Bachelor’s or equivalent degrees remain the most common tertiary qualification among first-time tertiary graduates in OECD countries. In 2018, on average across OECD countries, the majority of first-time tertiary graduates (78%) earned a bachelor’s degree, 18% a short-cycle tertiary diploma and 10% a master’s degree.
On average across OECD countries, at short-cycle tertiary level, 24% of students graduate from the fields of business, administration and law, whereas only 2% earn a diploma in natural sciences, mathematics and statistics.
Based on current patterns, it is estimated that 38% of young adults across OECD countries will graduate from tertiary education for the first time before the age of 30 (excluding international students).
Education at a Glance 2020
OECD Indicators
Education at a Glance
Indicator B5. Who is expected to graduate from tertiary education?
Highlights
Figure B5.1. Distribution of short-cycle tertiary, bachelor's, master's and doctoral graduates on average across partners and OECD countries, by field of education (2018)
Note: Agriculture, forestry, fisheries and veterinary are not included in the chart but data are available in the education database.
Fields of study are ranked in descending order of their share of short-cycle tertiary graduates (ISCED 5).
Source: OECD/UIS/Eurostat (2020), Education at a Glance (database), http://stats.oecd.org/. See Source section for more information and Annex 3 for notes (https://doi.org/10.1787/69096873-en).
Context
Tertiary graduation rates illustrate a country’s capacity to provide future workers with advanced and specialised knowledge and skills. The incentives to earn a tertiary degree, including higher salaries and better employment prospects, remain strong across OECD countries (see Indicators A1, A3, A4 and A5 for further reading on these themes). Tertiary education varies in structure and scope across countries, and graduation rates seem to be influenced by educational factors such as the flexibility of programmes, the supply of spaces available by education level and fields of study, as well as other factors during the educational year, that make students likely to complete their programme or not.
In recent decades, access to tertiary education has expanded remarkably, involving new types of institutions that offer more choice and new modes of delivery (OECD, 2016[1]). In parallel, the student population is becoming increasingly diverse in the study pathways they choose. Students are also becoming more likely to seek a tertiary degree outside their country of origin. Understanding current graduation patterns helps to understand student progression throughout higher education and anticipate the flow of new tertiary-educated workers into the labour force.
Policy makers are exploring ways to help ease the transition from tertiary education into the labour market (OECD, 2015[2]).To this end, short-cycle tertiary programmes, typically vocationally oriented, are central to preparing young people for work, developing adults’ skills and responding to labour-market needs.
Other findings
Advanced tertiary degrees attract more international students (see Definitions section) than bachelor’s degrees. Some 26% of students in OECD countries who graduated for the first time from a doctoral or equivalent programme in 2018 were international students, compared to 19% of those who were awarded a master’s degree and 8% of those who earned a bachelor’s degree for the first time.
Women’s participation in higher education has been increasing in recent years, and their share among first-time tertiary graduates (58%) remains higher than their share among first-time tertiary entrants (54%). This is in line with previous findings suggesting that women are more likely to complete their degree than men (OECD, 2019[3]).
Average age at graduation reflects a combination of average age at entry and the time taken to complete tertiary educational programmes. Across OECD countries with data, people graduate for the first time from a tertiary level programme on average at the age of 25.
Note
Graduation rates, when calculated for all ages, represent the estimated percentage of people from a given age cohort who are expected to graduate within the country at some point during their lifetime. This estimate is based on the number of graduates in 2018 and the age distribution of this group. Graduation rates are based on both the population and the current pattern of graduation and are thus sensitive to any changes in the education system, such as the introduction of new programmes and changes in the duration of programmes. Graduation rates can be very high during a period when an unexpected number of people go back to school.
In this indicator, age refers generally to the age of students at the beginning of the calendar year. Students could be one year older than the age indicated when they graduate at the end of the school year. Thirty is used as the upper age limit for completing short-cycle tertiary and bachelor’s degree, because across OECD countries, more than 95% of graduates from upper secondary general programmes in 2018 were under 25 (see Education at a Glance Database). People who graduate from upper secondary level at 25 or older are usually enrolled in second-chance programmes. Similarly, 35 is used as the upper age limit for completing master’s and doctorate degrees.
