6. The Cox Proportional Hazard regression model: Results and discussion

The KM analysis in the last section indicated trends that strongly associate particular groups with certain observed labour market outcomes, but the approach is limited in its ability to determine causation. In this section, we discuss results from survival analysis using the Cox Proportional Hazard modelling approach to identify causal factors and determine the extent of their impacts on a range of labour market outcomes with measurable degrees of confidence. In all the models we considered, the duration spell we wish to analyse is the time spent in unemployment after graduation, while the exit event (outcome) varies with each model. The spell is our dependent variable y and is fixed across the models, and our x regressor variables change with the models. To proceed, we test the impact of a set of regressors on four types of labour market outcomes – three of which are objective outcomes, and one is a subjective wellbeing measure. For the objective analysis, we use HILDA person-level data on the type of employment, level of earnings, field of education and job type. For the subjective well-being analysis, we use HILDA information on self-reported feelings of job and satisfaction measures. Further, for each model presented, three sets of results are discussed – one obtained using all people in the sample that includes a gender variable called female and two others obtained by stratifying the sample into all male and all female and estimating the models for each group.

To facilitate the discussion and understanding, it will be good to recall that the estimated coefficients pertain to the hazard ratios h(t) between a reference group r and the group of interest z, where these measure the relative speed of exiting unemployment. It will thus be very helpful to know which is the reference group. Further, in considering the numerical estimates, the following rule of thumb applies: If h(t) < 1, this means that z has a lower hazard rate compared to r, or equivalently, z has a longer median survival than r. Conversely, if h(t) > 1, this means that z has a higher valued hazard rate compared to r, or equivalently, z has a shorter median survival than r.

In Model 1 of Table 3, col (1) shows that on average, women graduates find full-time jobs 26 per cent slower than men graduates. This is about three months longer relative to the reference male who finds full-time employment within 12 months of graduation. Further, this model shows that (i) parents spend 25 per cent longer (or three months more in a year); in unemployment after graduation than their childless counterparts; (ii) those living in urban areas take 15 per cent longer (or two months more in a year) to find full-time jobs than those living in regional areas; (iii) migrants from non-English speaking countries take 16 per cent longer (or two months more in a year) to find full-time jobs than Australian-born graduates (iv) people living in areas with higher unemployment tend to be unemployed for longer than those living in areas with lower unemployment rates; and (v) more recent graduates take longer to find full-time employment than those who graduated in earlier years. The results further show that a person’s age, marital status, health, level of tertiary education and being born in an English speaking overseas country do not make a difference (positive nor negative) to one’s length of unemployment duration after graduation.

Table 3. Cox Proportional Hazard modelling results: Objective measures – employment and earnings models

+Binary; Base variables are male, no children, single, rural. ++ Tertiary Degree Base: Bachelors/Honours. +++Country of Birth base is Australia. ^aHealth Score ranges from 1 (excellent) to 5 (poor), self-rated. *Significant at the 1 per cent level **Significant at the 5 per cent level ***Significant at the 10 per cent level.

Overall, results in Model 1 provides strong empirical support for the claim that women face large labour market penalties based on their gender and parental status. The gender disaggregated results in columns (2) and (3) show that the parent variable is highly significant for women but insignificant for men, implying that being a father does not affect unemployment exit rates for men, but a high level of disadvantage is evident for mothers seeking full-time employment compared to women without children. The results also show that the impact of major city living on finding full-time employment is gendered, as women living in cities experience longer periods of unemployment than men, as well as women, in regional/rural areas. This result supports the claim that women in both inner and outer metropolitan areas are experiencing severe and entrenched disadvantage (Productivity Commission 2017).

In Model 2, the exit event is finding a permanent job. As in Model 1, we find that being a woman, living in major cities, being a migrant from a non-English speaking nation, area unemployment rate and year of graduation are significant factors holding back individuals from finding a permanent job. The associated coefficients’ signs are also all found to be negative and gendered, indicating higher wage penalties accruing to women than men. Unlike Model 1, however, results in Model 2 show that being a parent is not a significant factor in finding a permanent job, but that having a graduate diploma or certificate improves one’s chances of permanent employment, particularly for men. Further, we find that being a migrant from a non-English speaking country and year of graduation penalises men more than women, while living in areas where unemployment is high penalises women more than men.

