson, 2002).However, as they do not consider an identification strategy, their point estimates could be biased and inconsistent.
Combes, Duranton and Gobillon (2019), on the other hand, employed an instrumental variable approach as an identification strategy to estimate the elasticity of housing costs (i.e. house and land prices) with respect to city population using French data.However, their study was based on a pooled cross-sectional setting.Without employing panel data, their estimation approach was unable to account for city fixed effects, which could jointly determine both population and housing cost.In our study, we employ an instrumental variable approach in a panel data setting so that we may address both the issue of reverse causality and unobserved heterogeneity.
Secondly, our paper introduces a new method for estimating the relationship between urban population and housing cost.Previous studies have instrumented city population using historical population levels (Ciccone and Hall, 1996;Combes, Duranton and Gobillon, 2008;Duranton, 2016;Combes, Duranton and Gobillon, 2019).However, historical population levels may be unsuitable as instruments as they are endogenous to housing cost (Sharpe, 2019;Broxterman and Larson, 2020).Other studies have explored using geological characteristics such as fertile soil to explain population size (Combes et al., 2010;Combes, Duranton and Gobillon, 2011), but using such data to construct an instrument for population size may be difficult to justify for a country like Australia whose economy is not primarily driven by the agricultural sector.Finally, there are studies that linked city population to city amenities such as the number of hotel rooms (Carlino and Saiz, 2008;Combes, Duranton and Gobillon, 2019), but the theoretical justification for this relationship may be challenging and such fine-level data may not be available.Our approach has the advantage of constructing an instrument using publicly accessible data on national-level visa issuance and city climate, which makes the construction of such an instrument potentially more feasible for studies based on other countries.

Data
Our dataset comprises a panel of 513 Australian cities, specifically defined as Local Government Areas (LGA), covering the period from 2003 to 2016.The housing cost and supply data are obtained from the Australian Urban Research Infrastructure Network (AURIN) and are reported on a monthly basis.To capture housing costs in cities, we utilize the transacted average home and rental prices for each city.Additionally, the total number of houses listed in the market is used as a proxy for city housing supply.In order to align with the frequency of our data (population, visa issuance, and employment), we aggregate the monthly data into yearly frequencies.
Data on city populations and employment rates are sourced from the Australian Bureau of Statistics (ABS).2For visa issuance, we consider visas issued to permanent and temporary skilled migrants (residents), international students, and long-stay businessmen. 3The visa issuance data are obtained from the Department of Home Affairs. 4 The summary statistics on the variables are presented in Table 4.For instance, if a city's average annual temperature, average annual 9 am humidity, and average annual rainfall levels fell within the ranges of 18 to 24 degrees Celsius, 50 to 70 percent, and 1,000 to 2,000 millimeters, respectively, between 1961 and 1990, it is classified under "Zone 2: Warm humid summer and mild winter".On the other hand, cities with average annual temperatures between 9 and 18 degrees Celsius, average annual 9 am humidity levels of 70 to 80 percent, and average annual rainfall of 600 to 1500 millimeters within the same period are assigned to "Zone 7: Cool temperate".
To conserve space, we will not present the detailed construction of the remaining zones based on average humidity, temperature, and precipitation levels between 1961 and 1990.
Interested readers can refer to the climate zone map provided by the Australian Building Codes Board (ABCB) and the maps available on the Bureau of Meteorology's website.6 Population growth and visa issuance Australia has experienced significant population growth over the years.Examining the proportion of population growth attributed to new births and overseas migration, Figure 3 reveals that between 1982 and 1995, approximately 54% of population expansion came from new births while 46% was due to new overseas migrant intakes.8However, in 2017, new overseas migrants accounted for 65% of the population growth while births contributed to the remaining 35%.Thus, new overseas migrant intakes have become the primary driving force behind Australia's population expansion in recent years.Unsurprisingly, the growth in population driven by overseas migration is closely linked to the number of visas issued by the Australian federal government.The government carefully manages the influx of overseas migrants into Australia, taking into account the prevailing labor market conditions in the country (Productivity Commission, 2016).This approach allows the government to respond to labor supply shortages in specific sectors such as healthcare, information technology, engineering, and construction trades (Productivity Commission, 2016).
For example, starting from 1995, the federal government increased the issuance of visas to attract immigrants from these occupational groups (Spinks, 2010). 9Consequently, the number of visas issued had increased significantly since 1995, as shown in Figure 4. To examine the relationship between visa issuance and Australia's population, we analyze the log forms of both variables from 1996 to 2016, as shown in Figure 4.The upward trends of log(population) and log(visa issuance) indicate a positive relationship between visa issuance and Australia's population at the national level.Since national populations are composed of city populations, we can also infer a positive association between visa issuance and citylevel populations.To further explore this relationship, we select four Australian capital cities and plot their populations against the number of visas issued, as depicted in Figure 5.The similarity in the trends of the log number of visas issued and the log populations of these selected cities supports the argument that population growth in these cities is driven primarily by migration, which in turn depends on the number of visas issued.

