5.2 Regression analysis
While relatively simple to produce and interpret, descriptive bivariate analysis of the type presented in the previous subsection can often be misleading. This is because any apparent relationship (or lack thereof) could actually be the result of an omitted factor. For example, we saw that Europeans are a lot more likely to own houses than all other ethnicities. It may be the case that this is due to different preferences for homeownership amongst different ethnic groups. However, it could also be that Europeans are older and therefore have had longer to accumulate wealth, or on average are more likely to live outside of Auckland (the region with the highest house prices in New Zealand). To guard against the possibility of drawing spurious relationship between variables in this way, multivariate analysis is required.
The results of logistic random effects panel regressions of home ownership status are presented in Table 2, where the effects of a range of factors likely to affect the probability of owning a home are examined simultaneously.[11] The dependant variable is equal to one if an individual owns the home they live in and zero otherwise. Explanatory variables include those discussed in Section 5.1 as well as gender, years of schooling, whether or not the respondent was born in New Zealand and regional house prices.
Positive coefficient values associated with variables indicate that an increase in the value of that variable is associated with an increased likelihood of home ownership and vice versa. For readers interested in these results in more detail, coefficients can also be interpreted as log odds ratios. If one exponentiates the coefficient estimates then this provides odds ratios. For example, looking at the regression combining singles and couples, the ratio of the odds of owning a home (compared to not owning a home) for partnered versus non-partnered individuals is 9.4:1[12] (i.e. e2.2407).
Results are largely what one would expect, and confirm the associations illustrated by the descriptive analysis of the previous subsection. For example, focussing again on the regression combining singles and couples, the likelihood of owning a home improves with age (but at a decreasing rate), if one is partnered or lives outside of Auckland. The likelihood is reduced if an individual is any ethnicity other than European.
| Variables | Singles | Couples | Combined |
|---|---|---|---|
| Income | 0.0000** | -0.0000* | 0.0000 |
| (0.0000) | (0.0000) | (0.0000) | |
| Years of Schooling | 0.4538** | 0.0338** | 0.1223** |
| (0.0476) | (0.0095) | (0.0194) | |
| Age | 0.8764** | 0.1860** | 0.5228** |
| (0.0441) | (0.0101) | (0.0177) | |
| Age squared | -0.0060** | -0.0012** | -0.0038** |
| (0.0004) | (0.0001) | (0.0002) | |
| Partnered | 2.2407** | ||
| (0.0810) | |||
| Female | 1.0866** | 0.1140** | 0.3481** |
| (0.2262) | (0.0425) | (0.0890) | |
| New Zealand Born | 1.1820** | 0.2294** | 0.1323 |
| (0.3492) | (0.0631) | (0.1291) | |
| Regional House Price | -2.9378** | -1.0983** | -2.1505** |
| (0.3611) | (0.1273) | (0.1530) | |
| Maori | -5.3391** | 0.3765** | -2.4108** |
| (0.4049) | (0.0695) | (0.1596) | |
| Pacific Islander | -5.9337** | 0.9700** | -3.9320** |
| (0.6326) | (0.1474) | (0.2485) | |
| Asian | -2.5910** | 1.3886** | -1.1794** |
| (0.8262) | (0.1023) | (0.2350) | |
| Other Ethnicity | -3.3665** | 0.0431 | -2.5249** |
| (0.9938) | (0.1504) | (0.3663) | |
| Waikato | 1.5238** | 0.1600 | 0.6372** |
| (0.3698) | (0.0826) | (0.1572) | |
| Wellington | 0.5427 | 0.7771** | 0.9306** |
| (0.3522) | (0.0727) | (0.1417) | |
| Rest of North Island | 1.5073** | 0.4388** | 0.8507** |
| (0.3120) | (0.0628) | (0.1238) | |
| Canterbury | 1.4723** | 1.0748** | 1.0565** |
| (0.3405) | (0.0675) | (0.1365) | |
| Rest of South Island | 1.8052** | 0.7854** | 1.2099** |
| (0.3594) | (0.0729) | (0.1440) | |
| Constant | -33.9965** | -6.2264** | -16.4308** |
| (1.4248) | (0.3266) | (0.5530) | |
| Log Likelihood | -6023.3162 | -14716.7110 | -21261.7300 |
| Observations | 13910 | 31740 | 45650 |
| Groups | 7535 | 13985 | 19805 |
Source: Statistics New Zealand (SoFIE) data
Notes - The dependant variable is one if the person owns their own home, and zero otherwise. The effects of ethnicity and region are relative to being New Zealand European and living in Auckland respectively. Person specific effects are included in all regressions. Standard errors are in parenthesis. Two stars (**) indicates that the coefficient is significantly different from zero at the 1% significance level and one star (*) indicates that it is significant at the 5% level.
It is interesting that income is not found to have a statistically significant effect on the likelihood of homeownership. However, additional years of schooling are positively associated with the likelihood of homeownership. This suggests that people's lifetime earnings, rather than income at a point in time, may be a more important determinant of whether one owns a home.
Three further factors not discussed in the previous subsection, but likely to influence homeownership, have been included in our regressions: gender, whether or not the respondent was born in New Zealand and regional house prices. Being female and New Zealand born are both associated with increases in the likelihood of owning a home, though New Zealand-born is not statistically significant at conventional levels. It is probable, however, that if we were to split those individuals not born in New Zealand into recent arrivals (say in the last five to ten years) and those who have been living here longer, we would observe a stronger relationship. Finally, higher house prices have a significant negative effect on the likelihood of home ownership.
