Demographics, School Efficiency and School Enrollments: The Case of Vietnam
by
Channing Arndt1
Development Economics Research Group
Department Economics
University of Copenhagen
Pham Lan Huong
Central Institute for Economic Management
Ministry of Planning and Investment, Vietnam
Simon McCoy
Development Economics Research Group
Department of Economics
University of Copenhagen
Tran Binh Minh
Central Institute of Economic Management
Ministry of Planning and Investment, Vietnam
May 2009
JEL classifications: C5, I2, O2. Key words: Transition matrix, demographics, migration,
education.
1
The corresponding author is Channing Arndt, Studiestraede 6; DK-1455 Copenhagen K
Denmark; e-mail: [email protected]; +1 970 472 2620.
.
1
Abstract:
Using an information theoretic approach, probabilities that a given school pupil in
Vietnam will progress to a higher grade, drop out, or repeat are estimated. These
probabilities are compactly summarized using education transition matrices. Interregional migration probabilities, within Vietnam, are also estimated and incorporated into
the transition matrices. It is shown that the probability of progression to a higher grade is,
on the whole, high though there is variation between regions and grades. A relatively
high drop out rate of about 26% is found for the transition from lower to upper secondary
school. Future enrollments are projected using the estimated transition matrices. The
projections show a decline in total school enrollments until roughly 2012 followed by a
gradual increase thereafter. Finally, teacher and classroom numbers are presented, and the
implications of the transition probabilities and enrollment predictions are discussed in the
context of the allocation of state investment in education in Vietnam.
2
Demographics, School Efficiency and School Enrollments: The Case of Vietnam
1
Introduction
Education often plays a prominent role in development strategy for many low
income countries. This is true of Vietnam where education expenditures represent about
20% of total government expenditure. As will be discussed in the literature review, recent
studies, using both microeconomic and macroeconomic perspectives, point to educational
attainment as a significant contributor to growth via human capital accumulation and via
acceleration of the rate of technical change. With the stakes so large, it is obviously
desirable for the education sector to function as efficiently as possible.
This paper uses administrative data from the education sector to formally consider
how students move through the education system in Vietnam (grades 1 to 12).
Specifically, the paper estimates education transition matrices by region. These matrices
are then employed to consider three issues of importance to the education system for
Vietnam.
1) The efficiency of movement through the system, as represented by pass,
repetition and drop-out rates.
2) Migration of students between regions with a particular focus on migration
rates from rural to urban zones.
3) Enrollment projections by grade and region. These projections can be used to
help assess the appropriate mix of investments across grades and regions as
well as between “hard” investments, such as building new schools and hiring
more teachers, meant to increase the supply of education services and “soft”
1
investments such as teacher training, materials per pupil, and curriculum
development meant to improve the quality of education on a per student basis.
We find that repetition and dropout probabilities are reasonably low in most
grades though some regional variation is observed. Elevated dropout probabilities of
more than 25% at the national level are observed at the end of ninth grade, which
represents the transition from lower secondary to upper secondary school. The
methodology employed was unable to accurately estimate migration rates by region.
However, the approach did robustly point to a tendency for children to migrate at the end
of primary and lower secondary school and thus begin lower secondary or upper
secondary school in a new region. As expected, migration flows tended to occur from
rural to urban areas.
The efficiency and migration results are broadly in line with expectations. In
contrast, the results of the enrollment projections to 2024 are more striking. The ongoing
demographic transition in Vietnam implies that peak enrollments during the projection
period have already been attained. Total enrollments across grades 1-12 are already
declining and can be expected to continue to decline until about 2012 before beginning a
gradual increase. A reduction in the dropout rate between grades 9 and 10 would imply
slightly higher total enrollments over the projection period but leaves the major
qualitative conclusion--the end of the era of rapidly growing school enrollments-- intact.
Shifts in the composition of enrollments across scholastic levels (primary, lower
secondary, and upper secondary) are also noteworthy.
We conclude that investment patterns in the education system need to be
redesigned to accommodate flat to decreasing overall student numbers. This new era of
2
relatively constant enrollments may require a substantial shift in focus by an education
system accustomed to increasing student numbers at all levels throughout the system. The
end of growing enrollments provides an opportunity to focus “hard” investments, such as
new schools, in underserved and high growth areas. This new era of relatively constant
enrollments also permits greater emphasis on “soft” investment aimed at increasing the
quality of education services by, for example, reducing pupil to teacher ratios, increasing
teacher training, and increasing materials per student.
