Housing Markets and Migration:Evidence from New Zealand
MAIN REGRESSION RESULTS
We posit a linear relationship between the log of house prices and the log of population since both variables exhibit considerable skewness, and allow measurable characteristics of the local population (XLMA,t) to influence house prices. We also allow for area-specific amenities and local differences in the housing stock to have a permanent influence on each area's house prices, and for mean house prices to be different in each period. This specification is shown in Equation (1).
`Ln(House Price)_(LMA,t)=alpha+betaLn(pop)_(LMA,t)+deltaX_(LMA,t)+e_(LMA,t)`
` e_(LMA,t) = lambda_(LMA) + tau_t + eta_(LMA,t)`
We estimate this relationship in differences, approximating the change in logs by percentage changes.[16] The key parameter of interest (β) is identified from the covariation of house prices and population change within each area. Focusing on the relationship between changes in population and changes in housing markets allows us to control for time-invariant unobservable characteristics of local areas that either attract or repel individuals and lead to differential costs of housing (λLMA). Consistent with the inclusion of time effects (τt) in equation (1), the estimating equation (2) allows for a different mean growth rate in house prices in each period (`bar tau_t`)
`Ch(HP)_(LMA(t,t-5))=alpha+betaCh(Pop)_(LMA(t,t-5))+deltaDeltaX_(LMA(t,t-5))+Delta e_(LMA,t)`
(2)
where `Ch(z)_(LMA,t)=(z_(LMA,t)-z_(LMA,t-5))/z_(LMA,t-5)`
Table 5 presents estimates of β from various specifications of equation (2). Each coefficient is from a separate regression, reflecting differences in local area definition, inclusion of covariates and choice of house price variable. All estimates are variance weighted by the population size in each geographic area averaged over the current and previous census and standard errors are robust to clustering at the location level. The first entry in the table shows the population elasticity of house prices estimated from variation across the 140 LMAs. The estimate of 0.255 is identical to the slope of the bottom left graph in Figure 2, and implies that a 1 percent increase in population is associated with a 0.26 percent increase in house prices. The estimate in the second column reveals the impact of controlling for changes in the composition of the local population that may have led to a change in house prices. Controls are included for changes in the age composition, gender composition, qualifications, employment status, marital status, household type, household composition and income of the local population.[17] The estimated elasticity decreases slightly to 0.133 and becomes insignificantly different from zero due to an increased standard error. At the individual level, many of these control variables are endogenously determined with both locational and housing market choices, thus it is unclear whether we should be including them in the regression. Furthermore, to the extent that changing population characteristics are a direct consequence of migration flows, their influence should be included as part of the effect of migration. Thus, we continue throughout the paper to present regression results both with and without control variables.
In the following rows of Table 5, comparable estimates are obtained using different definitions of local areas. Neither changing the level of geographic aggregation nor including control variables yields any estimates that differ significantly from the base estimate of 0.257, though the standard errors are admittedly relatively large. The estimates derived from variation across 16 Regional Council areas are particularly imprecisely estimated, perhaps not surprisingly given the relatively small number of observations.
As noted earlier, the housing market is not homogeneous. In the remaining columns of Table 5, we examine the impact of population change on sale prices for rental units (flats), and rents for both houses and apartments (flats). Population growth appears to be associated with a larger increase in the sales price of flats than in house prices, with an elasticity of between 0.42 and 0.58. The evidence for rents is more mixed, when control variables are not included in the regression, we estimate a significant elasticity between 0.19 and 0.30 for house rents and between 0.17 and 0.26 for flat rents, but, when control variables are included, we find no relationship between population change and house rents and a significant negative relationship with flat rents (with elasticities between -0.33 and -0.71). This suggests that the positive relationship between population change and local rents is largely a consequence of changes in the composition of the local population that accompany, and may be partly caused by, the population change. Overall, these results are consistent with the evidence presented in Figure 2 and imply that while overall changes in population are positively related to changes in both house sales prices and rents, the relationship is much weaker than that found in the aggregate data for NZ and when examining local housing markets in the US.