In this edition of Education at a Glance, the focus is predominately on first-time graduates below the typical age (30 for short-cycle tertiary and bachelor’s and 35 for master’s and doctoral levels). The concept of graduates (i.e. all graduates, not only first-time graduates) is used when measuring graduation rate at each tertiary level and graduates by field of study (see Definitions section).
Analysis
Graduation patterns at tertiary level
Over the past two decades, tertiary education in OECD countries has changed significantly. The student body is more international, more women than men are graduating and choices of fields of study have evolved. These changes might reflect concerns about competitiveness in the global economy and the labour market, but also the interests and priorities of a growing student population.
The first-time graduation rate from tertiary education among people under the age of 30 is an indicator of how many young people are expected to enter the labour force for the first time with a tertiary qualification. Based on current patterns of graduation, it is estimated that 41% of young adults will graduate from tertiary education for the first time in their life before the age of 30 on average across OECD countries. The proportion ranges from 10% in Luxembourg (although this percentage is negatively biased by the high percentage of secondary graduates who pursue tertiary studies abroad) to 71% in Japan (Table B5.1).
International students (see Definitions section at the end of this indicator) can have a marked impact on graduation rates by inflating the estimate of graduate students compared to the national population. In a country with a high proportion of international graduates, such as Australia where they make up 46% of all first-time graduates, the difference can be significant. Australia’s first-time tertiary graduation rate drops from 70% to 37% when international students are excluded (Table B5.1).
Age distribution of first-time tertiary graduates
For some years now, many OECD countries have been concerned about the length of time tertiary students take to complete their studies. They have developed policies to encourage students to graduate more quickly, so as to get more workers into the labour market at an earlier age.
Across OECD countries, in 2018 86% of first-time tertiary graduates graduated before they turned 30, and the average age of graduation was 25. The variation among countries is large, however, ranging from 23 in the United Kingdom, to 28 in Latvia, Sweden and Switzerland (Table B5.1). The average age at which most students graduate reflects a combination of their average age at entry and the length of tertiary programmes. Entrance to tertiary education can be delayed by the structure of upper secondary education systems, processes for entry and admission into tertiary education, conscription requirements, or diverse pathways to transition from study to work. Programme duration depends on the structure of the educational programme and on the intensity of study, i.e. full time or part time.
In Iceland, Sweden and Switzerland, students graduate relatively later but the average age of entry is also two to three years older than the OECD average (24-25 compared to the average of 22). These older ages for both graduation and entry in these countries reflect students’ varied trajectories before entering higher education, the flexibility of their education systems to accommodate transitions between educational programmes or between work and study, and adults’ lifelong learning. Greater enrolment in part-time studies, as observed in Sweden, also tends to delay the average graduation age (see data available on OECD.Stat at http://stats.oecd.org/).
Some education systems accommodate a wider range of ages than others. This suggests that these education systems are more flexible about access to programmes and their duration, particularly for students outside typical student age. It may also reflect the different policies and attitudes towards adult and lifelong learning. In Latvia, Sweden and Switzerland, the average age of first-time graduates is more than two years higher than the OECD average.
Gender distribution of first-time tertiary graduates
Recognising the impact that education has on participation in the labour market, occupational mobility and quality of life, policy makers and educators have emphasised the importance of reducing differences between men and women in education opportunities and outcomes.
In 2018, more women than men graduated from tertiary education: on average 58% of first-time graduates from tertiary education in OECD countries were women, ranging from 50% in Switzerland to 64% in Latvia (Table B5.1). Furthermore, the share of female first-time graduates was higher than the share of female first-time new entrants into tertiary education (54%) in all OECD and partner countries with available data. This confirms previous findings that women are more likely to complete tertiary education than their male counterparts (OECD, 2019[3]). On average across OECD countries, excluding international students, 44% of women are expected to obtain a tertiary degree before the age of 30, compared to 29% of men. In all countries with available data, first-time tertiary graduation rates are lower for men than for women, but the size of the gender gap varies significantly across countries, ranging from 2 percentage points in Luxembourg to 26 percentage points in Lithuania (Table B5.1).
Although the majority of tertiary graduates in 2018 were women, men still have better labour-market outcomes. Earnings for tertiary-educated men are higher, on average, than those for tertiary-educated women, and tertiary-educated men tend to have higher employment rates than women with the same level of education (see Indicators A3 and A4).