Climate and population spatial variation in Australia
The population distribution in Australia exhibits significant spatial variation.As shown in Figure 6, the populations of certain cities, such as MacDonnell and Diamantina, located in the middle of Australia, average less than 10,000 between 2001 and 2020.By contrast, the coastal city of Brisbane has consistently housed over 1 million people during the same period.
The considerable disparity in city populations across Australia can be attributed, in part, to variations in climate conditions (Cheshire and Magrini, 2006;Albouy and Stuart, 2014).When selecting their residential locations, households take into account local climate conditions and are more inclined to settle in areas with a more favorable climate for living (Jordan, 2007).For instance, individuals often prefer suburban, sunny, and coastal areas characterized by mild, warm, or cool climates (see, e.g., Cragg and Kahn, 1997;Jordan, 2007;Albouy, Leibovici and Warman, 2013;Albouy and Lue, 2015).On the other hand, they are generally reluctant to reside in remote areas characterized by hot-dry summers or extremely cold winters (Maddison and Bigano, 2003;Sinha and Cropper, 2013;Albouy et al., 2016).
To gain further insight into how climate conditions are associated with population spatial variation in Australia, we adopt the climate zone classification provided by the Bureau of Meteorology (BoM) in Australia.As shown in Figure 7, the Australian cities are categorized into seven climate zones. 10Examining the population levels of cities within each climate zone, Table 5 provides the average city population between 2001 and 2018, as well as the average number of overseas migrants in each city from 2016 to 2019, for each climate zone.
The data reveal that cities characterized by a warm-summer, mild, or cool climate have significantly higher populations compared to those with hot or hot-dry summer climates.
Hence, the disparity in climate conditions may explain the spatial distribution of Australian city populations, with cities possessing a more livable climate (i.e., warm, mild, or cool) attracting larger populations and overseas migrants.
10 These climate zone data are developed by BoM to assist the Australian Building Codes Board (ABCB) in regulating the building and construction industry.
The data can be accessed at https://www.abcb.gov.au/Resources/Tools-Calculators/Climate-Zone-Map-Australia-Wide.BoM developed eight zones for ABCB, but for this study, we consider the cities with some alpine-climate areas as having a cool temperate climate, resulting in seven climate zones being analyzed.The model Our primary model examines the relationship between the logarithm of housing costs (i.e., home and rental prices), denoted as log(price k is,t ), and the logarithm of population, denoted as log(population is,t ), for city i, state s, and year t.The equation is specified as follows: where the superscript k indexes home or rental price.The vector x is,t consists of a set of control variables that include the log of housing supply and employment rates.The terms µ i and and µ st represent the city fixed effects and state-year fixed effects, respectively.The variable ǫ is,t denotes the idiosyncratic error term clustered at the city level.
The main focus of this study is to estimate the parameter α in Eq. ( 1).This represents the elasticity of housing cost with respect to city population.To achieve this objective, we incorporate various fixed effects and control variables into Eq.( 1).The inclusion of city fixed effects, µ i , enable us to control for time-invariant city-specific characteristics such as location and land size and other unobserved location-related attributes.The inclusion of state-year fixed effects, µ st , enable us to control for the influence of macroeconomic variables and macroeconomic shocks (e.g., interest rates and Global Financial Crisis), as well as for factors that vary across states and years such as annual economic and labor market conditions within states.We also incorporate city housing supply and employment rate in Eq. ( 1) to control for local housing and labor market conditions, which are likely correlated with population sizes and housing costs (Zabel, 2012).
Despite the inclusion of these fixed effects and control variables, we may still encounter challenges that would hinder the identification of α, the effect of city population on housing costs.The first challenge arises from measurement errors in log(population is,t ).Since the city population data used in our study are estimated, measurement errors could be prevalent.
Consequently, if these measurement errors were classical, the estimate of α would be biased toward zero.
The second challenge is related to reverse causality.On the one hand, the expansion of city population can drive up local housing costs (see, for example, Gonzalez and Ortega (2013); Accetturo et al. (2014); Combes, Duranton and Gobillon (2019).On the other hand, high housing costs may discourage people from moving to certain cities (Cannari, Nucci and Sestito, 2000).Therefore, given this bi-directional relationship, it is important to disentangle the effect of city population on housing cost from the reverse confounding effect.
Lastly, other determinants of city housing costs that are correlated with population may be captured in the error term ǫ is,t .For example, the safety of a city can influence both population levels and house prices (Klimova and Lee, 2014).If the influence of unobserved characteristics on housing cost and city population is not eliminated, the OLS estimates could still be susceptible to omitted variable bias.