As previously discussed, it is possible that different components of population change have differential impacts on the housing market. To investigate this, we decompose the population growth rate in each local area into four additive components relating to different sources of population change: New Immigrants; Returning Kiwis; net changes in the population of Previous Immigrants; and net changes in the population of Local Kiwis.
`Ch(Pop)_(LMA(t,t-5))=("NewImm"_(LMA,t)/(Pop_(LMA,t-5)))`
`+ ("ReturnNZ"_(LMA,t)/(Pop_(LMA,t-5)))`
`+ ((EarlierImm_(LMA,t)-Imm_(LMA,t-5))/(Pop_(LMA,t-5)))`
`+ ((LocalNZ_(LMA,t)-NZ_(LMA,t-5))/(Pop_(LMA,t-5)))` (3)
If each component of population change affects housing prices in the same way, all four terms in equation (3) will enter equation (2) with a coefficient of β. We relax this constraint and allow each term to have a different coefficient, as shown in equation (4).
`Ch(Pop)_(LMA(t,t-5))=alpha=beta_1("NewImm"_(LMA,t)/(Pop_(LMA,(t-5))))`
`+ beta_2("ReturnNZ"_(LMA,t)/(Pop_(LMA,t-5)))`
`+ beta_3((EarlierImm_(LMA,t)-Imm_(LMA,t-5))/(Pop_(LMA,t-5)))`
`+ beta_4((LocalNZ_(LMA,t)-NZ_(LMA,t-5))/(Pop_(LMA,t-5)))`
`+deltaDeltaX_(LMA(t,t-5))+Delta e_(LMA,t`
`Delta e_(LMA,t)=bar tau_t+bar epsilon_(LMA,t)`
(4)
The results in Table 6 show that different sources of population change are associated with quite different changes in house prices. Whereas the results in Table 5 indicate that a one percent population increase is associated with a 0.26 percent increase in house prices, those in Table 6 imply that a one percent population increase resulting solely from Returning Kiwis is associated with a 9.1 percent increase in house prices. Controlling for general changes in the population composition of local areas, the estimated elasticity falls to 7.6, which indicates that about one-sixth of the overall relationship between inflows of Returning Kiwis and changes in house prices is accounted for by the fact that Returning Kiwis locate in areas where observable population characteristics change in ways that are expected to raise house prices (for example, they located in areas where overall incomes were increasing). Some of this change may, of course, be attributable to the inflow of Returning Kiwis. In contrast, population increases resulting from New Immigrant inflows are associated with lower house prices, although the estimate is statistically different from zero only when controlling for population characteristics.
Other sources of population change have no significant relationship with changes in house prices. This general pattern is evident for all four geographic area definitions, albeit with differences in the statistical significance of particular estimates. Table 6 reports estimates of equation (4) not only for house price changes but also for changes in flat prices and rents for houses and flats. The impact of the population change components on the sales price of flats is very similar to the impact on house sales prices, with Returning Kiwis being most strongly associated with flat price appreciation. Rents are also higher in areas where Returning Kiwis locate, though the elasticity of 3 to 5 is lower than the impact on sales prices.[18]
It is perhaps surprising that components of population change can be related to house price changes in such markedly different ways. It is unlikely that the quantity of housing demanded by Returning Kiwis and New Immigrants differs greatly, although Tables 1 and 2 do show that Returning Kiwis are much more likely than New Immigrants to own homes. Some of the differential impact of New Immigrants compared with Returning Kiwis may occur because of stronger self-selection of Returning Kiwis into markets that would have had high house price appreciation anyway or into markets where housing supply is relatively inelastic. In this context, housing markets may be defined by local areas or by the type of housing demanded if there is imperfect local substitutability between different housing types.