The remainder of this article is structured as follows. Section 2 first discusses
literature on the link between education expenditure, human capital accumulation, and
economic growth from an international perspective. Next, literature focused on human
capital accumulation and labor markets in Vietnam is summarized. Section 3 presents the
transition matrix estimator, including some background on information theory, and the
approach employed to project enrollments in grade 1 over the projection period.
Estimation results and projections are presented in section 4. Implications of these
projections are considered in Section 5. A final section concludes and provides
suggestions for future research.
2
2.1
Literature Review
International Literature
The intellectual foundations for heavy emphasis on education spending in low
income economies are reviewed by Psacharopolous (1994). Relying on microeconomic
studies, he finds positive returns to education with particularly high returns to primary
schooling. Further support was obtained by Bloom, Canning and Sevilla (2001). They
3
employed macroeconomic panel data to examine the issues of health, human capital, and
economic growth. They found, consistent with the microeconomic evidence, a positive
association between schooling and aggregate economic output. However, in an influential
and widely cited article, Pritchett (2001) employed cross national data and found “no
association between increases in human capital attributable to increased educational
attainment of the labor force and output per worker.” Pritchett’s finding generated a
micro-macro paradox where the positive returns found in micro studies could not be
discerned in macro data. Despite the microeconomic evidence, Pritchett concluded that
the developmental impact of education expenditure had “fallen short of expectations.”
More recent macro studies are far more supportive and reestablish rough
consistency between microeconomic and macroeconomic studies. Cohen and Soto (2007)
point to issues of measurement of human capital, particularly data quality. They assert
that the lack of impact obtained by Pritchett (2001) stems largely from inadequate
measurement. They present improved measures and generate an improved data set.
Properly measured, human capital accumulation returns as a major contributor to
economic growth with impacts on the order of those implied by microeconomic studies.
Baldacci, Clements, Gupta and Cui (2008) go on to establish a causal chain between
spending on education (and health) and human capital accumulation and from human
capital accumulation to economic growth. Finally, Jamison, Jamison, and Hanushek
(2007) link education quality and income growth. They find that higher quality education
increases the rate of technical progress. Generally, the weight of international evidence
continues to place significant investments in human capital as a centerpiece of
development strategy.
4
2.2
Literature on Vietnam
A number of papers have been written in or about Vietnam regarding the labour market.
Tran (2008) provides a good overview of demand-side labour market literature1 As is
noted, while the focus varies, it is commonly the case that studies conducted by
international researchers have relied upon national household survey data collected by the
General Statistics Office (GSO), whereas Vietnamese studies have drawn more upon data
collected by the Ministry of Labour. Moreover, while the former tend to have a broad
area of interest, including but certainly not restricted to wage analysis, such as Pham
Hung and Barry (2007a) and John Like Gallup (2002), the latter group tend to have a
heavy focus on the determinants of labour demand, labour migration, and labour market
forecasting in Vietnam- see for example, Le Xuan Ba (2006) and The Institute of Labour
Science and Social Affairs (ILSSA) (2006).
To date no other paper has been written explicitly employing transition matrices to
examine pupil progression through the Vietnamese education system. More generally, the
supply side of the labour market, or the educational sector, has received relatively little
attention. There are, however, a few papers considering this.
Glewwe (2002) analyses the determinants of school progression using national household
survey data. He finds that, ceteris paribus, being part of an ethnic minority exerts a strong
negative influence on academic achievement. Gender is not found to have any
statistically significant effect, while age and wealth, proxied by expenditure, are found to
1
See http://www.ciem.org.vn/home/en/home/InfoDetail.jsp?area=1&cat=358&ID=1457
5
have a negative and positive effect, respectively, on the probability of completing
primary school.
Other studies include Anh et al (1995) who find gender to be a significant determinant of
enrollment rates, with boys taking longer to complete any given level of schooling than
girls, and Truong et al (1999) who confirm the role of family income in scholastic
achievement.