Estimation strategy
To address the aforementioned issues, we propose an instrumental variable (IV) approach within a panel data framework to estimate the relationship between city populations and housing costs.Our IV strategy involves interacting two variables that exhibit exogenous variations across cities and over time.
The first variable is city climate, which is considered to be exogenous to economic outcomes such as housing cost (Roos, 2005;Dell, Jones and Olken, 2014).Climate can influence residential choices, and cities with more favorable climates, characterized by mild, warm, or cool conditions, tend to have larger populations compared to cities with less favorable climates, such as those with hot-dry summers or extremely cold winters (Cragg and Kahn, 1997;Jordan, 2007;Albouy and Lue, 2015). 11In the context of Australia, cities with more livable climates tend to have larger populations compared to cities with hot-dry summer cli-11 Please also refer to Albouy, Leibovici and Warman (2013).
mates.Therefore, we classify mild, warm, and cool climates as favorable climates and indicate them with a dummy variable, favorable climate is .This variable serves as the cross-sectional component of our IV.
The second variable is the number of visas issued, which we argue is plausibly exogenous with respect to housing cost.As shown earlier, overseas migration is the primary driver of population expansion in Australia since 1995.The Australian federal government operates the Migration Program, and the issuance of visas positively influences overseas migration to Australia.Thus, the annual number of visas issued can be considered a determinant of Australian city populations (see Figure 5).Importantly, since the number of visas issued is determined by the federal government based on the country's labor market needs, visa issuance should be exogenous to current housing costs in the cities.Therefore, we utilize log(visas t−j ), the log of the number of visas issued at time t − j where j = 1 or 2, as the time-varying component of our IV.
Our first-stage regression model is defined as follows: log(population is,t ) =c + β j × favorable climate is × log(visas t−j ) + θ ′ x is,t where our IV is the interaction between favorable climate is and log(visas t−j ).The main identifying assumption is that the number of visas issued affects housing cost solely through its impact on city populations.This assumption would be violated if: 1) visa issuance directly affects local housing costs, implying that it is not an excluded factor, or 2) housing costs reverse causally influence visa issuance.The first concern is irrelevant since the number of visas issued by itself does not directly impact city housing costs, but rather, potentially influences them through its effect on city population size. 12The second concern is also unlikely as visa issuance is influenced by the Migration Program designed by the Australian federal government to address the labor conditions of the entire country (Productivity Commission, 2016).Nevertheless, to ensure the validity of our instrument, we utilize the lagged number of visas issued, which is predetermined with respect to home and rental prices.
Our main estimation approach employs two-stage least squares (2SLS) regression, where Eq. ( 1) is estimated as a second-stage model in conjunction with Eq. ( 2) as the firststage model.This allows us to address the issues of reverse causality and measurement error associated with city populations.In addition, we also estimate the influence of our instrument on housing costs via the following reduced form regression: This specification allows us to explore the combined effect of favorable climate and visas issuance on housing costs, while controlling for other factors captured by the vector of control variables ψ ′ x is,t .
Further remarks on the estimation strategy Our estimation strategy bears similarities to the shift-share instrument commonly used in urban and housing literature (e.g., Saiz, 2007;Gonzalez and Ortega, 2013;Accetturo et al., 2014;Sharpe, 2019).These studies construct instruments by interacting the historical share of migrant population to total population at the local level, which provides cross-sectional variation, with the current national migrant level, which provides time variation.The rationale is that the current location decisions of immigrants are expected to be influenced by the location decisions of earlier immigrants (say, from the same country of origin).Therefore, this interaction term can be interpreted as an approximation of the yearly immigration level to a local area.
However, the validity of such an IV has been subject to debate.For it to be valid, the cross-sectional variation, i.e. the historical share of migrant population to total population, must be exogenous.However, Sharpe (2019) and Broxterman and Larson (2020) have argued that the historical migrant population share could be influenced by housing costs.Moreover, it could also be correlated with initial economic conditions, city characteristics, and housing cost (Sharpe, 2019).Consequently, the exclusion restriction assumption necessary for the validity of such instruments may not hold.
By contrast, our new instrument addresses these issues by relying on climate conditions to generate the cross-sectional variation in our instrument rather than the historical share of migrant population.Unlike the latter, a city's climate is exogenous to economic variables including housing costs (Hsiang, Burke and Miguel, 2013;Dell, Jones and Olken, 2014;Hsiang, 2016).Additionally, the time-varying component in our instrument -national-level visa issuance -is determined by the Australian federal government based on the country's overall labor market conditions.Therefore, our proposed instrument, which is based on the interaction between city climate and visa issuance, is plausibly exogenous to city housing costs.