Population increase due to the arrival of New Immigrants is almost always estimated to be relatively small and negative, though the estimates are rarely statistically significant. There are obvious issues of endogeneity, as New Immigrants may choose locations partly on the basis of expected house price growth. The direction of bias is not, however, clear. New Immigrants may choose to locate in areas where economic prospects are improving, leading to an upward bias in the estimated elasticity, or they may be choosing areas that are becoming relatively less expensive, in which case the estimated elasticities will be understated. To gauge the importance of endogeneity, we use an instrumental variables approach to estimate the elasticity of local house prices with respect to a component of the New Immigrant inflow that is independent of local house prices. Maré et al. (2007) show that migrant networks are the most important factor in the settlement decisions of recent migrants to New Zealand. Thus, following the approach taken by Bartel (1979), Altonji and Card (1991) and others, we instrument the inflows of New Immigrants to a local area with the concentration of immigrants from the same region of birth in that area in the previous census.[19]
The specification for this model is similar to that in equation (4), but only the inflow rate of New Immigrants is included as a population component,
`Ch(HP)_(LMA(t,t-5))=alpha+beta("NewIMM"_(LMA,t)/(Pop_(LMA(t-5))))+deltaDeltaX_(LMA(t,t-5))+Delta e_(LMA,t)`
`Delta e_(LMA,t)-bar tau_t+bar epsilon_(LMA,t)`
(5)
We adopt this specification to allow comparability with findings in other studies, such as Saiz (2007) and Ottaviano and Peri (2007) which estimate similar models.
The IV and corresponding OLS estimates are shown in Table 7. The top-left entry in the table is the OLS estimate for the elasticity of house prices in one of 140 LMAs with respect to New Immigrants. The coefficient of -0.270, implies that a 1 percent population increase from New Immigrants is associated with a 0.27 percent decrease in house prices. This elasticity is larger than the estimated elasticity when controlling for other sources of population change (-0.730 from Table 6), although neither coefficient is significantly different from zero. The omission of the other population change components in Table 7 thus leads to an understatement of the negative relationship between inflows of New Immigrants and house prices. Even though this is the case, a comparison of the OLS and IV estimates in this specification still provides a useful indication of the degree to which New Immigrants self-select into areas with stronger or weaker house price inflation.
The IV estimates in Table 7 are generally smaller (more negative) than the corresponding OLS estimates. Across all of the different specifications, the OLS estimates are reduced by about 0.2-0.5 in specifications that do not control for population characteristics, and by a larger amount (1.0 to 2.8) when these covariates are included. This suggests that New Immigrants are choosing areas that have rising house prices, and that the OLS estimates consequently overstate the positive impact of New Immigrants on house price appreciation. Adjusting for this bias strengthens our conclusions from Table 6 that New Immigrant inflows are associated with lower house price appreciation. These estimates are starkly different from comparable estimates from studies on the US housing market, being of a similar magnitude but opposite sign. For example, Saiz (2007) finds elasticities of around 1 for rents and greater than 2 for house prices, compared to our IV estimates of around -3 for both house prices and rents (140 LMAs, including covariates).
We next extend this model to also include controls for the other population components. A lack of credible instruments for each of the four population components prevents us from estimating a full instrumental variables version of equation (4). Instead, we divide population change into two rather than four components, allowing for separate impacts of changes in the local New Zealand-born and immigrant populations.
`Ch(HP)_(LMA(t,t-5))=alpha=beta_1(("Imm"_(LMA,t)-Imm_(LMA,t-5))/(Pop_(LMA,(t-5))))`
`+ beta_2(("NZ"_(LMA,t)-NZ_(LMA,t-5))/(Pop_(LMA,(t-5))))`
`+deltaDeltaX_(LMA(t,t-5))+Delta e_(LMA,t`
`Delta e_(LMA,t)=bar tau_t+bar epsilon_(LMA,t)`
(6)
Then, for instruments, we use the predicted inflow of New Immigrants, as in Table 7 and the inflow rates of return New Zealanders from the previous inter-censal period. The quality of the instruments is lower in this extended model; in the case of 140 LMAs, the partial R2 is 0.32 and the Wald statistic for the significance of the instrument has a value of 67 for the first-stage regression first-stage predicting the change in the immigrant population and the partial R2 is 0.24 and the Wald statistic for the significance of the instrument has a value of 11 for the first-stage regression first-stage predicting the change in the NZ-born population.
