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

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.

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).

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

11

)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

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)

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;

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

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-;

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%;

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.

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.

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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