Along similar lines, Vo and Trinh (2004) seek to identify the underlying determinants of
school drop-out in Vietnam and take the further step of projecting this until 2015. They
find the probability of school drop-out to be highly sensitive to changes in household per
capita expenditure and the direct costs of schooling. Moreover, drop-outs are found to be
highly dependent on public spending on education. The authors use their results to form a
judgment on the likelihood of Vietnam realizing its Millennium Development Goal
targets for education. The answer is highly sensitive to assumptions made on household
expenditure and schooling costs, however, the tentative assessment shows a high chance
of reaching the net enrollment rates targeted in 2015.
6
3
Estimation and Projection Approaches
As mentioned above, we estimate transition matrices as a vehicle to examine three
important issues for the educational system in Vietnam. The transition matrices are
estimated for grades 1-12 using data from the period 2000-2006. Transition matrices are a
compact way of expressing the probability that a student enrolled in grade g will advance
to grade g+1, repeat grade g, or exit the school system (and presumably join the
workforce). Here, the education transition matrices are estimated using an information
theoretic approach. The approach is flexible permitting, in addition to the repeat, pass,
and exit probabilities mentioned above, estimation of the propensity to migrate across
regions within Vietnam by grade level. These transition matrices are then combined with
population projections by age and estimates of propensity to enter school by age in order
to project enrollments to the year 2024.
The next subsection presents background on entropy estimation approaches.
Section 3.2 presents the national transition matrix estimator (no migration). Section 3.3
modifies the estimator in order to permit migration. Under this approach, regional
transition matrices are estimated jointly allowing the possibility for a student enrolled in
grade g in region r to move to grade g+1 in region s. Section 3.4 relates to enrollments
projections. In order to project enrollments using the transition matrices, the number of
new students entering grade 1 must be exogenously supplied. Section 3.4 explains how
available population projections, which are published by five year age cohort, were
employed to project enrollments in grade 1 to the year 2024.
7
3.1
Entropy Estimation
Entropy approaches to estimation are motivated by “information theory” and the
work of Shannon (1948), who defined a function to measure the uncertainty, or entropy,
of a collection of events, and Jaynes (1957a; 1957b), who proposed maximizing that
function subject to appropriate consistency relations, such as moment conditions. The
maximum entropy (ME) principle and its sister formulation, minimum cross entropy (CE),
are now used in a wide variety of fields to estimate and make inferences when
information is limited and/or when traditional estimation approaches prove unwieldy
(Kapur and Kesavan 1992). The basic philosophy of entropy estimation is to use all
available information and no more.
In economics, the ME principle has been successfully applied to a wide and
rapidly growing range of estimation problems. Theil (1967) provides an early
investigation of information theory in economics. Mittelhammer, Judge, and Miller (2000)
provide a recent text book treatment which is focused more tightly on the ME principle
and its relationships with more traditional estimation criteria such as maximum likelihood.
Golan (2002) edits a special issue of the Journal of Econometrics focused on cuttingedge applications of the entropy principle.
In general, information in an estimation problem using the entropy principle
comes in two forms: (1) information (theoretical or empirical) about the system that
imposes constraints on the values that the various parameters to be estimated can take;
and (2) prior knowledge of likely parameter values. In the first case, the information is
applied by specifying constraint equations in the estimation procedure. In the second, the
information is applied by specifying a discrete prior distribution and estimating by
8
minimizing the entropy distance between the estimated and prior distributions—the
minimum cross entropy (CE) approach. The prior distribution does not have to be
symmetric and weights on each point in the prior distribution can vary. If the weights in
the prior distribution are equal (e.g., the prior distribution is uniform), then the CE and
ME approaches are equivalent.
For most applications, the real power of the framework is that it makes efficient
use of scarce information in estimating parameters. As stated by physicists Buck and
McAulay (1991, p. ix), “the intention is to give a way of extracting the most convincing
conclusions implied by given data and any prior knowledge of the circumstance.”
3.2
Estimation of a National Education Transition Matrix
We would like to track the way that children move through the education system.
For simplicity, we start with the national level transition matrix, which ignores regional
migration. In this case, for a child enrolled at a given education level, we permit three
possibilities for the following year with respect to enrollment:

The child progresses to the next educational level;

The child repeats the same educational level or;

The child exits the educational system.
