4.1.1. Variables

The two dependent variables are (a) enrollment (headcount) in ISCED-Level 5, or short-cycle tertiary education [4] and (b) the percentage of ISCED-Level 5 students within tertiary education. The sector incorporating ISCED-Level 5 is often designed to provide students with professional knowledge, skills, and competencies and offer a tertiary level of education below the status of a bachelor's degree or equivalent (See Appendix A, Definitions of the Variables).

Guided by the conceptual framework, this study selected 18 independent variables from WDI to address the research questions. We use three blocks of independent variables. First, education finance policy variables include government expenditure on tertiary education as a percentage of governments' education expenditures, public expenditure per student at primary, secondary, and tertiary levels (as a percent of GDP per capita), and public spending on education (as a percent of GDP). Government expenditure on tertiary education as a percentage of government expenditure on education provides an indicator of government priority in financing the tertiary sector relative to elementary and secondary education. Public spending on education as a percentage of GDP indicates a country's prioritization of education compared with resource allocation to other public sectors (e.g., health, military). Public expenditure per student at each level as a percent of GDP per capita represents the government's role in sharing the cost of education.

Second, economic indicators include GDP per capita and total manufacturing output (in constant 2015 USD). GDP per capita can capture global economic changes and represent income level and education affordability. Since tertiary vocational education mainly supplies the labor force to the manufacturing industry in many countries [55], including manufacturing output may provide insights into how a country's manufacturing size and global competitiveness affect its growth in tertiary vocational education.

Third, the set of educational system variables includes the percentage of students enrolled in vocational and technical secondary education programs, gross enrollment ratios, and gender parity indices (GPI) at the three education levels (See Appendix A, Definitions of the Variables). The gross tertiary enrollment ratio is the total enrollment in tertiary education (ISCED 5 to 8), regardless of age, expressed as a percentage of the total collegeaged population of the five-year age group after leaving secondary school. GPI is the female gross enrollment ratio at each educational level compared with males; a value less than 1 indicates a disparity in favor of males, and a value greater than 1 indicates a disparity in favor of females. Lagging variables for gross tertiary enrollment ratios and GPI at the tertiary education level by one year allowed countries time to respond to previous years' changes in higher tertiary vocational education systems.

Like Yang and McCall's [13] study, the analytical framework also includes a set of control variables on population characteristics, including the percentage of the population 65 years and older, the percentage of females in the population, and the total population size. These control variables partial out the impact of socio-demographic factors, such as aging trends and the gender gap in the school-aged population, on the dependent variables [13].

In addition, the literature review suggests that the purpose, access, and design of tertiary vocational education systems differ between developed and less-developed countries [36,55]. Thus, in the preliminary stage, this study included a dummy variable to classify the development level of the 67 countries (1 = developed countries; 0 = lessdeveloped countries) based on the classification developed by the United Nations [5]. We created a series of interaction terms from the dummy variable and the first three blocks of indicators. Five interaction items between the dummy variable (countries' development level) and critical economic, education finance, and systems variables appeared statistically significant in the preliminary statistical analyses. Thus, this study retained only five interaction terms in the final models—manufacturing output, GDP per capita, tertiary expenditure, secondary expenditure, and secondary vocational education. The interaction terms can provide insights into whether the effects of a country's economy, education finance, and secondary vocational education on short-cycle tertiary vocational education depend on its development level.

We took steps to address multicollinearity, a potential limitation in regression analyses. We reviewed pair-wise correlations between all independent variables to check for severe collinearity. Additionally, our panel dataset includes a long time series with a maximum of

19 years of entries (2000–2018, with no missing data) clustered for each country, causing high intra-class correlation and serial correlation [97]. In this case, the traditional correlation matrix does not sufficiently capture the panel dataset's variance structure; thus, the correlation table is not provided (but available on request). Finally, all variables in dollar units or population headcounts were transformed using a natural logarithm to model a linear relationship.
