4 The Dunedin Study results
The results in this section are based on the Dunedin Study data described in Section 3.1. Table 1 shows intergenerational income elasticity rates for nine models of intergenerational mobility. The first model used fathers' incomes to explain the incomes of males from Dunedin who were living in New Zealand at age 32, and included the standard intergenerational income mobility controls of fathers' ages and fathers' ages squared (Couch and Lillard, 2004, p. 198; Solon, 1992, p. 399). The intergenerational income elasticity for model one was 0.253, although the large standard error suggests considerable variability (95% confidence interval: 0.081 to 0.424).[17]The elasticity implies that if an average man's father earned 1% more than the father of another man, he himself would earn 0.253% more annually at age 32. The age controls are not statistically significant for any model, and have been included simply to ensure that the equations for men and for women are the same as those used in overseas studies.[18]
The elasticity for model one is identical to Andrews and Leigh's intergenerational income elasticity of 0.25 for New Zealand men aged between 25 and 54 (95% confidence interval: .03 to .46). They used 1999 national survey data on respondents' recall of their fathers' occupations to impute incomes (Andrews and Leigh, 2008, p. 13).
The Dunedin results are easier to understand by considering an example. When the participants were in their teens, the average income of fathers in the Dunedin Study was about $48,000 in 2008 values, while the level of income imputed for fathers in the top income group was approximately $80,600. Suppose a man from Dunedin had grown up with a father who was in the top income group and who was the average age of 41.4 when they were 13. The intergenerational income elasticity for model one of 0.253 implies that this man would, on average, earn almost $7,000 more annually at age 32 than another man whose father had been the same age but had been in the average income group.[19] Because of the large standard error for the parameter and because of measurement errors, however, we have to be very cautious. Model one explained only 2.5% of the variance in the incomes of men (see the adjusted R2 line in Table 1). This indicates that a wide range of other factors influence participants' incomes.
The estimated intergenerational income elasticity for women from Dunedin living in New Zealand was just 0.167 (see model two), but was not statistically significant even at a 10% level. Model two also explained just 0.09% of the variance in women's incomes. Measuring intergenerational mobility for women is difficult because the labour force participation of some women was limited by the time they were spending looking after children. At age 32, 15.4% of women and 1.4% of men in the Dunedin Study who were living in New Zealand were out of the workforce because they were homemakers or beneficiaries. The difference between the intergenerational income elasticities for men and women is not statistically significant.
For the third model we included all Dunedin Study participants living in New Zealand but added a gender control. We also dropped the statistically insignificant variables for the age of fathers. Since age details are missing for some fathers this slightly improves our sample size, although the results were very similar with the age controls included (not shown here). Model three implies an intergenerational income elasticity of 0.212 for males and females. Although the proportion of variance explained is higher than for the first two models, this has occurred because we have pooled men and women. Model three quantifies the “between gender” variation by including a control for the tendency for men to earn more than women. Tests of whether the effect of father's income differed for men and women indicated no statistically significant difference, so no interaction term is included in the model. The pooled model without the gender control (not shown here) explained only 1.4% of the variance in incomes. This implies that the gender control explains more of the variance in incomes than fathers' income alone.
| Model 1 | Model 2 | Model 3 | Model 4 | Model 5 | Model 6 | Model 7 | Model 8 | Model 9 | |
|---|---|---|---|---|---|---|---|---|---|
|
Income of males in New Zealand |
Income of females in New Zealand |
Income of those in New Zealand | Income of all males irrespective of country | Income of all females irrespective of country | Income of everyone, irrespective of country | Income of everyone, with parents' income as explanatory variable | Income of everyone with controls for education | Income of everyone with controls for education and country | |
Constant |
6.585 (1.62)*** | 8.198 (2.41)*** | 7.838 (.709)*** | 6.067 (1.54)*** | 7.813 (2.12)*** | 7.418 (.666)*** | 7.246 (.714)*** | 8.226 (.697)*** | 8.002 (.676)*** |
Income effects |
|||||||||
| Father's income | .253 (.087)*** | .167 (.102) | .212 (.066)*** | .290 (.08)*** | .215 (.096)** | .264 (.062)*** | |||
Parents' income |
.272 (.064)*** | .144 (.064)** | .162 (.062)*** | ||||||
| 95% CI | .081, .424 | -.034, .368 | .083, .341 | .127, .454 | .027, .403 | .143, .385 | .146, .398 | .019, .269 | .041, .283 |
Parental age control |
|||||||||
| Father's age | .065 (.064) | .005 (.103) | - | .075 (.063) | .002 (.090) | - | - | - | - |
| Father's age squared | -.00071(.0007) | -.00005(.0012) | - | -.00083(.0007) | .00003 (.0010) | - | - | - | - |
Gender control |
|||||||||
| Male | - | - | .631 (.067)*** | - | - | .584 (.060)*** | .596 (.061)*** | .644 (.059)*** | .621 (.057)*** |
Educational qualifications (base=no school qualification) |
|||||||||
| School Certificate | - | - | - | - | - | - | - | .166 (.107) | .158 (.104) |
| Finished high school | - | - | - | - | - | - | - | .428 (.090)*** | .373 (.088)*** |
| Bachelor's degree | - | - | - | - | - | - | - | .641 (.103)*** | .565 (.101)*** |
| Higher degree | - | - | - | - | - | - | - | .994 (.143)*** | .853 (.141)*** |
County (base=New Zealand) |
|||||||||
| Australia | .402 (.081)*** | ||||||||
| Britain | .705 (.126)*** | ||||||||
| Rest of world | -.165 (.153) | ||||||||
| Adjusted R2 | 2.5% | 0.09% | 14% | 3.3% | 0.7% | 13% | 13% | 20% | 25% |
| Probability > F | .018 | .437 | 0 | 0 | .144 | 0 | 0 | 0 | 0 |
| Number of cases | 289 | 291 | 592 | 393 | 372 | 780 | 764 | 763 | 763 |
Column entries are unstandardised linear regression coefficients. Values are for log income. Standard errors are in brackets. *=p<.10, **=p<.05, ***=p<.01. Those whose income is missing or declared zero income (eg homemakers) have been excluded. Income is an extremely sensitive topic and missing values, usually for the fathers of participants, have reduced the number of cases.
Notes
- [17]In a random sample or a repeatable experiment, the true parameter value has a 95% likelihood of being contained within a 95% confidence interval. The confidence intervals in this section apply to people from Dunedin who were born in the early 1970s, rather than to all New Zealanders.
- [18]Father's age has been included in overseas studies because income often changes over a person's lifecycle. The effects of father's age seem to vary between country, and appear to be larger in the United States than in Britain (Zimmerman, 1992, p. 418). Researchers using a very large dataset of Canadian men found that including controls for the ages of fathers did not change the elasticities (Corak and Heisz, 1999, p. 514).
- [19]The elasticity is for the effect of the log of fathers’ incomes on the log of sons’ incomes. To calculate an estimated income multiply the log of father’s income by the elasticity, multiply the father’s age and age squared by the coefficients for these variables, add the intercept, then take an anti-log. Note that in this model the only requirement is that these men have the same-aged father. The model does not control for the effect of any other characteristic on income. This example also assumes the relationship between the logs of incomes is linear, when there is some evidence from overseas that immobility is highest at the extremes of the income distribution.