Robustness checks on 2SLS regression
Tables S3 and S4 present the 2SLS estimates when climate is or log( visa t−j ) are used to construct our alternative instruments.The first-stage regression results show that these alternative IVs are positive and statistically significant for city population at the 1% level.
Additionally, the Kleibergen-Paap F-statistics all exceed the critical value from Stock and Yogo at the 10% level, indicating that these IVs are strong.In the second-stage regression, the new elasticity estimates of housing costs with respect to city population remain statistically significant and fall within the two standard deviation bands of the baseline estimates in Table 3.Therefore, the baseline 2SLS estimates are robust to different approaches of constructing the variables to measure favourable climates and visa issuance.
Figure 1 illustrates this trend, showing an increase in population from 3.7 million in 1901 to 25 million in 2019, with a projected growth to 40 million by 2051.Among OECD countries, Australia had the third fastest growing population (OECD, 2019).Notably, the population expansion in Australia has been particularly rapid in the last two decades, with an annual increase of over 325,000 people.This population growth can be attributed to two main factors: new births and overseas migration.Figure2sheds some light on the contribution of each factor.Before 2006, the quarterly average of new births remained around 60,000, but modestly increased to 78,000 in 2017.By contrast, the quarterly average of new overseas migrants arriving in Australia had more than tripled, rising from below 50,000 in 1982 to 138,000 in 2017. 7

Figure 2 :
Figure 2: Australian Population Expansion: New Births vs Overseas Migrants (Time Series)

Figure 4 :
Figure 4: Populations vs Visa Issuance in Australia

Figure 5 :
Figure 5: City Populations and Visa Issuance

Figure 7 :
Figure 7: Climate Zones in the Australia

Table 1 :
OLS Estimates of City Population on Housing Cost Note: Robust standard errors clustered in the city level are reported in the parentheses.* p < 0.05, ** p < 0.01, *** p < 0.001 Table 2 presents the reduced form estimates of the effect of our instrument (favourable climate is × log(visas t−1 ) or favourable climate is × log(visas t−2 )) on home and rental prices based on Eq.

Table 2 :
Reduced Form Estimates of Instruments on Housing Cost

Table 4 :
Summary StatisticsFor the climate of cities, we utilize the city climate zone data provided by the Bureau of Meteorology (BoM).The BoM categorized all Australian cities into seven climate zones based on historical climate conditions, specifically precipitation, temperature, and humidity levels between 1961 and 1990.The climate zone classification is depicted in Figure7above. 5

Table 5 :
Climate and Population and Migrant Spatial Variation

Table S1 :
Reduced Form Estimates of New Instruments on Housing Cost (Alternative Favorable Climate Definition) Note: Robust standard errors clustered in the city level are reported in the parentheses.* p < 0.05, ** p < 0.01, *** p < 0.001

Table S2 :
Reduced Form Estimates of New Instruments on Housing Cost (Excluding Short-Term Visitors in Visa Measure) Robust standard errors clustered in the city level are reported in the parentheses.* p < 0.05, Note:** p < 0.01, *** p < 0.001

Table S3 :
2SLS Estimates of City Population on Housing Cost Using New Instruments (Alternative Favorable Climate Definition) The variable climate is an indicator for climates that are mild, warm, cool and hot-humid.Robust standard errors clustered in the city level are reported in the parentheses.* p < 0.05, ** p < 0.01, *** p < 0.001 Note:

Table S4 :
2SLS Estimates of City Population on Housing Cost Using New Instruments (Excluding Short-Term Visitors in Visa Measure) The variable visas is the number visas issued for permanent skill migrants/residents and all migrants with an intention of staying over one year.Robust standard errors clustered in the city level in parentheses.* p < 0.05, ** p < 0.01, *** p < 0.001 Note: