In this paper, the functional definition of literacy and numeracy is used. That definition is consistent with the human capital approach to literacy and numeracy.

Functional measures of literacy and numeracy give a more sophisticated view of people’s abilities than proxy measures (such as years of schooling) used in the formal approach. Although years of schooling is a measure of an input into the education system, literacy and numeracy skills directly measure educational outcomes (Osberg 2000). Furthermore, while people’s highest level of educational attainment or years of education remains largely unchanged over the course of their lives, their actual skills may vary at different points in time, depending on how they are used in daily activities.

Compared with the social and cultural approach, the functional definition of literacy and numeracy is easier to measure, making it more useful for the empirical analysis in this paper.

Functional literacy and numeracy skills of the Australian population were obtained from the Adult Literacy and Lifeskills Survey (ALLS) for 2006. It is only the second survey of its kind for Australia. The first survey, for 1996, contained survey data that were highly aggregated, which restricted its use in exploring links between skills and labour market outcomes. The ALLS includes information for almost 10 000 survey respondents, covering the population aged 15 to 74. Each respondent is assigned a test score for various literacy and numeracy skills. There is also information for each person’s labour market status, education and income.

The ALLS measures several ‘domains’ of literacy and numeracy, which relate to the different types of skills necessary to function in a modern society. These are:

Each skill domain is measured in two different ways.

First, based on test responses, each skill is measured on a continuous scale ranging from 0 to 500. Each person is located along this continuum, with those people who have poorer literacy or numeracy obtaining a lower rating than those who have higher literacy and numeracy skills.

1 An exception is for the problem solving domain, for which there are only four skill levels.

Tasks in this level tend to require the respondent either to locate a piece of information based on a literal match or to enter information from personal knowledge onto a document. Little, if any, distracting information is present.

Tasks in this level are more varied than those in Level 1. Some require the respondents to match a single piece of information; however, several distractors may be present, or the match may require low-level inferences. Tasks in this level may also ask the respondent to cycle through information in a document or to integrate information from various parts of a document.

Some tasks in this level require the respondent to integrate multiple pieces of information from one or more documents. Others ask respondents to cycle through rather complex tables or graphs which contain information that is irrelevant or inappropriate to the task.

Tasks in this level, like those at the previous levels, ask respondents to perform multiple-feature matches, cycle through documents, and integrate information; however, they require a greater degree of inferencing. Many of these tasks require respondents to provide numerous responses but do not designate how many responses are needed. Conditional information is also present in the document tasks at this level and must be taken into account by the respondent.

Tasks in this level require the respondent to search through complex displays that contain multiple distractors, to make high-level text-based inferences, and to use specialised knowledge.

In the descriptive analysis in this paper (chapters 3 and 4), both the continuous and discrete skill measures are used when presenting results. The econometric analyses (chapters 5 and 6) uses only the discrete skill level, because these skill levels have more interpretable definitions than the continuous variable. For example, level 3 is regarded by the survey developers as the ‘minimum required for individuals to meet the complex demands of everyday life and work in the emerging knowledge-based economy’ (ABS 2006, p. 5).

For the analysis in this paper (and as the ABS has done in their summary publication), level 4 and level 5 are grouped together (when using the discrete measure) because few people were assessed at level 5.

The various literacy and numeracy skills are highly correlated. More than 70 per cent of the population reported the same document literacy and numeracy skill level (bold numbers in table 2.1). A similar pattern occurs for correlations between other skill variables in the survey.

Per cent of population

Total 20.31 30.91 33.15 15.63 100.00

As well as test scores, the ALLS also has subjective measures of literacy and numeracy skills. For example, respondents were asked to rate their ability to use their reading, writing and mathematical skills at work as being either ‘good’, ‘very good’ or ‘poor’. As noted above, self-assessed indicators of functional literacy and numeracy have potential measurement errors. Furthermore, Finnie and Meng (2005) showed that objective measures of skill consistently gave a better explanation of labour market outcomes (employment and income) than subjective measures did.

For these reasons, only the objective test scores of literacy and numeracy skills are used in this paper (for both descriptive and econometric analyses).

3 A profile of literacy and numeracy skills in Australia

In this section, the literacy and numeracy skills of Australia’s population in 2006 are explored using the ALLS data. Comparisons are also made over time and with other countries. Following this, the literacy and numeracy skills of specific demographic groups are described.

As noted in chapter 2, there is a strong correlation across the different types of skills assessed. Looking at each skill type, up to half of those people surveyed in 2006 (44–50 per cent) had low (level 1 or 2) prose literacy, document literacy or numeracy and almost 70 per cent had low problem solving skills (table 3.1). About one third of the population had level 3 skills for each type of skill (except problem solving).

By skill type, 2006

Prose 14.5 29.0 43.5 38.8 17.7

Document 15.5 28.0 43.5 37.1 19.4

Numeracy 19.7 30.0 49.7 32.8 17.5

Problem solving 32.1 35.7 67.8 26.3 5.9

The above information suggests that a substantial proportion (almost 50 per cent) of

working age Australians have ‘low’ skills, which is in contrast with 2009 NAPLAN

results that reported about 90 per cent of students met basic literacy and numeracy

standards. The discrepancy between the NAPLAN test results and the ALLS may

be, in part, due to the different age brackets for people tested under NAPLAN

(students in years 3, 5, 7 and 9) and the ALLS, which was conducted for persons

aged 15–74. More likely, however, is that the NAPLAN tests and the ALLS have

different interpretations of the benchmark regarding ‘basic’ or ‘minimum’ skill levels.

The COAG Reform Council provides some useful guidance on how to interpret

these benchmarks. It states that NAPLAN is designed to measure student

performance in meeting the ‘minimum standards’ of literacy and numeracy,

whereas the ALLS measures the proportion of working age Australians with a

‘proficient standard’ of literacy and numeracy to effectively participate in society

(COAG Reform Council 2009, p. 47). Thus, while some students may have only

level 1 or level 2 literacy and numeracy in the ALLS, they may still meet the

minimum standard of literacy and numeracy under the NAPLAN definition.

Of the five skills measured in the ALLS (2006), only prose and document literacy

are directly comparable with the Survey of Aspects of Literacy (SAL) for 1996.

Problem solving and health are new dimensions, while numeracy has been expanded.

There were small, but statistically significant, changes in both prose and document

literacy between 1996 and 2006 (ABS 2006). There was a statistically significant

decrease in the proportion of people with level 1 prose and document literacy. This

corresponded with an increase in the proportion of people with level 2 prose and

document literacy between 1996 and 2006.

Level 1 and level 2 are considered to be below the level required to function in daily

activities, including work. When looking at skill levels 1 and 2 combined, the

proportion of people with low (level 1 or level 2) prose literacy decreased slightly,

from 47.4 per cent in 1996 to 46.4 per cent in 2006. Similarly, the proportion of

people with level 1 or 2 document literacy decreased from 47.9 per cent in 1996 to

1 These figures are from the ABS (2006) summary publication, which reported level 1 and level 2

skills separately. It is not known whether the changes are statistically significant.

Although the ALLS and the SAL can be used to examine changes over time, the

respondents to be re-interviewed). However, the cohort analysis presented below is

a reasonable measure of the change over time in the populations the two surveys

represent. To follow how skills of the population have changed over time, a

particular age group (spanning 10 years) in 1996 has been compared with a 10-year

older age group in 2006.

The synthetic cohort analysis (depicted in figure 3.1), shows that there was lower

document literacy for age groups 35–54 in 1996 (who were aged 45–64 in 2006)

and higher literacy for those aged 15–24 in 1996 (aged 25–34 in 2006).

Determining how skills vary according to age and over time is difficult. Cohort

effects and period effects can all influence skill development (Willms and Murray

2007). However, these results give support to a hypothesis of skill depreciation with

age and are also consistent with a hypothesis of general skill improvement in the

population over time, perhaps because younger people are now undertaking more

education. (These are discussed in more detail below.)

1996 and 2006

0.0

0.5

1.0

1.5

2.0

2.5

3.0

1996

(15 to

24yrs)

2006

(25 to

34 yrs)

1996

(25 to

34 yrs)

2006

(35 to

44 yrs)

1996

(35 to

44 yrs)

2006

(45 to

54 yrs)

1996

(45 to

54 yrs)

2006

(55 to

64 yrs)

The ALLS was conducted as part of a wider, international survey (IALS). There are

seven countries for which the 2006 Australian data can be compared. Norway had

the smallest proportion of people with skill levels 1 or 2 for prose literacy,

document literacy and problem solving (table 3.2). Switzerland had the smallest

proportion of people with numeracy levels 1 and 2. Italy had the largest proportion

of people with skill levels 1 and 2 across all four measures. (Health literacy results

are not available.)

Per cent of population aged 16–65 with skill levels 1 or 2

Australia 43.5 43.5 49.7 67.8

Bermuda 38.1 46.1 54.1 69.9

Canada 41.9 42.6 49.8 68.5

Italy 79.5 80.6 80.2 90.6

Norway 34.1 32.4 40.2 60.8

Switzerland 52.2 49.0 39.3 66.1

Australia was ranked fourth on prose literacy, with Norway, Bermuda and Canada

having lower rates of prose literacy level 1 or 2. Australia was ranked third on

document literacy, with Norway, and Canada having lower rates of document

literacy level 1 or 2. For numeracy and problem solving literacy, Australia was

ranked third behind Norway and Switzerland.

The analysis above has shown that Australia ranked in the middle compared with

the selected countries. However, there were many people deemed to have skills

below those required for day-to-day living and working, based on the standard set

by the survey designers. This section looks more closely at which groups of people

have higher and lower skill levels.

The distribution of people with high and low literacy and numeracy skills varies

depending on the particular type of literacy and numeracy being assessed and

according to gender. The main differences in particular types of literacy and

numeracy between genders (figure 3.2) are:

assessed at skill level 1 or 2, compared with 48 per cent for males)

These differences hold for most age groups (all ages in the case of numeracy) and

are consistent with previously observed patterns for other countries (Statistics

Canada and OECD, 2005).

2006

0

10

20

30

40

50

60

70

80

Males Females

Statistics Canada and OECD (2005, p. 43) state ‘Skills can be acquired, developed,

maintained and lost over the lifespan, making the relationship between skills and

age complex’. At the aggregate level, an examination of skills according to age

suggests that skills of older people are lower than younger people. Using document

literacy as an example, skills are highest for 20–24 year olds, as indicated in

figure 3.3. Skills appear to decrease as people age. This observation also is apparent

with other skill types, and occurs across countries.

200

220

240

260

280

300

15-19 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-69 70-74

A number of possible explanations for this observation are discussed below:

1. Age and up-skilling.

Up-skilling can include formal, and non-formal up-skilling. Formal up-skilling

refers to participation in a course that leads towards a certificate, diploma or degree,

whereas non-formal up-skilling does not lead towards a certificate, degree or

diploma (Satherly and Lawes 2008). As most people undertake formal education

until the age of about 20–24, their skills might increase until that age because skill

levels increase with higher levels of education. Depending on their literacy

engagement after this age, people may maintain, enhance or experience a

depreciation in their skills during late and middle age (Willms and Murray 2007).

On average, people undertake less formal or non-formal education as they get older,

which may explain, in part, the lower skill level of older persons.

2. Labour force withdrawal and skill depreciation.

The pattern of skills decreasing as people age (from about the ages of 40–44

onwards) might reflect that older people withdraw from the labour force and do not

actively use their literacy and numeracy skills, thereby lending to a depreciation in

them.

3. Cohort effects.

The quality and quantity of education provided to younger people today might be

better than it was at the time when older people obtained their education. If this

were the case, then it would be expected that younger people would have higher

skill levels compared with other people, all else equal. (This is explored in more

detail below.)

“In most societies, a principal and widely accepted goal of the educational system is

to produce a population able to read, write and count’ (Statistics Canada and

OECD 2005, p. 60). Therefore, it is not surprising that a large body of empirical

research shows that higher educational attainment is associated with higher skills.

Figure 3.4 shows the average literacy and numeracy skills for people in Australia,

by years of education undertaken (grey line) and qualification (dot points, with

average years to complete). Skills appear to increase with the number of years of

education undertaken, but at a decreasing rate.

2006

150

175

200

225

250

275

300

325

350

4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

indexes. Four years of education includes all people who acquired up to four years of education. 23 years of

education indicates people who may have taken 23, or more, years of education.

Undertaking more years of education may not improve skills in the same way for all

people. Some individuals may take more time to complete a qualification than

others (for instance, if they repeat year 12, or if they change courses at university).

Higher educational attainment is associated with higher skills. However, people

with year 12 or a degree or higher both have, on average, level 3 skills. Undertaking

more years of education than required for a degree does not lead to a noticeable

increase in skills.

These results might reflect that early years of education (primary and secondary

school) primarily serve to improve basic skills needed for day-to-day functioning,

whereas higher education (for example, VET or university) is tailored to more

vocational or job-specific skills, which do not have a noticeable impact on

functional literacy and numeracy.

In this respect, it might also be useful to examine information from the NAPLAN

results to develop an understanding of skill deficiencies in the formative years of a

person’s education. (This, and other areas for further research, are mentioned in

chapter 7.)

It was mentioned above that an education cohort effect might explain the increase in

skills between 1996 and 2006. To examine this, the distribution of document

literacy skill levels by qualification, for both 1996 and 2006, is shown in figure 3.5.

Higher qualifications are associated with higher skill levels –– the proportion of

people with level 4 or 5 document literacy is much higher for those with a degree

compared with other levels of education.

1996 and 2006

0%

20%

40%

60%

80%

100%

1996 2006 1996 2006 1996 2006 1996 2006

Degree or higher Diploma or certificate Year 12 Year 11 or

lower

Level 4/5

Level 3

Level 2

Level 1

Proportion of

people with

qualification

For the same qualification, the proportion of people with document literacy above

level 2 did not change much between 1996 and 2006. This suggests that any cohort

However, there was a shift in the proportion of people with higher levels of

education (depicted by the lines in figure 3.5). For example, 20 per cent of the

population held a degree in 2006 compared with 15 per cent in 1996. So there is an

might partly explain the overall increase in skills between 1996 and 2006.

A number of overseas studies have shown that skills vary according to country of

birth and, for immigrants, vary according to their time of arrival. Satherly, Lawes

and Sok (2008) found that, for both the United States and New Zealand, native born

people had higher skills than immigrants. In the United States, recently arrived

immigrants (those who arrived within five years at the time of the survey) had

higher skills than established immigrants (those who arrived more than five years

ago), but the opposite was the case for immigrants in New Zealand.

The skills of immigrants by both country of birth and time of arrival can also be

explored for Australia using data from the ALLS.

Recent immigrants are, on average, 31 years old, whereas established immigrants

are 48 years old. (Australian born people were 40 years old, on average, in 2006).

As shown above, there is evidence indicating that older people have lower literacy

and numeracy skills than younger people. Therefore, the skills of recent immigrants,

established immigrants and Australian born people were compared for only 20–44

year olds. This age group was chosen because, after these ages, skill levels decrease

noticeably. The sample size for this group is still large enough to make reliable judgements.

After controlling for age, there is not much difference between the prose literacy

skills of recent immigrants and established immigrants (figure 3.6). Thus, the period

of time immigrants have spent in Australia does not appear to influence their skill

levels. However, compared with the Australian born population, the skills of all

immigrants are lower (even after controlling for age).

20–44 year olds

0%

20%

40%

60%

80%

100%

Recent Established Australian born

Level 4/5

Level 3

Level 2

Level 1

undertaken, while an ‘established’ immigrant is someone who arrived more than five years from when the

survey was undertaken.

The skills of immigrants vary significantly, according to their country of birth. In

particular, immigrants born in countries the ABS defines as a main English

speaking country (including the United States, United Kingdom, Canada and South

Africa) have much higher average literacy and numeracy skills than immigrants

from other (mainly non-English speaking) countries. That is not unexpected,

because the tests were conducted in English. The literacy and numeracy skills of

immigrants from English speaking countries are higher than those of Australian

born people as a whole (figure 3.7). Immigrants from main English speaking

countries comprise about 36 per cent of all immigrants.

0%

20%

40%

60%

80%

100%

Australia Main English speaking Other

Level 4/5

Level 3

Level 2

Level 1

Zealand, Republic of Ireland and the United Kingdom.

Variations in immigrants’ skills might be influenced by the quality of schooling in

the country of origin. The ALLS also has data on where a person obtained their

highest educational qualification.

It was found that people who obtained their qualification from a non-English

speaking country tended to have lower skills compared with those with a

qualification from an English speaking country. This finding is consistent with a

study comparing results from a range of countries for which data were available:

Education credentials do not necessarily translate into functional levels of literacy,

numeracy and problem solving skills in the official language(s) of the host country.

This is especially the case if the credentials were attained abroad in a language other

than that used in the host country. (Statistics Canada and OECD 2005, p. 209)

Having an English speaking background not only affects literacy and numeracy

skills, but also labour market outcomes. For example, the Commission (PC 2006b)

found earnings of immigrants to be positively related to their English speaking

ability, after controlling for factors such as educational attainment. The effect of

non-English speaking background on labour market outcomes is explored in more

detail in the econometric analysis presented in chapter 6.

4 Literacy and numeracy skills and

labour market outcomes

Chapter 3 considered how literacy and numeracy skills vary across different

demographic groups. It was shown that some groups had much lower literacy and

numeracy skills than others, suggesting there is some potential to raise the skills of

those groups of people. This chapter considers the relationship between literacy and

numeracy skills and labour market outcomes, to help identify the potential benefits

from improving literacy and numeracy. Specifically, the relationship between

literacy and numeracy skills and the following labour market outcomes are

explored: labour force participation; occupation; and income. It will be shown that

people who have higher literacy and numeracy skills generally have much better

labour market outcomes than those with lower skills.

While participation depends on a range of factors, including the presence of

children (Cai 2010), for most people having higher human capital (including

literacy and numeracy) will encourage greater labour force participation. People

with higher functional literacy and numeracy skills are likely to achieve greater

returns from working than lower skilled people. Therefore, the higher people’s

skills are, the more likely they are to participate in the labour force, all else equal.

For various age groups, the document literacy test score according to labour force

status is presented in figure 4.1. (While the results presented in figures 4.1 and 4.2

are for document literacy, a similar pattern emerges for other skill types measured

in the ALLS.) A few observations can be made. Those in the labour force have

higher document literacy than those who are not in the labour force. This holds

across all age groups.

The difference between document literacy of those in and those not in the labour

force varies with age –– the difference is smaller for younger people (aged less than

30) compared with older people. Labour force participation might affect skills if

working utilises and maintains a person’s skills. If that were the case, the results

might reflect that older people have been out of work for a longer period, so their

skills might have decreased compared with younger workers.

175

200

225

250

275

300

325

15-19 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-69 70-74

In labour force Not in labour force

Another way this can be examined is to look at skills and the participation rate.

There is a strong correlation between the labour force participation rate and

document literacy (figure 4.2). This gives some support to the idea that people’s

skills decline if they do not participate in the workforce. (However, as shown

previously, literacy and numeracy skills decline with age, regardless of labour force

status.)

200

225

250

275

300

15-19 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-69 70-74

0

25

50

75

100

Document literacy (score - LHS) Participation rate (Per cent - RHS)

It would be expected that, all else equal, people who have high literacy and

numeracy skills are likely to be employed in professions that require the use of those skills.

Occupational data in the ALLS showed that, for those people with an average

document literacy, prose literacy and numeracy skill level of 3 or more, most were

employed as professionals, managers, and clerical and administrative workers

respectively (figure 4.3). They were least represented as machinery

operators/drivers and labourers. Conversely, people with skill level 1 or 2 were

most likely to be employed as labourers and technicians/trade workers.

0

5

10

15

20

25

30

35

Manager Professional Technician

& Trade

Community

& Pers.

Services

Clerical &

Admin

Sales Machinery

Operator &

Driver

Labourer

Level 1 or 2 Level 3, 4 or 5

(scale 0-500), converted to the equivalent level (as measured by the ABS –– see chapter 2).

Within each occupation, the proportion of people with average literacy and

numeracy skill levels 1 or 2, level 3 and levels 4 or 5 are shown in figure 4.4. Fewer

than 30 per cent of managers had low (level 1 or 2) literacy and numeracy skills. In

contrast, about two-thirds of machinery operators/drivers and labourers had level 1

or 2 literacy and numeracy skills.

SKILLS AND LABOUR

MARKET OUTCOMES

0

20

40

60

80

100

Manager ProfessionalTechnician

& Trade

Community

& Pers.

Services

Clerical &

Admin

Sales Machinery

Operator &

Driver

Labourer

Level

4/5

Level 3

Level

1/2

(scale 0-500), converted to the equivalent level (as measured by the ABS –– see chapter 2).

The ALLS also has information on whether people agree that their reading, writing

and maths skills are good enough to perform their job. Using this information, it

appears that there is a greater return from improving the literacy and numeracy

skills of lower skilled workers than higher skilled workers. For example, about

15 per cent of workers with level 1 numeracy stated that their maths skills were not

good enough to do their job (compared with about 5 per cent of workers with skill

level 2 and just one per cent of workers with level 3 numeracy). Thus, the economic

payoff from improving workers’ skills –– that is, having a more capable/effective

workforce ––– would be larger from improving workers’ skills from level 1 to

level 2 compared with further improvements of relatively high-skilled workers.

Understanding the links between literacy and numeracy skills and income/wages is

important, because wages can be used to measure productivity (Forbes, Barker and

Turner 2010).

NUMERACY SKILLS &

LABOUR MARKET

Marks (2008) outlined demand, supply and institutional factors that explain how

higher education and skills may lead to higher wages, as discussed below.

Individuals invest in education and training to improve their skills. Employees with

higher skills (obtained through education) are expected to be more productive and

can earn higher wages than less-skilled workers, all else equal.

Employers may view a person’s educational qualification as a signal that a worker

is more productive than others, and offer higher wages. As Leigh (2008) notes, if

education is merely a credential then it would signal ability, without raising

productivity.

In Australia, many professional and technical occupations have pay rates linked to

qualifications. For example, industrial award structures specify that wage rates for

workers with certain qualifications are higher than wage rates for unqualified

workers.

The ALLS data supports the theoretical relationship set out above –– people with

higher skills earn more than people with lower skills. On average, weekly income is

higher for more highly skilled workers (figures 4.5 and 4.6 for men and women,

respectively).

For men, there is a larger increase in income from moving from skill level 1 to

level 2, compared with increases in income from moving at level 2 to level 3 (or

level 3 to level 4/5).

For women, the opposite occurs, with the largest increase in average weekly income

occurring in moving from skill level 3 to level 4/5.

SKILLS AND LABOUR

MARKET OUTCOMES

15–64 year olds

0

500

1000

1500

2000

2500

3000

Level 1 Level 2 Level 3 Level 4/5

average test score for document literacy, prose literacy and numeracy (scale 0-500), converted to the

equivalent level (as measured by the ABS –– see chapter 2).

15–64 year olds

0

500

1000

1500

2000

2500

Level 1 Level 2 Level 3 Level 4/5

to the average test score for document literacy, prose literacy and numeracy (scale 0-500), converted to the

equivalent level (as measured by the ABS –– see chapter 2).

NUMERACY SKILLS &

LABOUR MARKET

However, these results are only for weekly earnings, and do not capture the

differing amounts of hours worked by men and women, or hours worked across the

skill distribution. The average hourly wage rate for a worker with skill level 1 is

about 60 per cent of that earned by a worker with skill level 4/5 (table 4.1). For

men, hourly wage rates increase at each skill level, but the largest increase in hourly

wages occurs at the higher end of the skill distribution. This is the opposite for

women, although the result for skill level 2 should be treated with caution (see note

b in table 4.1).

Dollars per hour in main job, 25–64 year olds

Level 1 22.13 16.87 19.69

Level 3 30.21 26.54 26.82

Level 4/5 36.64 27.51 32.23

(scale 0-500), converted to the equivalent level (as measured by the ABS –– see chapter 2). Results are

treated with caution.

ECONOMETRIC

METHOD AND DATA

5 Econometric method and variable

construction

The analysis in chapter 4 highlighted that people with higher literacy and numeracy

skills are more likely to participate in the workforce, be employed in more highly

skilled jobs and earn more, compared with people who have lower skills.

In chapter 3 it was suggested that people’s skills vary according to demographic

factors such as country of birth, age, gender and educational attainment. These and

other individual characteristics are also likely to affect labour market outcomes, so

cross-tabulations (between skills and labour market outcomes) will not accurately

predict how much an improvement in literacy and numeracy skills can improve

labour market outcomes. In this section of the report, multivariate econometric

models are presented which control for demographic factors to estimate the effect of

literacy and numeracy skills on the following labour market outcomes:

Following this, a description of the variables used in the econometric analyses is

presented. Modelling results are reported in chapter 6.

Econometric models of labour force participation and wages can help answer the

following research questions:

participation/wages, holding other factors (including education) constant?

measure the effect of human capital on participation and wages?

human capital (for example, education and labour market experience) in raising

labour force participation and wages?

NUMERACY SKILLS &

LABOUR MARKET

along different points of the skill distribution, and are there differences between

genders?

The framework used in the analysis draws upon approaches used by other

researchers including Chiswick, Lee and Miller (2003) for labour force participation

and Barrett (2009) for wages. Both of those papers used Australian data, allowing

for comparisons with the results in this paper.

Two models of labour force participation are estimated, using a similar approach to

Chiswick, Lee and Miller (2003). In the first instance, a ‘traditional’ human capital

model is estimated. That model assumes that labour force participation is a function

participation (including age, marital status, children –– see output in

appendix B for full list).

In this specification, education is an indicative measure of a person’s skill level.

Such an assumption might be valid under the ‘formal’ or ‘abstract’ approach to

literacy and numeracy, which assumes that years of education is a good measure of

a person’s skills (chapter 2).

The functional approach to literacy and numeracy –– which is consistent with a

human capital framework –– suggests that literacy and numeracy are only loosely

correlated with education. The empirical analysis presented in chapter 3 supported

this framework. Education may enhance literacy and numeracy skills, but it may

also be important for developing other skills relevant for work –– for example,

affective skills of cooperation and perseverance (Chiswick, Lee and Miller 2003).

1 In their analysis, Chiswick, Lee and Miller (2003) used potential labour market experience as a

control variable. Age is used here, but in practice both are highly correlated as potential labour

market experience is defined as age minus years of education minus 5.

ECONOMETRIC

METHOD AND DATA

gives additional insight that traditional human capital models do not. In particular,

inclusion of the skills variable allows us to estimate the:

people’s functional skills

functional literacy and numeracy skills and other skills that education provides).

Therefore, a second model of participation is estimated, which explicitly controls

for functional literacy and numeracy skills:

numeracy skills on participation. Education is modelled as having a direct effect on

undertaking more education leads to greater skills. Education is likely to improve

literacy and numeracy skills, but those skills may also be developed, or enhanced,

outside of the school sector. Equation 2 does not distinguish how skills are

developed.

The two models above are estimated because important findings can be obtained by

comparing results. If education is a good proxy for skills, then inclusion of the skills

variable (in equation 2) should not add to the explanatory power of the model.

Furthermore, it may cause collinearity problems –– either the literacy and numeracy

skill variable, or education variable, would not be significant. If, however, literacy

and numeracy skills are influenced by education (but they are not the same) then

both variables would be significant (in equation 2). The magnitude of the education

coefficient would diminish if education influences literacy and numeracy, with

education now a measure of the effect from other skills that education provides on

the likelihood of participation.

Participation is a binary variable (1 if in the labour force, 0 otherwise). The

model results in appendix B for those variables used in the analysis, and a

description of each variable in appendix A).

Previous research has used logit and probit models to estimate labour force

participation. Greene (2008) states that there is no theoretical reason to prefer one

model over the other. In the analysis here, the labour force participation equations

NUMERACY SKILLS &

LABOUR MARKET

were estimated with a probit and logit model. Results were very similar, and

therefore are reported only for the probit model of labour force participation

(presented in chapter 6 and appendix B). The probit model was chosen for

consistency –– as explained below, it was also used as a first step in some of the

wages models estimated.

A problem commonly identified in the human capital literature ‘is that higher ability

individuals may systematically choose more schooling, leading to an upward bias in

the estimated return to schooling’ (Hanushek and Zhang 2006, p. 2). Put another

way, models that do not explicitly control for ability may overestimate the return to

education –– people who undertake more education may choose to do so because

they have higher ability than those people who do not undertake education.

The inclusion of a skills measure may partly reduce this ability bias, as people with

higher ability are likely to have higher skills. However, as Barrett (2009, p. 6) notes,

the literacy and numeracy tests ‘drew on cognitive skills typically used in daily

underlying abilities or potential’. Insofar as the education and skills variables used

in the analysis do not adequately capture a person’s innate ability, motivation or

potential, then the results may be biased upwards.

There is likely to be some ability bias in the results. People with higher ability are

more likely to increase their education which, in turn, is likely to increase their

skills more than otherwise. Ability bias can be controlled for by following

individuals and their skill development over time. However, because the ALLS data

The potential problem of ability bias, in practice, might not have a material effect

on the results. Laplagne, Glover and Shomos (2007) used a panel model of labour

force participation (which accounts for unobserved factors such as ability) and

estimated that having a degree increased the likelihood of participation for females

by 20 percentage points compared with a female who only had year 11 or lower

education. This compared with a 16 percentage point increase when estimated with

a standard model. The differences in model results were smaller when estimated for

males, and smaller again when estimated for other qualifications (because the

impact of other qualifications on participation is smaller than from having a degree).

Therefore, any ability bias present in the data is unlikely to change the qualitative

findings.

2 Ability bias may also affect results for the wages model presented below.

ECONOMETRIC

METHOD AND DATA

To estimate the effect of literacy and numeracy skills on wages, a model developed

by Mincer (1974) is used, where wages are modelled as a function of human capital

variables including potential experience in the labour market and education. That

model takes the form:

appendix B for full list).

This model is analogous to equation 1, used to estimate the effect of education on

participation. Like that model, equation 3 is then re-estimated to include the effect

of functional literacy and numeracy skills:

If workers with higher functional skills are likely to earn higher wages regardless of

their level of education then in equation 3, which only examines the effect of

education and income, the observed effect of education on income will reflect the

literacy and numeray skills (equation 4) enables the effect of these skills to be

estimated separately from education. Therefore, the addition of the skills variable is

expected to reduce the coefficient for education (because skills are now modelled

separately).

Sample selection bias can arise if the group of observations for which a model is

estimated is not taken from a random sample. In the wages model, the hourly wage

rate is the dependent variable. However, wage rates are only observed for people

who are employed. As people who are employed tend to have characteristics

different to those who are not in the labour force or unemployed, excluding these

groups results in a non-random sample being used, which may bias results.

NUMERACY SKILLS &

LABOUR MARKET

A large literature has evolved to address this potential problem, and a common

approach is to run a two-step model, first developed by Heckman (1979).

Conceptually, a ‘selection equation’ is first estimated for labour force participation,

which has a binary outcome (1 or 0). An ‘inverse Mills’ ratio is estimated from this

equation, and incorporated into a second equation –– the earnings equation –– as a

correction term. A ‘selection effect’ is present if the two error terms from each

equation are correlated. By including the correction term, coefficients are adjusted

to take account of the selection effect.

In this paper, wage models were first estimated using ordinary least squares (OLS)

on the sample of employed persons only. Next, Heckman models were used to

estimate a selection equation (on all persons), and a wage equation (for employed

persons). The selection equation uses a probit model specification for labour force

participation. Although results showed no evidence of a sample selection error, the

Heckman model results are presented in chapter 6 as the preferred estimates. For

completeness, both the Heckman and standard OLS model results are presented in

full (appendix B). The model results were very similar between the OLS and

Heckman models.

This section describes how the main variables of interest used in the analysis were

constructed. Appendix A contains a full list of variables used in all models,

including their mean and standard deviations.

Participation is treated as a binary variable, taking the value 1 for persons in the

labour force (employed and unemployed persons) and 0 otherwise.

Wages are estimated using a measure of the hourly wage rate. The hourly wage rate

is defined as weekly income divided by number of hours worked per week.

There are two income measures in the survey data that can be used. One is income

from all sources (including government allowances). Another is based on income

from a person’s main job only. Similarly, hours worked are reported for a person’s

ECONOMETRIC

METHOD AND DATA

main job only, and for all jobs. In the analysis, the hourly wage rate is obtained

using the income and hours data pertaining to a person’s main job only.

Explanatory variables are those commonly found in the labour supply literature.

Only the human capital variables are described in detail below, as it is the effect of

those variables on participation and wages that is the primary focus of this paper.

There are five different skills formally tested for in the ALLS. In addition, there are

subjective measures of skills, but these were not used in the analysis (chapter 2).

There are two broad approaches to account for skills in the modelling.

First, a separate variable could be included for various skills (for example,

document literacy, prose literacy, and numeracy test scores). However, there is a

strong correlation between each skill variable (table 2.1) and there may be

collinearity problems if all are included. In their analysis, Chiswick, Lee and Miller

(2003) found that only one or two variables were needed to obtain most of the

model’s explanatory power. A problem with that approach, however, is that it is

difficult to determine which skill(s) should be included and which should not.

A second approach is to construct an index of literacy and numeracy skills by

combining the measures that are in the survey. A disadvantage with this approach is

that combining the variables makes it difficult to isolate the effect of numeracy

from, say, prose literacy on labour market outcomes.

The aim of this paper is to identify the effect of overall functional literacy and

numeracy skills on labour market outcomes, and not necessarily the effect of

particular components within these functional skills. Therefore, the second approach

is the one chosen in the analysis. This method has also been used by others (Barrett

2009; Green and Riddell 2001; Hanushek and Zhang 2006), primarily because the

skills are highly correlated with each other.

A single skill variable capturing a person’s literacy and numeracy skills was

constructed as follows:

1. The principal component of the document literacy, prose literacy and numeracy

test scores (0–500) was estimated. The indicator of problem solving skill was not

included in estimation as it is not a measure of functional literacy or numeracy.

NUMERACY SKILLS &

LABOUR MARKET

Furthermore, it is only aggregated to four levels, so it cannot be converted into a

skill level 1 to 5 in the same way the other variables are assigned a skill level

(see point 4 below).

2. The first principal component (which accounted for about 96 per cent of

variation and had almost equal weights for each of the three test scores) was

used to weight each of the three skills above (see table 5.1 for principal

component analysis). The second and third principal components were not used,

as their additional explanatory power was negligible, and the different signs on

the weights made their interpretation difficult.

3. The resulting test score was re-indexed to a scale of one to 500, by dividing the

aggregate test score by the sum of the principal component weights.

4. The test score was converted into five categorical levels, using the same interval

points as in the ABS survey.

5. The following binary variables were also created:

(a) Skill level 2 = 1 if skill level 2, 0 otherwise

(b) Skill level 3 = 1 if skill level 3, 0 otherwise

(c) Skill level 4/5 = 1 if skill level 4 or 5, 0 otherwise

Document literacy 0.5818 -0.2618 -0.7701 0.9604 0.9604

Prose literacy 0.5721 0.8047 0.1586 0.0289 0.9894

Numeracy 0.5782 -0.5328 0.6179 0.0106 1.0000

In each model that was estimated, either the continuous literacy and numeracy

measure (defined in point 3) was used, or the binary variables (defined in point 5)

were used. The continuous measure has the benefit of providing more data points,

while the skill levels approach provides a more meaningful interpretation of what is

being estimated. For example, with only skill level 1 excluded from the model, the

coefficient for skill level 3 estimates the effect of increasing functional literacy and

numeracy skills from level 1 (representing a person with the lowest level of

literacy/numeracy) to level 3 –– the minimum level required for a person to

effectively participate in the workforce.

The preferred approach in the analysis, and presented in chapter 6, was to use the

skill level variables. (However, full estimation output using a continuous skill

variable can also be found in appendix B.) The resulting vector of skill variables

ECONOMETRIC

METHOD AND DATA

functional literacy and numeracy (as defined in chapter 2). Barrett (2009) and others

have also said that this variable can be interpreted as measuring cognitive skills.

Four categories of educational attainment were used: Year 11 or lower; Year 12;

Diploma or Certificate; and Degree or higher. These were aggregated from more

detailed levels of education reported in the survey (table 5.2). Years of education

was not used because, as discussed above and in other studies, the time taken to

complete a course of study can vary significantly among individuals.

Year 11 or lower is the benchmark from which the effects of the other three

categories of highest education level were estimated and compared. As such,

Year 11 or lower does not appear in the modelling results presented in chapter 6.

Postgraduate degree Degree or higher

Graduate Diploma/Graduate Certificate Degree or higher

Bachelor Degree Degree or higher

Advanced Diploma/Diploma Diploma/Certificate

Certificate III/IV Diploma/Certificate

Certificate I/II Year 11 or lower

Certificate not further defined Year 11 or lower

Year 12 Year 12

Year 11 Year 11 or lower

Year 10 Year 11 or lower

Year 9 Year 11 or lower

Year 8 or below including never attended school Year 11 or lower

The particular education levels were chosen because they were also used to analyse

the effects of education (and health) on labour force participation by Laplagne,

Glover and Shomos (2007) and on wages by Forbes, Barker and Turner (2010).

Therefore, modelling results can be compared with the results from those papers.

Each model was estimated separately for males and females. This was done for a

number of reasons. The decision to participate is likely to vary according to sex ––

NUMERACY SKILLS &

LABOUR MARKET

females typically work less after the birth of a child. Thus, the impact of some

variables on participation and wages is likely to differ for men and women.

In particular, the effect of education on the likelihood of participation and on wages

has been shown to vary in its magnitude for men and women (Laplagne, Glover and

Shomos 2007; Forbes, Barker and Turner 2010). Thus, for the variables of interest

in this analysis –– education and literacy –– it is useful to examine their effects on

men and women separately.

The sample was restricted to 25–64 year olds. Educational attainment is a variable

of interest, and was estimated using indicators for highest level of educational

attainment a person has completed. As many people under 25 might not have

completed their highest level of education (Leigh 2008), they were excluded from

the analysis. Similarly, people aged 65 and over were excluded as the majority of

that group would have reached pensionable age.

Unweighted data were used in estimation. Models were estimated with Stata, and

processed using the ABS’s Remote Access Data Laboratory (RADL).

In the next chapter, results from the econometric models above are presented. (Full

estimation output is in appendix B.)

6 Modelling results

In this section of the paper, econometric results for the models of labour force

participation and wages are presented. The focus of the results is for the marginal

effects of education and literacy and numeracy skills on labour force participation

and wages. Full estimation output (including coefficients and marginal effects for

all variables) is in appendix B.

Section 5.1 set out two models of labour force participation –– one which included

literacy and numeracy skills (equation 2) and one which did not include those skills

(equation 1). Econometric results from those models are presented below. As

explained in chapter 5, the literacy and numeracy variable should be interpreted as

measuring people’s overall functional literacy and numeracy skills –– not a specific

type of literacy or numeracy.

literacy and numeracy skills) are presented in table 6.1.

Year 12 1.56 -0.01 8.13*** 5.65***

Diploma/Cert 4.07*** 2.93*** 13.08*** 10.53***

Degree 5.20*** 2.78** 19.11*** 14.90***

*** significant at 1 per cent, ** 5 per cent and * 10 per cent.

1 All marginal effect estimates are calculated at the mean of the variable under consideration.

NUMERACY SKILLS &

LABOUR MARKET

Those results are of the expected sign, and consistent with other studies. The

marginal effects on participation from having a degree relative to having year 11 or

lower education were estimated to be 5.2 percentage points and 19.1 percentage

points for men and women respectively. These compare with results from a

multinomial logit model estimated by Laplagne, Glover and Shomos (2007) of 8.6

percentage points and 19.7 percentage points for men and women respectively.

As explained in chapter 5, if education and skills are synonymous (equation 1), then

there would be collinearity problems when equation 2 is estimated –– either the

skills or the education variables may be insignificant. Table 6.1 shows the marginal

effects for educational attainment when skills are included in the model

(equation 2). Compared with results from equation 1, it can be seen that marginal

effects are reduced by about one quarter when skills are included. These results

imply that a ‘traditional’ model of human capital, which uses education only to

proxy skills, might overestimate the direct effect of education on participation. Put

another way, about one quarter of the effect education has on participation (in

traditional human capital models) occurs because the more highly educated are also

more highly skilled. (Education may improve literacy and numeracy skills, but

those skills can also be obtained from other means. The model does not examine the

factors affecting skills.)

As will be shown below, the marginal effects for all of the skills variables (and most

of the education variables) are statistically significant in equation 2. Furthermore,

the explanatory power of the model was improved (by about 1 percentage point, for

both men and women) when the functional literacy and numeracy skills variable

was included in estimation. Therefore, a model which assumes that education may

skills, is the more appropriate specification.

In the analysis below, the focus turns to how skills affect participation, so results are

presented only for equation 2. Figure 6.1 presents the marginal effects of skills (and

educational attainment) on labour force participation.

Educational attainment relative to year 11 or lower, literacy and numeracy skills

-5

0

5

10

15

20

Year 12 Diploma or

Certificate

Degree or

higher

Level 2 Level 3 Level 4/5

Men Women

for a given variable, the bars overlap, then those estimates are not statistically different at the 5 per cent level

of confidence. If a bar reaches the horizontal axis, that marginal effect is not statistically significant at the

5 per cent level of confidence.

The following observations regarding literacy and numeracy skills can be made:

a positive, and statistically significant, impact on labour force participation, for

both men and women.

for women than for men (consistent with the effects of greater education, and

likely to occur because of the higher participation rate for men).

improvement in literacy and numeracy skills varies along the skill distribution,

with differences between genders.

– For women an increase in skills from level 1 to level 2 raises participation by

11 percentage points. Raising skills from level 1 to level 3 (or level 4/5)

raises participation by about 15 percentage points. Thus, the largest

NUMERACY SKILLS &

LABOUR MARKET

marginal effect of increasing skills from level 1 to level 2 is not statistically

different than from increasing skills from level 1 to level 3).

– For men, an improvement in skills from level 1 to level 2 raises participation

by almost 4 percentage points, and from level 1 to level 4/5 raises

participation by about 6 percentage points. So, there is a more even effect on

participation from improving skills along the distribution for men than there

is for women.

Compared with raising educational attainment, improving people’s skills leads to a

relatively large increase in participation. For example, raising skills from level 1 to

level 2 has a larger effect on participation than from increasing educational

attainment from year 11 or lower to year 12 or a diploma/certificate (and a larger

effect than from raising educational attainment to a degree for men). To put that into

context, the time taken to complete a degree or higher is roughly seven years longer

than the time taken to complete year 11 or lower (figure 3.4).

The joint effect from improving education and improving literacy and numeracy

skills was not formally estimated in the models (this would require an interactive

term for education and skills to be included). However, the results indicate that

the largest increases in participation. For example, if a person has low skills and low

education, then increasing education increases the likelihood of participation. The

likelihood of participating is increased further if the person also increases his or her

literacy and numeracy skills. It is likely that education does improve skills, so the

cumulative effect of increasing education is likely to be greater than the predicted

estimate for education alone.

The effects of education and skills were robust to different model specifications. For

example, years of education was used as an alternative to educational attainment,

and the continuous literacy/numeracy skill test score (0–500) was used in other

variations of the models presented here. The key results did not change. In

particular, the effect of improving skills on participation was stronger for women

than for men, and statistically significant across all models.

Results for literacy and numeracy skills are also consistent with other studies.

Chiswick, Lee and Miller (2003) found that document literacy and (self-assessed)

2 Strictly speaking, the effect on participation from increasing skills from level 3 to level 4/5 is not

the difference between the marginal effects of skill levels 3 and 4/5 presented in figure 6.1. That

would require re-estimating the model with level 3 as the base skill level. Alternative models,

with different skill level bases, were estimated for comparison and gave similar results to the

differences in marginal effects between skill levels above.

mathematical ability both had a positive and statistically significant effect on

participation, using 1996 Australian data. They also found the direct effect of

education to be overestimated (by up to 50 per cent) if skills are not controlled for.

A number of other explanatory variables were included in the estimation. This

section briefly reports some of those results (appendix B contains full estimation

output).

In chapter 3, it was shown that skills vary according to country of birth. The models

estimated include explanatory variables for being born in either a main English

Australia. Being born in a non-English speaking country had a negative effect on

female participation (it reduced the likelihood of participation by 10 percentage

points in equation 1). However, the negative effect reduced markedly once skills

were controlled for (to minus 5 percentage points in equation 2). These results

demonstrate that the negative effect on participation from being born in a

non-English speaking country is overestimated in ‘traditional’ models (which do not

include skills). It is the lower literacy and numeracy skills that people from a

non-English speaking background have that, in part, explains their lower

participation.

Most of the other explanatory variables were statistically significant, and of the

expected sign. Being married and having at least one child aged 0–4 or 5–14 had a

negative effect on female participation. Mothers are more likely to spend time out

of the labour force to care for younger children rather than older children, because

looking after younger children is more time-intensive (Birch 2005). Recent

empirical research for Australia (Cai 2010) also supports this theory. High levels of

physical and mental health both had a positive effect on participation, for both men

and women, consistent with results from previous Commission research (Laplagne,

Glover and Shomos 2007).

In this section, results from the wages models are presented. As was done for the

participation models, the effects of education in both wages models are presented

first, before the focus turns to the effect of literacy and numeracy skills on wages.

3 Some countries included in this definition may be English speaking. However, the vast majority

of countries are non-English speaking.

NUMERACY SKILLS &

LABOUR MARKET

Marginal effects of educational attainment on wages are presented in table 6.2.

Based on equation 3, it was found that improving educational attainment had a

large, statistically significant effect on wages. For example, increasing education

from year 11 or lower to a degree increased hourly wages by about 60 per cent. This

is larger than other estimates in the literature, although the marginal effect from

increasing education from year 11 or lower to year 12 or a diploma/certificate was

much smaller (between 11 and 18 per cent). All education effects were statistically

significant.

The estimated marginal effects for educational attainment for equation 4

(controlling for skills) were lower than those that were obtained for equation 3

(table 6.2). This pattern is the same which occurred for the labour force

participation model. The estimated marginal effects for education were reduced by

about half for men, and by a lesser amount for women.

The effect of increasing schooling to year 12 (relative to year 11 or lower) was not

statistically significant in equation 4. That is, raising education from year 11 to year

12 is not predicted to have any effect on hourly wages (unless skills are also

improved by undertaking that education).

Degree 59.58*** 34.21*** 61.05*** 49.42***

Diploma/Cert 17.65*** 9.77*** 13.76*** 10.28**

Year 12 15.35*** 5.18 10.97** 7.24

or lower to the education levels estimated.

*** significant at 1 per cent, ** 5 per cent and * 10 per cent.

Therefore, like the participation model, wage models which only use education may

overstate the direct effect of education on hourly wages. Some of the expected

increase in hourly wages occurs because more highly educated people also have

higher literacy and numeracy skills.

Like the participation model above, ability bias might also affect the results

presented for the wages models. A number of studies have attempted to address this

issue. Data on twins has been used by Ashenfelter and Kreuger (1994) for the

United States and Miller, Mulvey and Martin (1995) for Australia. Those studies

‘reveal that there is little evidence of upward bias in the typical OLS estimate of the

return to education’ (Miller, Mulvey and Martin 1995, p. 597). This arises because

any upward bias is largely offset by measurement error, which has a downward bias

on results.

More recently, Leigh and Ryan (2008) estimated returns to education using various

natural experiment techniques to control for ability bias. Their returns to education

were higher than from studies using twins, and the authors attribute this to having

better measures of income and schooling. Their results suggest that about 10 to 40

per cent of the return to schooling in standard OLS regressions may be due to ability

bias.

Equation 4 models the effects of both education, and literacy and numeracy skills,

on wages. Marginal effects are presented in figure 6.2.

Educational attainment relative to year 11 or lower, literacy and numeracy skills

-10

0

10

20

30

40

50

60

70

Year 12 Diploma or

Certificate

Degree or

higher

Level 2 Level 3 Level 4/5

Men Women

for a given variable, the bars overlap, then those estimates are not statistically different at the 5 per cent level

of confidence. If a bar reaches the horizontal axis, that marginal effect is not statistically significant at the 5 per

cent level of confidence.

NUMERACY SKILLS &

LABOUR MARKET

The following observations regarding the effect of improving functional literacy

and numeracy skills on wages can be made:

significant effect on wages, for both men and women.

women. This is in contrast to the effect that skills had on the likelihood of

participation for men and women.

– For men, increasing skills from level 1 to level 3 increases wages by

32 per cent, (14 percentage points more than from increasing skills from level

1 to level 2). However, an increase in skills from level 1 to level 4 or 5 raises

wages by 54 per cent (a difference of 22 percentage points compared with

raising skills from level 1 to level 3). Furthermore, the increase in wages

from increasing skills from level 1 to level 2 is significantly different than

from increasing skills to level 4 or level 5.

– For women, the additional increase in wages is roughly 10 per cent from

increasing skills from level 1 to level 2, compared with increasing skills from

level 1 to level 3. The additional increase from improving skills to level 4 or

5 (compared with level 3) is also about 10 per cent. Furthermore, there is no

statistical difference from improving skills from level 1 to level 2 compared

with increasing them to any other level.

Results were robust to various model specifications (for example, when literacy and

numeracy was estimated as a continuous variable).

In a similar analysis using the ALLS data, Barrett (2009) considered how the

returns to skills vary along different points of the wage distribution. He found that

the return to skills is uniform across the wage distribution.

Finnie and Meng (2007) found that not only do skills benefit individuals at the top

and bottom ends of the labour market, but that the effect of literacy and numeracy

skills on labour market success is just as important as education. ‘Indeed, in some

cases, the effects of functional literacy appear to be substantially greater than the

number of years of education’ (Finnie and Meng 2007, p. 10). Likewise, the model

4 Strictly speaking, the effect on wages from increasing skills from level 3 to level 4/5 is not the

difference between the marginal effects of skill levels 3 and 4/5 presented in figure 6.2. That

would require re-estimating the model with level 3 as the base skill level. However, alternative

models, with different skill level bases, were also estimated for comparison and gave similar

results to the differences in marginal effects between skill levels above.

results above suggest that improving skills has a larger impact on wages than

improving education, particularly for men. For men, increasing skills from level 1 to

level 4/5 has a larger effect on wages than from increasing education from year 11

to any of the other higher levels of educational attainment modelled. Even smaller

improvements in skills for men (from level 1 to 2) have twice the impact on wages

than from increasing educational attainment from year 11 to year 12 or to a

diploma/certificate (although differences are not statistically different from one

another). For women, increasing educational attainment to a degree or higher (from

year 11 or lower) had a larger effect than improving literacy and numeracy skills.

This could reflect that education acts as a stronger signalling device (of motivation

or expectations at work) for women, compared with men.

Potential labour market experience was included as a control variable in the wages

equations. The results for equation 3 show that additional years of experience

increase hourly wages, but at a decreasing rate (see appendix B for results). The

magnitude of the effect of the experience variables was largely unaffected by

including the skills variable (in equation 4), consistent with other results for

Australia (Barrett 2009) and results for Canada (Green and Riddell 2002). This

indicates that work experience might not improve literacy and numeracy skills.

Descriptive analysis in chapters 3 and 4 suggested that literacy and numeracy skills

might deteriorate once a person exits the workforce. Therefore, it may be the case

that literacy and numeracy skills are developed prior to entering the workforce, but

are maintained (and not enhanced) by using them in the workplace. They may

deteriorate after leaving work, or may deteriorate due to other factors. This would

be a useful area to explore in future research.

Being born in a non-English speaking country was estimated to have a negative

impact on wages. However, as in the participation model, once literacy and

numeracy skills were controlled for, the negative effect was lessened (by about

25–50 per cent, depending on sex). Again, this highlights that human capital models

which do not explicitly control for skills overstate the effect of being born in a non-

English speaking country –– some of the effect occurs because this group has lower

(English) literacy and numeracy skills.

Most other explanatory variables are of the expected sign. Of those that are

statistically significant, better mental or physical health, residing in the city, and

being married (for men only) had a positive impact on hourly wage rates.

NUMERACY SKILLS &

LABOUR MARKET

Working part-time had a negative impact on wages of men and a positive impact for

women, but was not statistically significant in either case. In contrast, a recent study

of the Australian labour market showed that there was a wage premium from

working part-time for both men and women (Booth and Wood 2008).

The econometric modelling results in this chapter have highlighted that improving

functional literacy and numeracy skills has a large and statistically significant effect

on labour force participation and hourly wages.

The estimated benefits of education, after controlling for functional skills, were

reduced but still significant. Thus, education develops other skills used in the

workplace, and may act as a signal to employers that people with higher education

have higher human capital.

The above findings suggest that both educational qualifications and functional skills

are valued in the labour force. The modelling did not formally estimate the impact

of factors likely to affect functional skills.

Green and Riddell (2001) estimated a joint model of skills, education and wages.

They found education to be a strong factor explaining literacy and numeracy skills.

However, formal education is usually undertaken prior to entering the workforce.

Although education is likely to improve younger persons’ skills, people who are

older and already working can also improve their functional skills. Understanding

the determinants of a person’s literacy and numeracy skills, and how they can be

improved (or maintained) at different stages of the life cycle, would be a good area

for further research. The above analysis indicates that work experience might not

improve functional literacy and numeracy skills. However, only a crude measure of

work experience was used. The ALLS also has information on how often a person

uses various skills in the workplace, and at home. Identifying whether using skills at

work improves functional skills would be a good first step in understanding ways to

improve the skills of older workers.

CONCLUDING

REMARKS

7 Concluding remarks

In this paper, the links between literacy and numeracy skills and labour market outcomes were examined using recent Australian data. The motivation for the project has arisen from growing policy interest on the impact that literacy and numeracy skills have on key labour market outcomes. As mentioned in chapter 1, governments are committed to improving literacy and numeracy outcomes of the population, as this component of human capital is seen as crucial to raising productivity and participation.

A summary of the key findings from the empirical analysis in this paper and how they can be used by policy makers is presented below. Areas for further research are also mentioned.

A profile of Australian’s functional literacy and numeracy skills in 2006 showed that skills typically:

Skills were also shown to be important for labour market outcomes –– people with higher skills are more likely to -

*    participate in the labour force,

*    be employed in higher-skilled occupations, and

*    earn more,

compared to people with lower skills.

Econometric models were used to formally estimate the effect of functional literacy and numeracy skills on labour force participation and on hourly wages (which is an indicator of productivity).

Modelling results should be used with caution. There may be unobserved characteristics which influence education and skills. People with greater motivation, potential or innate ability are more likely to undertake education, meaning that the effects of education might be overstated. Although the addition of the skill variable used in this paper might capture more accurately people’s skills (and other unobserved factors that education does not), it might not capture motivation or innate ability. If that were the case, there may be some upward bias in the results meaning that they should be regarded as an upper estimate of the benefits from improving literacy and numeracy skills on labour market outcomes.

Notwithstanding those limitations, the qualitative conclusions from this research are likely to remain unchanged.

Model results showed that education has a positive effect on labour market participation and wages. Education is likely to improve a person’s human capital, of which literacy and numeracy is one component. Once literacy and numeracy skills were controlled for, the effect of greater education on labour market outcomes was reduced, but it was still positive for most levels of attainment. This suggests that schooling develops skills other than functional literacy and numeracy, which are also rewarded in the labour market. Such skills may be vocational or job-specific.

Increasing literacy and numeracy skills had a positive, statistically significant effect on both labour force participation and hourly wages. Thus, from a policy perspective, if people’s literacy and numeracy skills can be improved, then they will tend to achieve better labour market outcomes.

As stated above, a person’s innate ability or motivation could affect his or her skill development. Thus, in practice, it might be difficult for a person with low literacy and numeracy to move to the highest skill level. Nevertheless, it is possible to increase the literacy and numeracy skills for the population as a whole.

Theory, and analysis of the data, both suggest that education is one factor likely to affect skills. However, the analysis also showed that education and skills are not perfectly correlated. Other studies have found ‘the development and maintenance of cognitive skills is more complex than simply attending school or achieving a certificate of completion, and that education does not “fix” skill levels for life’

(Statistics Canada and OECD 2005, p. 60). Modelling results supported this view, showing that, even after controlling for educational attainment, increasing people’s skills will lead to higher wages and increased labour force participation.

Other findings may also be of interest. For example, the effect of literacy and numeracy skills was different for men and women –– improving skills had a larger impact on participation for women than for men, but had a larger impact on hourly wage rates for men compared with women.

Returns to skills also varied slightly along the distribution of lower and higher skilled workers. Raising the skills of lower-skilled people had a larger effect on increasing participation, compared with further improving high-skilled workers’ ability.

Compared with raising educational attainment, most of the results showed that there was a larger payoff to labour market outcomes from improving skills.

Finally, an important finding from the research was that people born in a non-English speaking country were much more likely to have lower functional skills than people born in Australia or a main English speaking country. This was the case regardless of a person’s educational attainment. Thus, improving language proficiency is paramount to enhancing the functional skills and, in turn, the labour market outcomes for that group. The empirical results support the findings of previous Commission research on migration, which found that ‘English language proficiency is significantly related to migrant labour market success and performance’ (PC 2006b, p. 172).

Modelling results highlighted that education and functional literacy and numeracy skills have a positive effect on labour force participation and on wages. Estimates

were based on standard econometric models often used in the literature, but they

could be further refined using more sophisticated techniques. Although the

qualitative conclusions are likely to remain unchanged, further research could be

useful for policy makers if they wanted a more precise estimate of the effect of

literacy and numeracy skills (and education) on labour market outcomes.

There are many different model specifications that could be used. Some of these are

mentioned below.

1. Hours worked. The effect of skills on participation could be estimated using

‘hours worked’ as the dependent variable instead of participation. Alternatively,

a multinomial logit could be used to model participation (that is, the states of

labour force status could be expanded to include people unemployed, working

part-time, or working full-time).

2. Simultaneous equations. In the descriptive analysis, there was some evidence

that people who are out of the labour force might experience skill deterioration.

If participation does affect skills, then there is reverse causality. To account for

this, a simultaneous equations model could be estimated with participation and

literacy and numeracy skills jointly estimated. Using this model would help shed

light on the direction of causality regarding skills and participation for people in

the workforce nearing retirement age, which is likely to be of policy interest in

the future.

3. Three-stage least squares. Literacy and numeracy skills are influenced by many

factors, including education, engagement in reading and writing activities at

work or home, English speaking background and parents’ education levels.

Models could be estimated to examine which factors are more important for skill

development. For example, Green and Riddell (2001) used a three-stage least

squares model to jointly estimate wages, education and skills for Canada.

Understanding the factors affecting literacy and numeracy skills, and how those

skills can be improved at different stages of the life cycle would also be

important. Thus the modelling could be done for different age groups.

The econometric models in this paper can also be used to examine other links

between literacy and numeracy skills and labour market outcomes.

For example, separate marginal effects were estimated for increasing educational

attainment and literacy and numeracy skills. These marginal effects are interpreted

as the effect of changing one variable, holding all others constant. For example, the

estimated marginal effect of improving education assumes that a person’s skill level

is held constant. In practice, greater educational attainment is associated with higher

skills (chapter 3). Therefore, a more realistic estimate of improving educational

attainment for a person with relatively low education and low literacy and numeracy

numeracy. This could be incorporated with an interactive term for literacy and

numeracy skills and education.

and numeracy, the skill variable could be replaced and the effects of different types

of literacy or numeracy could be estimated in isolation. Using data for the United

States, Dougherty (2003) found that the effect of numeracy on earnings is much

larger than that of literacy.

A Descriptive statistics

This appendix lists the variables used in the econometric models. The sample was

restricted to 25–64 year old persons.

Table A.1 contains a description of all the variables, and their means and standard errors.

Labour force 1 if in labour force, 0 otherwise 0.7728

Log wage Log of hourly wage rate x 100 234.3692 1.8906

Degree or higher 1 if degree or higher, 0 otherwise 0.2411

Diploma/certificate 1 if diploma/certificate, 0 otherwise 0.2743

Year 12 1 if year 12, 0 otherwise 0.1347

Skill level 2 1 if skill level 2, 0 otherwise 0.2849

Skill level 3 1 if skill level 3, 0 otherwise 0.3991

Skill level 4/5 1 if skill level 4/5, 0 otherwise 0.1695

Lives in city 1 if lives in city, 0 otherwise 0.5895

Married 1 if married, 0 otherwise 0.6122

Child 0–4 1 if child aged 0–4, 0 otherwise 0.1602

Child 5–14 1 if child aged 5–14, 0 otherwise 0.2672

Child 15–24 1 if child aged 15–24, 0 otherwise 0.0878

Age Age (years) 44.1943 0.1345

Age squared Age squared/100 20.7588 0.1205

Age cubed Age cubed/10 000 10.2670 0.0851

Experience Potential work experience (years) 26.3904 0.1490

Experience squared Potential work experience squared 8.4703 0.0827

Physical health SF12 physical health score (1–100) 49.8385 0.1175

Mental health SF12 mental health score (1–100) 50.6485 0.1165

Pension recipient

1 if receives any pension excluding disability

and Department of Veteran Affairs (DVA)

service pension, 0 otherwise 0.0102

Part-time 1 if works part-time, 0 otherwise 0.2127

COB – English speaking

(not Aus)

1 if born in English speaking country (not

Australia), 0 otherwise 0.1239

COB – other

1 if born in non-English speaking country, 0

otherwise 0.1531

B Estimation output

This appendix contains output from all of the models estimated, including those

models presented in chapter 6. As explained in chapter 5, each model was estimated

separately for men and women, with the sample population being 25–64 year old persons.

Equations 1 and 2 (presented in section 6.1) were estimated using a probit model of

labour force participation. The two states are either being in the labour force

(employed or unemployed) or not in the labour force. Models were estimated with

two specifications for functional literacy and numeracy skills. In the first instance,

discrete skill levels were first estimated (results using this approach were presented

in chapter 6). An alternative specification, with the continuous test score, was also

used. Selected output from both of these models is presented below.

The probit labour force participation model results for equations 1 and 2 are

presented for men and women in tables B.1 and B.2 respectively. Results include

coefficients and goodness of fit measures. Tables B.1 and B.2 also contain the

associated marginal effects for key variables of interest.

Marginal effects for all models were calculated at the mean (using the ‘mfx’

command in Stata). This method was chosen, rather than calculating the average

marginal effect, because that command is not available in the version of Stata run

through RADL. In either case, previous literature does not indicate any strong

preference for choosing a particular method when estimating marginal effects.

LitNum Skill level 2 – 0.2934***

LitNum Skill level 3 – 0.3575***

LitNum Skill level 4 and 5 – 0.5730***

Degree or higher 0.4397*** 0.2195*

Diploma/Certificate 0.3118*** 0.2239***

Year 12 0.1188 -0.0010

Age 0.1898*** 0.1858***

Age squared -0.2503*** -0.2452***

Married 0.5010*** 0.4780***

Child 0–4 -0.0489 -0.0522

Child 5–14 -0.1365 -0.1327

Child 15–24 0.3619** 0.3527**

Lives in city -0.0285 -0.0285

COB – English speaking (not Aus) 0.1792* 0.1424

COB – Other -0.0406 0.0671

Physical health 0.0420*** 0.0406***

Mental health 0.0214*** 0.0210***

Constant -5.4808*** -5.5340***

LitNum Skill level 2 – 3.69***

LitNum Skill level 3 – 4.67***

LitNum Skill level 4 and 5 – 6.16***

Degree or higher 5.20*** 2.78**

Diploma/Certificate 4.07*** 2.93***

Year 12 1.56 -0.01

COB – English speaking (not Aus) 2.28* 1.82

COB – Other -0.58 0.89

*** significant at 1 per cent, ** 5 per cent and * 10 per cent.

LitNum Skill level 2 0.3744***

LitNum Skill level 3 0.5030***

LitNum Skill level 4 and 5 0.5743***

Degree or higher 0.7012*** 0.5284***

Diploma/Certificate 0.4609*** 0.3637***

Year 12 0.2796*** 0.1901**

Age -0.3115** -0.3093**

Age squared 0.9027*** 0.8980***

Married -0.0752 -0.0921*

Child 0–4 -0.5852*** -0.6051***

Child 5–14 -0.2406*** -0.2435***

Child 15–24 0.0178 0.0159

Lives in city -0.0349 -0.0223

COB – English speaking (not Aus) 0.0952 0.0985

COB – Other -0.3028*** -0.1579**

Physical health 0.0306*** 0.0290***

Mental health 0.0154*** 0.0142***

Constant 1.9685 1.7111

LitNum Skill level 2 11.03***

LitNum Skill level 3 15.17***

LitNum Skill level 4 and 5 15.25***

Degree or higher 19.11*** 14.90***

Diploma/Certificate 13.08*** 10.53***

Year 12 8.13*** 5.65***

COB – English speaking (not Aus) 2.91 3.00

COB – Other -10.12*** -5.12**

only using a squared term.

*** significant at 1 per cent, ** 5 per cent and * 10 per cent.

The probit labour force participation model was also estimated using the continuous

skills variable (test score 1–500) rather than with skill levels (1, 2, 3 and 4/5). Other

variables used in estimation remained unchanged. Selected marginal effects for

equation 2 with the continuous skills variable are presented for men and women in table B.3.

The results confirm that higher literacy and numeracy has a positive effect on

participation. The effect is larger for women (about three times greater than the

effect for men, broadly in line with results using skill levels). The marginal effect of

other variables of interest (education and country of birth) are also very similar to

those results obtained with models using skill levels (those results are reported

under equation 2 in tables B.1 and B.2 for men and women, respectively).

Equation 2

Degree or higher 2.40* 13.24***

Diploma/Certificate 2.69** 10.00***

Year 12 -0.30 5.12**

COB – English speaking (not Aus) 1.82 2.97

COB – Other 1.29 -3.35

for an additional one point in a person’s literacy/numeracy test score (which can be between 1 and 500).