Fields studied by tertiary graduates
The distribution of graduates by field of study is related to factors such as the relative popularity of these fields among students, the number of study spaces offered in universities and equivalent institutions, and the degree structure of the various disciplines in each country.
Currently, in most OECD countries, the largest share of graduates across all tertiary education programmes complete degrees in business, administration and law, with a few exceptions (Table B5.2). In 2018, on average, 25% of tertiary students graduating in that year obtained a degree in this broad field across OECD countries, although this ranges from 15% in Korea to 46% in Colombia. In Korea, the most popular field among tertiary graduates is engineering, manufacturing and construction; in Belgium, Finland, Norway and Sweden it is health and welfare; in India it is social sciences, information and journalism; and in Indonesia it is education. Some of these differences can be explained by the structure of educational systems and the type of institutions offering qualifications in each field of study across countries. For example, degrees in fields of study such as nursing (included under health and welfare) are more likely to be offered as a tertiary programme in countries that have integrated most of the post-secondary vocational education into their tertiary education system.
In most countries, the broad field of natural sciences, mathematics and statistics is less popular than other fields of study. In more than half of the OECD and partner countries with available data, the combined share of students graduating from natural sciences, mathematics and statistics; engineering, manufacturing and construction; and information and communication technologies is still lower than the share of students graduating from business, administration and law.
Figure B5.2. First-time short-cycle tertiary graduation rate, for students under 30 and excluding international students (2010 and 2018)
1. Year of reference 2013 instead of 2010.
Countries are ranked in descending order of the first-time short-cycle tertiary graduation rates for students under 30 in 2018.
Source: OECD/UIS/Eurostat (2020), Education at a Glance Database, http://stats.oecd.org/. See Source section for more information and Annex 3 for notes (https://doi.org/10.1787/69096873-en).
Profile of first-time graduates from short-cycle tertiary levels
In 2018, the second most common tertiary qualification among first-time tertiary graduates that year remained a short-cycle tertiary degree. On average across OECD countries 18% of those graduating earned a short-cycle tertiary qualification ranging from 1% or less in the Czech Republic, Germany, Italy and Switzerland to 49% in Austria, where short-cycle tertiary accounted for the largest share of first-time graduates.
Although the large majority of first-time tertiary graduates are awarded a bachelor’s degree, some OECD countries are also encouraging participation in short-cycle tertiary programmes to improve employability and smooth transitions into work. Generally professionally oriented, these programmes develop occupation-specific skills and most often prepare students for direct entry into the labour market. The first-time graduation rate for students under 30 from these programmes has increased by more than 4 percentage points in Australia and Turkey between 2010 and 2018, excluding international graduates. In contrast, the rate has remained stable over this period in Austria, the Czech Republic, Iceland, the Netherlands and the Slovak Republic, increasing by less than 1 percentage point over this period (Figure B5.2). In some cases, this limited growth over time could suggest that short-cycle tertiary programmes are not an attractive option in many countries. To remedy this situation, many countries are trying to develop future education opportunities for those entering this level, by promoting professional or vocational programmes at bachelor’s and master’s levels.
Based on patterns of graduation prevailing in 2018 and excluding international students, on average across OECD countries, 8% are expected to graduate from a short-cycle tertiary programme before the age of 30 (Table B5.3).
Analysis by age
On average across OECD countries in 2018, 75% of first-time short-cycle tertiary graduates graduated before the age of 30, and the median age at graduation was 25, ranging from 19 in Austria to 38 in Poland (Figure B5.3). The variation across countries is large and older first-time graduation ages could be explained in some cases by short-cycle tertiary programmes specifically designed for older students, as well as students taking longer to graduate.
Figure B5.3. Age distribution of first-time graduates at short-cycle tertiary level (2018)
Countries are ranked in descending order of the median graduation age of first-time graduates at short-cycle tertiary level.
Source: OECD/UIS/Eurostat (2020), Education at a Glance Database, http://stats.oecd.org/. See Source section for more information and Annex 3 for notes (https://doi.org/10.1787/69096873-en).
