Central Institute for Economic Management (CIEM) Hanoi, 21 November 2008

1. Education Transition Matrices in Vietnam(work in progress)Study Team:Channing Arndt, Pham Lan Huong, Simon McCoyand Tran Binh Minh Central Institute for Economic Management (CIEM) Hanoi, 21 November 2008

2. Objectives • Assess how students move through the education system from grade 1 to grade 12. • Evaluate how the current demographic transition is affecting enrollments. • Estimate migration of students between regions in Vietnam. • Project enrollments to 2024 on the basis of disaggregated population projections. • Introduce information theory estimation techniques to CIEM. • Consider implications for policy: • Investment needs in the education sector. • (Future research) Implications of shifting skill composition of the labour force.

3. Methodology: Vietnam National Matrix • At the end of grade t in year n, a school pupil can do one of three things in transition to year n+1: • Repeat Grade t; • Progress to Grade t+1; • Exit from Schooling System. • Notes: • The system excludes jumping from grade 2 to grade 6 or falling from grade 7 to grade 1, for example. • The system excludes international migration. Students remain in Vietnam and new students do not arrive from abroad.

4. Simple National Transition Matrix All empty cells have value zero. Row sums are equal to one. Grade 1 enrollments are exogenous. Projection of enrollments in t+1:St+1 = T’St + Et. Where: St+1= column vector of enrollments in t+1; St= column vector of enrollments in t Et = column vector of entrants into grade 1.

5. Methodology: Sub-national Matrices • Extra dimension introducedhere: Migration • Pupil canmigrate to another region within Vietnam and enter at at the next grade; • Migration assumed to bezero for country as a whole; • Inter-Regional migration probabilitiesestimated. Repeat grade Progress to higher grade Exit from School Migrate to higher grade in another region

6. Data • For the purposes of estimation of the transition matrices: • Administrative data from the Ministry of Education • Enrollments • Repeaters (not used) • Estimatespresentedare for 2001-2005 (wenow have data for 2000-2006) • Prior estimates of transition probabilities • For the purposes of projection of enrollmentsinto the future: • Population projections from GSO to 2024 by provincedisaggregated to provide data by age ratherthan age category.

7. The Education Transition Matrix for Hanoi

8. Information Theory Approach • “The intention is to give a way of extracting the most convincing conclusions implied by given data and any prior knowledge of the circumstance.” • Buck and McAuley (1991).

9. Applications of Information Theory • National Accounts/SAM estimation • Physics • Image processing

10. Information Theory • Shannon (1948) developed a formal measure of “information content”

11. Information Theory • For a set of events, the expected information content of a message before it arrives is the entropy measure:

12. Claude Shannon

13. E.T. Jaynes • Jaynes proposed to use the Shannon entropy measure in estimation. • Maximum entropy (MaxEnt) principle: • Out of all probability distributions that are consistent with the constraints, choose the one that has maximum uncertainty (maximizes the Shannon entropy metric). • In the absence of any constraints, entropy is maximized for the uniform distribution.

14. E.T. Jaynes

15. Estimation With a Prior • The estimation problem is to estimate a set of probabilities that are “close” to a known prior and that satisfy various known moment constraints. • Jaynes suggested using the criterion of minimizing the Kullback-Liebler “cross entropy” (CE) distance between the estimated probabilities and the prior.

16. Cross Entropy Estimation

17. Mathematical Form: Equations

18. Additional Notes • The estimated matrix (at the National and Sub-National level) is static. • Probabilities do not vary through time. • Is this a fair assumption? Example of Repeat Ratios post-2006. • The input into the education system (pupils entering Grade 1) is exogenous; • Based on the disaggregated population projections, and specifically those children aged 7 years. • School enrolment patterns will therefore largely reflect demographic patterns for the population as a whole. • Inter-regional migration assumed to be higher at the end of Primary School (Grade 5) and the end of Lower Secondary School (Grade 9); • Migration probabilities are constant across all other grades.

19. Whole Country Enrolments: Key Trends (i) • Total enrolments falling 2001 - 2015, then starting to rise;

20. Whole Country Enrolments: Key Trends (ii) • Primary School enrolments trough in 2008 then gradually rise; • Lower Secondary enrolments peaked in 2004, and will trough in 2012; • Upper secondary enrolments peaked in 2007 and will trough in 2016; • 2024 vs 2001: Less Primary (-21%), much less Lower Secondary (-26%), slightly less Upper Secondary (-6%); • 2024 vs 2008: More Primary (+14%), less Lower Secondary (-12%), much less Upper Secondary (-29%).

21. Whole Country Enrolments: Key Trends (iii) • Exit Probability for Whole Country fairly constant (and low) through primary school; • Starts to rise in Lower Secondary School; • Peak in g9 reflecting large number of school leavers at end of Lower Secondary School.

22. Results: Grade 5 • Most students progress from Primary to Lower Secondary; • High exit probabilities in Hai Phong, North West and Mekong Delta; • Below average exit probabilities in North Central, Red River ex-, and Coastal Central ex-;

23. Results: Grade 9 • High drop-out rates at the end of Lower Secondary School, but with more regional variation; • Urban areas of Hanoi and HCMC (but also Central Highlands…?) showing low exit rates of c15%;

24. Results: Urban Areas • Hanoi: Fairly constant enrolment rates across school categories and time; • HCMC: Rises in all school categories ; • Urban Areas showing constant or rising enrolments due to in-migration.

25. Results • South East: Relatively constant enrolments. • North East: Dramatic decline in Primary 2001-08; • Also falls in Lower and Upper Secondary.

26. Draft Policy Implications • In general, total school enrolments will be lower than in 2001 for a long time. • Compared with 2008, Primary enrolment will be higher in the future, Secondary will be lower. • Implications for Education expenditure: • Infrastructure investment (building more schools) should not be the priority; • Expenditure better spent on: • Reducing the Teacher:Pupil ratio (i.e recruiting more teachers), • Curriculum improvements.

27. Future Work • Incorporate additional data. • Run projection scenarios with a non-static matrix • Reduce exit probabilities particularly for the 9-10 transition? • Increase repeat probabilities due to higher standards? • Project implications for the composition of the labour force by education level. • Use VHLSS to determine historical trends. • Employ projections of “exit” from the system, combined with assumptions about death or retirement rates, to project future stocks (by region?). • Consider implications for university education?