As in Table 6, increases in the immigrant population are associated with lower house price appreciation, whereas increases in the New Zealand-born population are associated with higher house prices. The top-left entry in the table is the OLS estimate for the elasticity of house prices in one of 140 LMAs with respect to changes in the local immigrant population. The coefficient of -0.480, implies that a 1 percent population increase from immigrants is associated with a 0.48 percent decrease in house prices. The next entry down is the OLS estimate for the elasticity of house prices with respect to changes in the local NZ-born population. The coefficient of 0.810, implies that a 1 percent population increase from immigrants is associated with a 0.81 percent increase in house prices. Instrumenting to take account of endogenous locational choices strengthens these patterns, with the house price elasticity for immigrants decreasing to -0.98 and for NZ-born increasing to 1.31 (in 140 LMAs). The difference between the OLS and IV estimates are significantly larger when controling for covariates. Overall, these results imply that immigrants are choosing to live in areas with higher house price growth while the New Zealand-born are choosing to live in areas with low house price appreciation, and controling for this, there is an even stronger negative relationship between movements of immigrants and house prices and an even stronger positive relationship between movements of New Zealanders and house prices.
[16] This approximation is adopted to facilitate the subsequent additive decomposition of population growth into components due to New Immigrants, Returning Kiwis, population changes in Previous Immigrants and population changes in Local Kiwis. Fixed effects regression provide an alternative approach for estimating this model, but since house prices are serially correlated, first difference models are more likely to produce unbiased standard errors.
[17] Controls include changes in the following characteristics for the local population: mean age and age-squared, percent aged 18-24 and aged 65+ (omitted percent aged 25-64), percent female, percent with school qualifications, with post-school qualifications, with degree qualifications and with missing qualifications (omitted percent with no qualifications), percent employed part-time in a wage/salary job, employed full-time in a non-wage/salary job, employed part-time in a non-wage/salary job, unemployed and not in the labour force (omitted percent employed full-time in wage/salary job), percent married, de-facto, divorced/separated, widowed and missing marital status (omitted percent never married), percent couple without kids, couple with kids and single with kids (omitted non-family), mean number of 0-5, 5-12, 13-17, 18-24, 25-64, and 65+ year-olds in private dwellings, the same characteristics for non-private dwelling, the percent of individuals living in private dwellings, mean log income, the percent with zero or negative income and the percent with missing income. Unlike in the individual regressions of Table 2, we do not control for the ethnic distribution in local areas because this is higher collinear with the number of immigrants in the local population.
[18] Another fairly consistent pattern across the various specifications is that an increase in the number of Previous Immigrants in an area is associated with a moderately strong increase in local sales prices (an elasticity of around 0.5 to 2) and a similar sized decrease in local rents. However, these estimates are mostly not significant.
[19] Formally, let RMgt represent the number of New Immigrants from source country g in census t, and let λgk(t-5) represent the fraction of immigrants from country g that is observed living in location k in the previous census. In the absence of endogenous location decisions, the number of New Immigrants from country g who would be expected to live in location k in census t is λgk(t-5) * RMgt. Summing over all countries, we calculate the component of the supply of New Immigrants in each location that occurs because of an individual’s desire to live near other migrants from their home country. In practice, we group individuals into thirteen regions when calculating this instrument (Australia; Pacific Islands; British Isles; Western Europe; Eastern Europe; North America, Central and South America; North Africa and the Middle East; Sub-Saharan Africa; South-East Asia; North-East Asia; Southern and Central Asia; and missing country of birth). The first stage regression of actual New Immigrant flows into an area on the predicted flow performs well. In the case of 140 LMAs, the partial R2 is 0.47 and the Wald statistic for the significance of the instrument in the first-stage regression has a value of 199 (see Baum et al (2007) for a discussion on evaluating the quality of an instrument).