The age distribution of first-time graduates at short-cycle tertiary level provides insights into the diversity of graduates’ ages, compared to the median value. In some countries, the age distribution is closely centred on the median, implying relatively small age differences at this level. This is the case in Austria, France, Korea, Luxembourg, Mexico and Portugal, where no more than 4 years separate the 80th and 20th percentile age groups. In other countries, the age distribution is much wider. For example in Ireland, New Zealand, Poland and Switzerland, first-time short-cycle tertiary graduates in the 80th percentile are at least 20 years older than those in the 20th percentile. However on average across OECD countries, the median age is closer to the 20th percentile, indicating the age distribution skews more towards the younger than the older age group (Figure B5.3).
Analysis by mobility status
On average across OECD countries, 5% of first-time graduates from short-cycle tertiary programmes were international students in 2018, the lowest share across all tertiary levels of education. The more limited share of international students in short-cycle tertiary programmes could be due to the relative low prevalence and limited attractiveness of short-cycle tertiary programmes, compared to the other tertiary levels. However, this pattern does not hold for every country: in Denmark, Italy, Japan and Luxembourg, the share of international students in short-cycle tertiary level is substantially higher than in bachelor’s programmes, by more than 2 percentage points. However, there are large disparities across countries. The share of international students in short-cycle tertiary programmes varies from close to zero in Austria, Chile, Germany, Iceland, the Netherlands, Poland, Sweden and Turkey to 29% in New Zealand (Table B5.3).
Analysis by field of study
On average across OECD countries, at short-cycle tertiary level, 24% of students graduate from the broad field of business, administration and law compared to only 2% in natural sciences, mathematics and statistics (Figure B5.1). However, some exceptions exist: Austria, Italy, Mexico, Norway, Portugal and Slovenia have the largest share of students graduating from engineering, manufacturing and construction at short-cycle tertiary level. In Chile, Japan, Korea, Latvia, Luxembourg, Switzerland and the United Kingdom the largest share of short-cycle tertiary graduates studied health and welfare; in Belgium and Poland, 100% studied this broad field. The largest share of short-cycle tertiary students in Germany and Iceland graduate from the field of services whereas the dominant field of study in the Czech Republic (with 100% of graduates), the Slovak Republic and the United States is arts and humanities (see data available on OECD.Stat at http://stats.oecd.org/). However, these results need to be analysed with caution as short-cycle tertiary represents less than 3% of the share of first-time tertiary graduates in the Czech Republic, Germany, Italy, the Netherlands, Sweden and Switzerland. These differences may result from the structure of the tertiary system, the promotion of short-cycle programmes, as well as the educational provision of short-cycle training in certain fields of study which require more vocational skills than others.
Profile of first-time graduates from bachelor’s, master’s and doctoral levels
In 2018, the large majority of first-time tertiary graduates were awarded a bachelor’s or equivalent degree. On average across OECD countries, 78% of first-time tertiary graduates earned a bachelor’s degree, 10% earned a master’s or equivalent degree and 18% earned a short-cycle tertiary diploma (Table B5.1).
More young people are expected to graduate from a bachelor’s programme than from any other level of tertiary education. Based on graduation patterns prevailing in 2018, on average across OECD countries, 33% of young people are expected to graduate with a bachelor’s degree before they turn 30, 16% are expected to earn a master’s degree and 1% are expected to graduate from a doctoral or equivalent programme (including international students) (Table B5.3).
Analysis by age
On average across OECD countries, 86% of first-time graduates at bachelor’s level are below the age of 30, this varies from 76% in Israel and Sweden to almost 100% in Japan. On average across OECD countries, 84% of first-time graduates from master’s programmes and 61% from doctoral programmes are below the age of 35. Master’s programmes may lead directly to a labour market-relevant qualification but they are also a prerequisite to accessing an advanced research qualification (i.e. a doctorate) in many countries. In Luxembourg, the share of first-time graduates below the age of 35 is slightly higher among doctoral graduates than among master’s (Table B5.3).
Analysis by mobility status
The share of first-time international graduates varies significantly across countries. The proportions are particularly high in Australia, Luxembourg and New Zealand, which have at least 20% of international graduates in bachelor’s programmes, at least 30% in master’s programmes, and at least 40% in doctoral programmes. In contrast, the smallest shares of international graduates at doctoral level are found in Chile, Greece and Lithuania where they account for no more than 5% of first-time graduates (Annex Table B5.3).
