central institute for economic management (ciem) hanoi, 21 november 2008
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Education Transition Matrices in Vietnam (work in progress) Study Team: Channing Arndt, Pham Lan Huong, Simon McCoy and Tran Binh Minh. Central Institute for Economic Management (CIEM) Hanoi, 21 November 2008. Objectives. - PowerPoint PPT PresentationTRANSCRIPT
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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
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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.
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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.
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Simple National Transition Matrix
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Tg1g1 Tg1g2 Tg1exit
Tg2g2 Tg2g3 Tg2exit
Tg3g3 Tg3g4 Tg3exit
T = Tg4g4 Tg4g5 Tg4exit
Tg5g5 Tg5g6 Tg5exit
Tg6g6 Tg6g7 Tg6exit
Tg7g7 Tg7exit
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.
All empty cells have value zero.
Row sums are equal to one.
Grade 1 enrollments are exogenous.
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Methodology: Sub-national Matrices
• Extra dimension introduced here: Migration• Pupil can migrate to another region within Vietnam and enter at at the next
grade;• Migration assumed to be zero for country as a whole;• Inter-Regional migration probabilities estimated.
Repeat grade
Progress to higher grade
Exit from School
Migrate to higher grade in another region
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Data
• For the purposes of estimation of the transition matrices:• Administrative data from the Ministry of Education
• Enrollments • Repeaters (not used)• Estimates presented are for 2001-2005 (we now have data for 2000-2006)
• Prior estimates of transition probabilities
• For the purposes of projection of enrollments into the future:• Population projections from GSO to 2024 by province disaggregated to provide
data by age rather than age category.
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The Education Transition Matrix for Hanoi
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g1 g2 g3 g4 g5 g6 g7 g8 g9 g10 g11 g12 Exit Migrate TOTAL
g1 0.00% 92.36% 5.69% 1.95% 100.00%
g2 0.86% 92.37% 4.82% 1.95% 100.00%
g3 0.89% 92.56% 4.60% 1.95% 100.00%
g4 0.92% 92.44% 4.69% 1.95% 100.00%
g5 0.71% 93.57% 3.65% 2.06% 100.00%
g6 1.73% 90.31% 6.00% 1.95% 100.00%
g7 0.97% 90.62% 6.46% 1.95% 100.00%
g8 1.10% 88.65% 8.30% 1.95% 100.00%
g9 1.60% 80.28% 15.20% 2.92% 100.00%
g10 0.88% 88.97% 8.20% 1.95% 100.00%
g11 0.74% 92.24% 5.07% 1.95% 100.00%
g12 0.67% 97.37% 1.95% 100.00%
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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).
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Applications of Information Theory
• National Accounts/SAM estimation• Physics• Image processing
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Information Theory
Shannon (1948) developed a formal measure of “information content”
)(0
0)(1
)/1log()(
phthenpIF
phthenpIF
pph
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Information Theory
For a set of events, the expected information content of a message before it arrives is the entropy measure:
n
iii
n
iii ppphppH
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)log()()(
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Claude Shannon
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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.
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E.T. Jaynes
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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.
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Cross Entropy Estimation
Minimize:
log log log
where is the prior probability.
ii i i i
i ii
i
pp p p q
q
q
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Mathematical Form: Equations
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Equations:
Minimize pe pp
pppepppepppe qrrZ )/ln(* ,,, d
tpedtkdpe t
ss )3/ln(* ,,,,
subject to:
(1)
pp
ppptpptptp tprestvaltotgestval ,*1 ,,,1, (2)
tpeehatestvalval tpetpetpe ,,,, (3)
tpevsehatd
tpedtpedtpe ,* ,,,,, (4)
perpp
pppe 1, (5)
tpesd
tped ,1,, (6)
),(),(01 , ppphpppr ppp (7)
pppr , = ),(),(0 ppphppp (8)
tpeds tped ,,01 ,,
(9)
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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.
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Whole Country Enrolments: Key Trends (i)
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0
5000
10000
15000
20000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
Enro
lmen
ts '0
00 st
uden
ts
Total enrolments
• Total enrolments falling 2001 - 2015, then starting to rise;
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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%).
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0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
2001 2003 2005 2007 2009 2011 2013 2015 2017 2019 2021 2023
Enro
lme
nts
'00
0 s
tud
en
ts
Enrolments over time by level of schooling
Primary
Lower Secondary
Upper Secondary
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Whole Country Enrolments: Key Trends (iii)
0.00%
5.00%
10.00%
15.00%
20.00%
25.00%
g1 g2 g3 g4 g5 g6 g7 g8 g9 g10 g11
Exit Probability
Exit
• 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.
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Results: Grade 5
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50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
100%
g5 probabilities across region
Migrate
Exit
Repeat
Progress0.00%
1.00%
2.00%
3.00%
4.00%
5.00%
6.00%
g5 exit probabilities
• 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-;
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Results: Grade 9
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50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
100%
g9 probabilities across region
Migrate
Exit
Repeat
Progress 0.00%5.00%
10.00%15.00%20.00%25.00%30.00%35.00%
g9 exit probabilities
• 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%;
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Results: Urban Areas
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0
100
200
300
400
500
600
2001 2008 2015 2024
Hanoi Enrolments
Upper Secondary
Lower Secondary
Primary
0
200
400
600
800
1000
1200
2001 2008 2015 2024
HCMC Enrolments
Upper Secondary
Lower Secondary
Primary
• 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.
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Results
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0
500
1000
1500
2000
2001 2008 2015 2024
Sth East ex-HCMC Enrolments
Upper Secondary
Lower Secondary
Primary
0
500
1000
1500
2000
2500
2001 2008 2015 2024
North East Enrolments
Upper Secondary
Lower Secondary
Primary
South East: Relatively constant enrolments.North East: Dramatic decline in Primary 2001-08;
Also falls in Lower and Upper Secondary.
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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.
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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?
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