*** significant at 1 per cent, ** 5 per cent and * 10 per cent.

Wages models for equations 3 and 4 were estimated using standard OLS and with a

Heckman selection model. Results from both of those models are reported below.

The dependent variable is the natural logarithm of the hourly wage rate.

For comparison, wages model results using a continuous skills variable are also

presented at the end of this section.

Wages model results using OLS (for employed persons only) are reported for men and women in tables B.4 and B.5 respectively.

Lives in city 0.0850*** 0.0844***

Married 0.1211*** 0.1021***

Experience 0.0215*** 0.0195***

Experience squared -0.0338*** -0.0278***

Degree or higher 0.4685*** 0.2952***

Diploma or certificate 0.1630*** 0.0936***

Year 12 0.1430** 0.0506

LitNum Skill level 2 0.1648***

LitNum Skill level 3 0.2786***

LitNum Skill level 4 and 5 0.4334***

Physical health 0.0041** 0.0033*

Mental health 0.0015 0.0016

COB – English speaking (not Aus) 0.0254 0.0202

COB – Other -0.1552*** -0.0698*

Works part-time -0.0693 -0.0620

Constant 2.3439*** 2.2139***

*** significant at 1 per cent, ** 5 per cent and * 10 per cent.

Lives in city 0.0604** 0.0597**

Married 0.0553* 0.0473*

Experience 0.0112** 0.0099*

Experience squared -0.0158 -0.0111

Degree or higher 0.4783*** 0.4030***

Diploma or certificate 0.1300*** 0.0988**

Year 12 0.1059** 0.0713

LitNum Skill level 2 0.1295**

LitNum Skill level 3 0.2086***

LitNum Skill level 4 and 5 0.2999***

Physical health 0.0072*** 0.0066***

Mental health 0.0036** 0.0033**

COB – English speaking (not Aus) 0.0410 0.0427

COB – Other -0.2221*** -0.1626***

Works part-time 0.0213 0.0250

Constant 2.1140*** 2.0077***

*** significant at 1 per cent, ** 5 per cent and * 10 per cent.

Marginal effects in an OLS model are equivalent to the corresponding coefficients.

However, the dependent variable used in the wages model was the logarithm of the

hourly wage. The marginal effects had to be converted to obtain a percentage

growth rate in wages from a percentage change in the explanatory variable.

Thornton and Inness (1989) show that the estimated marginal effect when the

dependent variable is in logarithmic form needs to be converted with the following

formula:

effects in tables B.4 and B.5 were converted using the following formula:

The marginal effects for the OLS wages models (for both men and women) are

presented in table B.6.

Degree or higher 59.75*** 61.34*** 34.34 *** 49.63***

Diploma or certificate 17.71*** 13.88*** 9.81 *** 10.39**

Year 12 15.37*** 11.17** 5.19 7.39

Skill level 2 17.92 *** 13.82**

Skill level 3 32.13 *** 23.19***

Skill level 4/5 54.25 *** 34.97***

COB – English speaking

(not Aus) 2.57 4.18

2.04 4.36

COB – Other -14.38*** -19.92*** -6.74 * -15.01***

*** significant at 1 per cent, ** 5 per cent and * 10 per cent.

In this section, a description of the Heckman model that was used to estimate the

wages models is provided below. Following that, estimation results for the wages

models (outlined in section 6.2) are presented.

A formal representation of the Heckman model is presented below.

The following selection equation is first estimated:

Prob(L = 1 | Z) = Φ(Zγ)

where: L = 1 if in labour force, and 0 otherwise

Z is a vector of explanatory variables,

and γ includes parameters to be estimated.

Z includes the education variables, skill variables (for equation 4) and other

demographic variables (those estimated for the labour force participation models).

A second (wage) equation, is then estimated:

where: w* is a wage offer, which is only observed if a respondent is working.

The conditional wage, given a person works is then:

The above equation can be rewritten as:

from zero. If it is, there is a ‘selection effect’ present. By controlling for this, wage

model estimates are unbiased. However, there was no statistically significant effect

(see below), meaning that sample selection bias is not a problem according to the

model results. A problem in estimating Heckman models like the above is finding

relevant ‘instruments’ –– variables that affect participation, but which do not

influence wages. The variables specifically used as instruments (that is, in the

participation equation only) were: having a child aged 0–4; child aged 5–14; child

aged 15–24; age (including squared and cubed terms).

The coefficient estimates for equations 3 and 4 are presented in tables B.7 and B.8 for men and women respectively. These results include explanatory variables used in both the selection and wage equations.

Lives in city -0.0463 -0.0467

Married 0.5433*** 0.5219***

Age 0.1744*** 0.1683***

Age squared -0.2304*** -0.2230***

Degree or higher 0.5022*** 0.2611**

Diploma or certificate 0.4117*** 0.3148***

Year 12 0.2124** 0.0824

LitNum Skill level 2 0.3020***

LitNum Skill level 3 0.3601***

LitNum Skill level 4 and 5 0.6250***

Physical health 0.0404*** 0.0388***

Mental health 0.0232*** 0.0227***

COB – English speaking (not Aus) 0.1625 0.1351

COB – Other -0.1779* -0.0594

Child 0–4 -0.0106 -0.0119

Child 5–14 -0.1200 -0.1181

Child 15–24 0.2526* 0.2359

Constant -5.5131*** -5.5195***

Lives in city 0.0847*** 0.0841***

Married 0.1249*** 0.1056***

Experience 0.0220*** 0.0200***

Experience squared -0.0352*** -0.0291***

Degree or higher 0.4706*** 0.2960***

Diploma or certificate 0.1654*** 0.0953***

Year 12 0.1443*** 0.0511

LitNum Skill level 2 0.1673***

LitNum Skill level 3 0.2813***

LitNum Skill level 4 and 5 0.4371***

Physical health 0.0045** 0.0036*

Mental health 0.0017 0.0017

COB – English speaking (not Aus) 0.0261 0.0208

COB – Other -0.1563*** -0.0702*

Works part-time -0.0696 -0.0623

Constant 2.3040*** 2.1745***

*** significant at 1 per cent, ** 5 per cent and * 10 per cent.

Lives in city -0.0061 0.0033

Married 0.0110 -0.0084

Age -0.3467*** -0.3486***

Age squared 0.9635*** 0.9678***

Age cubed -0.8647*** -0.8645***

Degree or higher 0.7765*** 0.5735***

Diploma or certificate 0.4627*** 0.3508***

Year 12 0.3172*** 0.2167***

LitNum Skill level 2 0.3886***

LitNum Skill level 3 0.5652***

LitNum Skill level 4 and 5 0.6704***

Physical health 0.0294*** 0.0276***

Mental health 0.0165*** 0.0151***

COB – English speaking (not Aus) 0.0959 0.0998

COB – Other -0.3925*** -0.2253***

Child 0–4 -0.6031*** -0.6273***

Child 5–14 -0.2548*** -0.2595***

Child 15–24 -0.0048 -0.0058

Constant 2.3188 2.1064

Lives in city 0.0610** 0.0603**

Married 0.0534* 0.0453

Experience 0.0125** 0.0110**

Experience squared -0.0189* -0.0136

Degree or higher 0.4970*** 0.4148***

Diploma or certificate 0.1416*** 0.1061***

Year 12 0.1129** 0.0751

LitNum Skill level 2 0.1396**

LitNum Skill level 3 0.2223***

LitNum Skill level 4 and 5 0.3148***

Physical health 0.0080*** 0.0072***

Mental health 0.0041** 0.0036**

COB – English speaking (not Aus) 0.0427 0.0443

COB – Other -0.2330*** -0.1681***

Works part-time 0.0177 0.0219

Constant 2.0074*** 1.9118***

*** significant at 1 per cent, ** 5 per cent and * 10 per cent.

Marginal effects for the education and skills variables were calculated using the same Stata command used for the models of participation (described above). This estimate had to be converted to obtain percentage change in the same way the OLS wages model estimates were converted.

Marginal effects of skills and educational attainment are presented in table B.9.

Degree or higher 59.58*** 61.05*** 34.21 *** 49.42***

Diploma or certificate 17.65*** 13.76*** 9.77 *** 10.28**

Year 12 15.35*** 10.97** 5.18 7.24

Skill level 2 17.97 *** 13.92**

Skill level 3 32.16 *** 23.20***

Skill level 4/5 54.26 *** 35.02***

COB – English speaking

(not Aus) 2.53 4.08

2.01

4.27

COB – Other -14.35*** -19.79*** -6.74 * -14.98***

*** significant at 1 per cent, ** 5 per cent and * 10 per cent.

The wages models were also estimated with the continuous test score variable,

instead of the skill level variables. Qualitative results were unchanged. For

information, the marginal effects from the OLS models estimated with the

continuous variable, or alternatively the skill level variable, are presented in

table B.10. (Results for the Heckman model with the continuous variable are not

reproduced here, but were similar to those of the OLS model). The marginal effect

of the literacy and numeracy test score variable for men is about 1.5 times the

magnitude for women, in line with results from models which use the skills level variables.

OLS regression, employed persons

Degree or higher 34.21*** 32.27*** 49.42*** 47.80***

Diploma or certificate 9.77*** 8.46** 10.28** 9.62**

Year 12 5.18 4.20 7.24 6.66

Literacy/numeracy test

score

0.27

***

0.19

***

Skill level 2 17.97*** 13.92**

Skill level 3 32.16*** 23.20***

Skill level 4/5 54.26*** 35.02***

COB – English speaking

(not Aus) 2.01

1.93

4.27

4.53

COB – Other -6.74* -4.38 -14.98*** -14.11***