In spite of these differences, there is a common pattern across countries with available data: advanced tertiary degrees attract more international students than bachelor’s degrees. Some 26% of students in OECD countries who graduated for the first time from a doctoral programme in 2018 were international students, compared to 19% of students who were awarded a master’s degree, and 8% of students who earned a bachelor’s degree for the first time (Annex Table B5.3). The high share of international students in advanced tertiary degrees may be due, in part, to the emergence of knowledge-based economies (economies directly based on the production, distribution and use of knowledge and information). This phenomenon has contributed to the internationalisation of research. Consequently, many students are seeking opportunities to study abroad at the master’s or doctoral level. From the point of view of host countries, attracting international students can be beneficial for several reasons, such as the fees and other living expenses the students pay, and the social and business networks that they help to build with their home countries.
In addition, international students, particularly at the master’s or doctoral or equivalent level, can contribute to research and development (R&D) in the host country, initially as students and later on potentially as researchers or highly qualified professionals. Doctoral students, in particular, form an integral part of the research staff of a country (OECD, 2016[4]).
Analysis by field of study
At tertiary level, only a small share of students graduate from the broad field of natural sciences, mathematics and statistics, on average across OECD countries. However, there are large variations across tertiary education levels. Graduation rates from this broad field of study increase with educational level: on average across partners and OECD countries, 6% of bachelor’s and master’s graduates in 2018 earned a degree in natural sciences, mathematics and statistics, while this rose to 22% of graduates at doctoral level (Figure B5.1).
The popularity of natural sciences, mathematics and statistics in doctoral programmes may be the result of policies that encourage academic research in these fields. Recent OECD work has highlighted that while innovation draws on a wide set of skills, excellence in scientific research is the basis of science-based innovation, and research competence is essential for building co-operation among the scientific community, business and society. Thus, developing scientific research skills through doctoral training has become an important aim of education policy in many countries (OECD, 2014[5]).
The broad fields of business, administration and law, and of education are among those most commonly pursued at master’s level. On average across partners and OECD countries, business, administration and law accounted for 28% of master’s graduates compared with 24% of bachelor’s graduates and 9% of doctoral graduates. Similarly, 12% of students graduating at master’s level studied in the field of education, compared to 6% graduating from a bachelor’s programme and 7% earning a doctorate (Figure B5.1). Tertiary students are more likely to graduate from the fields of social sciences, journalism and information at bachelor’s level (12%) than from any other long-cycle tertiary level (10% at master’s and doctoral levels), on average across partners and OECD countries (Figure B5.1).
Definitions
First-time graduates refer to students who have graduated for the first time at a given level of education during the reference period. Therefore, if a student has graduated multiple times over the years, he or she is counted as a graduate each year, but as a first-time graduate only once per level of education.
First-time tertiary graduates refer to students who graduate for the first time with a tertiary degree, regardless of the education programme in which they are enrolled. This definition is applied in Tables B5.1 and B5.3.
International students are students who left their country of origin and moved to another country for the purpose of study. In the majority of countries, international students are considered first-time graduates, regardless of their previous education in other countries. In the calculations described here, when countries could not report the number of international students, foreign students have been used as an approximation. Foreign students are students who do not have the citizenship of the country in which they studied (for more details, please refer to Annex 3, www.oecd.org/education/education-at-a-glance-19991487.htm).
Net graduation rates represent the estimated percentage of an age group who will complete a given level of education, based on current patterns of graduation.
Typical age is the age at the beginning of the last school/academic year of the corresponding educational level and programme when the degree is obtained.
Methodology
Unless otherwise indicated, graduation rates are calculated as net graduation rates (i.e.as the sum of age-specific graduation rates) up to an age threshold. The net graduation rate for a single age is obtained by dividing the number of first-time graduates of that age for each type of tertiary education by the total population of the corresponding age. The sum of net graduation rates is calculated by adding the rates for each year of age until the age threshold. The result represents the expected probability of graduating for the first time from tertiary education before the age threshold if current patterns are maintained. The age threshold refers to the upper limit for completing a tertiary degree. Age 30 is used as the upper limit for completing short-cycle tertiary, bachelor’s degrees and first-time tertiary education overall. At the master’s and doctoral levels, 35 is considered to be the upper age limit for graduation.
Gross graduation rates are used when data by age are missing and where the average age of graduation is well below the age threshold considered for the calculation of this indicator. In this case, the number of graduates of which the age is unknown is divided by the population at the typical graduation age (see Annex 1).