In Model 3, the exit event occurs when the individual’s annual earnings start to exceed the average earnings of everyone in the sample. Here, we again find that gender, being a parent, a migrant from a non-English speaking nation, living in high unemployment rate areas and recent years of graduation present significant downside risks. In contrast, living in major cities appears to be of no consequence. Other demographic variables like age, health and additional tertiary qualifications now also emerge as significant regressors. The coefficients for age across the various specifications are highly significant and positive, implying that the older a person is, the quicker their earnings can rise above that of the average person and we find these results hold with larger effects across the disaggregated men and women regressions. Health also becomes important in this model, with the model showing that poorer health causes a relatively slow progression to above-average levels of earnings, and that this effect is more pronounced for women compared to men. The two education variables are also found to be highly significant in influencing this earnings outcome. The PhD/masters and grad dip/cert variables are both significant and positive, meaning that people with these extra qualifications achieve this benchmark earnings quicker than those without them. Model 4 is a slight modification to Model 3 in that we benchmark total earnings with median, rather than mean, earnings. The results for this model are very similar to those of Model 3.

We now discuss our job-skills match models in Table 4, which examine the role of occupation type in the graduate labour market. To identify a job-skills mismatch in this article, we use the job analysis method used in McDonald and Valenzuela (2017). The educational requirements of the person’s occupation are ranked and compared to their educational qualifications, and a mismatch is identified if the former is less than the latter. In determining the educational requirements of particular occupations, guidance is taken from the Occupation ANZCO 2006 system which, at its broadest level, identifies four broad occupation skill levels and the educational qualifications required for each. In our sample, a match occurs if they are either a manager or a professional. Anything coded 2 or higher in the ANZCO value label is considered a mismatch and a higher value indicates a higher degree of occupational mismatching.

Table 4. Cox Proportional Hazard Modelling Results: Objective Measures - Job Skill Match Models

+Binary; Base variables are male, no children, single, rural, ++ Tertiary Degree Base: Bachelors/Honours. +++Country of Birth base is Australia. ^aHealth Score ranges from 1 (excellent) to 5 (poor), self-rated. bjob mismatch score ranges from 1 (match) to 4 (greatest mismatch). *Significant at the 1 per cent level **Significant at the 5 per cent level ***Significant at the 10 per cent level.

In Model 5, our exit variable is finding a job that matches the person’s qualification. Here, we find that gender, marital status, living in major cities, additional degrees, being a migrant and year of graduation are important determinants of labour market outcomes. The gender coefficient is significant and negative, implying that relative to men, women take longer to find a job that matches their tertiary qualifications. Marital status is not significant for men but highly significant for women. Age is not significant overall but becomes significant if the regression is restricted to women only. The same holds for the parent variable – it is not significant overall, but becomes significant in the women-only regressions, indicating lengthier spells for achieving a job-skill match for mothers than for fathers. In Models 6 and 7, the exit events are defined by achieving above-average mean and median earnings, respectively, and the job-skill match identifier is made a covariate rather than a dependent variable, as was done in Model 5. Here, we find that this job-skill variable is highly significant in both models, meaning that the greater degree of mismatch one experiences on the job, the longer it takes to achieve mean or median earnings level, which makes perfect sense. For the other covariates, we find that being a parent, health and being a migrant from a non-English speaking country can cause longer durations for women than men in this model, while the other significant covariates are non-gendered.

Lastly, we discuss Table 5, which presents the results from our subjective hazard rate models. These models are deemed subjective because the exit events are based on self-rated survey responses using feelings or impressions. In particular, the key survey responses we use are ‘I feel secure in my current job’ (Model 8) and ‘I use my skills in my current job’ (Model 9). The modelling exercise returned weaker effects compared to the more objective models presented earlier. For example, in Model 8, we find that health is very important in feeling secure in the job for both men and women, while a non-English language background matters more for men and area unemployment rate matters more for women. For Model 9, we find that having a non-English language background is highly significant for women only and that an additional graduate qualification (diploma or certificate) matters to men’s occupation-skill match impressions.

Table 5. Cox Proportional Hazard modelling results: Subjective measures

+Binary; Base variables are male, no children, single, rural. ++ Tertiary Degree Base: Bachelors/Honours. +++Country of Birth base is Australia. ^aHealth Score ranges from 1 (excellent) to 5 (poor), self-rated.