The average age of students is calculated from 1 January for countries where the academic year starts in the second semester of the calendar year and 1 July for countries where the academic year starts in the first semester of the calendar year. As a consequence, the average age of new entrants may be overestimated by up to 6 months while that of first-time graduates may be underestimated by the same.
Graduation rates are sensitive to changes in the education system, such as the introduction of new programmes or the number of international students. Rates could at times be very high, during periods when there are unexpectedly high numbers of graduates. This indicator also reports the share of first-time graduates below the age threshold, alongside the graduation rate, to provide contextual information on the relevance of the age threshold for each country.
International students are a significant share of the total student population in some countries, and their numbers can artificially inflate the proportion of today’s young adults who are expected to graduate from tertiary programmes. When international students are included in the calculation, the percentage of expected first-time graduates from tertiary programmes can change significantly.
For more information please see the OECD Handbook for Internationally Comparative Education Statistics (OECD, 2018[6]) and Annex 3 for country-specific notes (https://doi.org/10.1787/69096873-en).
Source
Data refer to the academic year 2017/18 and are based on the UNESCO-UIS/OECD/EUROSTAT data collection on education statistics administered by the OECD in 2019 (for details, see Annex 3 at https://doi.org/10.1787/69096873-en).
References
[3] OECD (2019), Education at a Glance 2019: OECD Indicators, OECD Publishing, Paris, https://dx.doi.org/10.1787/f8d7880d-en.
[6] OECD (2018), OECD Handbook for Internationally Comparative Education Statistics 2018: Concepts, Standards, Definitions and Classificatons, OECD Publishing, Paris, https://doi.org/10.1787/9789264304444-en (accessed on 16 April 2020).
[1] OECD (2016), OECD Science, Technology and Innovation Outlook 2016, OECD Publishing, Paris, https://doi.org/10.1787/sti_in_outlook-2016-en.
[4] OECD (2016), Trends Shaping Education 2016, OECD Publishing, Paris, http://dx.doi.org/10.1787/trends_edu-2016-en.
[2] OECD (2015), Education Policy Outlook 2015: Making Reforms Happen, OECD Publishing, Paris, http://dx.doi.org/10.1787/9789264225442-en.
[5] OECD (2014), OECD Science, Technology and Industry Outlook 2014, OECD Publishing, Paris, http://dx.doi.org/10.1787/sti_outlook-2014-en.
Indicator B5 Tables
Table B5.1. Graduation rate and profile of first-time tertiary graduates (2018)
Table B5.2. Distribution of tertiary graduates by field of study (2018)
Table B5.3. Graduation rate and profile of first-time tertiary graduates at short-cycle tertiary, bachelor's, master's and doctoral or equivalent levels (2018)
Cut-off date for the data: 19 July 2020. Any updates on data can be found on line at http://dx.doi.org/10.1787/eag-data-en. More breakdowns can also be found at http://stats.oecd.org/, Education at a Glance Database.
Statlink: https://doi.org/10.1787/888934163800
Table B5.1. Graduation rate and profile of first-time tertiary graduates (2018)
1. Year of reference 2017.
2. It is estimated that almost all students graduate from tertiary education before the typical graduation age.
Source: OECD/UIS/Eurostat (2020). See Source section for more information and Annex 3 for notes (https://doi.org/10.1787/69096873-en).
Please refer to the Reader's Guide for information concerning symbols for missing data and abbreviations.
Table B5.2. Distribution of tertiary graduates by field of study (2018)
1. Year of reference 2017.
2. Data on information and communication technologies are included in other fields.
Source: OECD/UIS/Eurostat (2020). See Source section for more information and Annex 3 for notes (https://doi.org/10.1787/69096873-en).
Please refer to the Reader's Guide for information concerning symbols for missing data and abbreviations.
Table B5.3. Graduation rate and profile of first-time tertiary graduates at short-cycle tertiary, bachelor's, master's and doctoral or equivalent levels (2018)
1. Year of reference 2017.
2. It is estimated that almost all students graduate from short-cycle tertiary education and bachelor's programmes before the typical graduation age.
Source: OECD/UIS/Eurostat (2020). See Source section for more information and Annex 3 for notes (https://doi.org/10.1787/69096873-en).
Please refer to the Reader's Guide for information concerning symbols for missing data and abbreviations.