These three possibilities embed a number of assumptions. First, we exclude the
possibility that children might jump two or more grade levels or fall backwards by any
number of grade levels. In addition, we implicitly assume that international migration
9
does not take place. Finally, we assume that children who exit the school system will not
re-enroll at a later date.2
The probabilities associated with each of these outcomes for each grade level are
of interest. In order to estimate these probabilities, we postulate a transition matrix, R,
giving probabilities associated with each possible outcome from period t to period t + 1
for each grade level. The matrix R shown in Figure 1 runs from grade 1 to grade 12
corresponding to the target population for estimation. All blank elements in the matrix are
assumed to have value zero. The rows of the transition matrix R sum to one thus
accounting for the entire enrollment at each scholastic level. For example, consider row 3,
which corresponds to children enrolled in grade 3. According to row 3, children at this
scholastic level could repeat the same level next year, (rg3g3), enroll in grade 4 (rg3g4), or
exit the school system with no probability of return (rg3exit). By assumption, children
enrolled in grade 3 cannot leap to grade 5 or higher and will not fall back to grades 2 or 1.
The remaining rows of the transition matrix R can be similarly interpreted.
Given an R matrix, the postulated evolution of enrollments proceeds as follows.
Let Et be a column vector (with twelve elements corresponding to the twelve grades of
the Vietnamese school system) containing enrollments in grade 1 in year t+1 in the first
element and zeros elsewhere. The number of individuals at each scholastic level in period
t + 1 is then: Estvalt+1 = T’Estvalt + Et. Note that, since enrollments in grade 1 (rather
2
This is, of course, not strictly correct. Some children may fail to enroll at all in year t and then enroll in
year t+1. Note that, if this phenomena is relatively constant, the impact on aggregate enrollment in a given
year will be small since roughly equal numbers of children should be expected to drop out for a period
(with eventual return into the system) as will return following a period of hiatus from the school system.
10
than new entrants to grade 1) are supplied exogenously, the transition probability, rg1g1, is
set equal to zero.
Following Karantininis (2002) and Wobst and Arndt (2004), stationary transition
matrices, where transition probabilities are constant through time, are estimated. The
mathematical form of the estimator is presented below. Note that the transition matrices
are constrained to meet all requirements of a transition matrix (e.g, rows sum to one and
all elements fall within the [0, 1] interval). Also, note that all variables and parameters are
indexed on regions, k. In this example, the set k contains only one element- the nation of
Vietnam.
Sets /set elements/:
t and te /1, 2, …,T/
d /lower,…, middle, …, upper/
p and pp / grade1, grade2, …, gradeN, exit /
pe(p) / grade2,…,gradeN /
h(p,pp) /(grade1,grade2) ... (gradeN, exit)/
k /Vietnam/
Time periods used in estimation
Discrete distribution points
All scholastic levels and exit
All scholastic levels but grade 1
Non-zero elements of R
Regions (only one element currently)
Parameters:
q p , pp
Prior probabilities for transition matrix
valk , p ,t
Enrollments (data for vector St)
v d , k , p ,t
Prior bounds on estimated values
E k , p ,t
Students in grade 1 and zeros elsewhere
Variables:
Z
rk , p , pp
Objective value
Posterior probabilities for transition matrix R
s d , k , p ,t
Posterior probabilities for error terms
estvalk , p ,t
Estimated enrollments (estimates for vector St)
ehat k , p ,t
Error term on known items
11
Equations:
Minimize Z   rk , pe, pp * ln( rk , pe, pp / q pe, pp ) 
pe

d
pe
t
pp
(1)
k
s d ,k , pe,t * ln( s d ,k , pe,t / 3)
k
subject to:
estvalk , p ,t 1  E k , p ,t   estvalk , pp,t * rk , pp, p
 k , p, t
(2)
pp
valk , pe,t  estvalk , pe,t  ehat k , pe,t
ehat k , pe,t   s d ,k , pe,t * vd ,k , pe,t
 k , pe, t
 k , pe, t
(3)
(4)
d
r
k , pe, pp
 1  k , pe
(5)
 1  k , pe, t
(6)
pp
s
d , k , pe,t
d
1  rk , p , pp  0  k , ( p, pp)  h( p, pp)
(7)
rk , p , pp = 0  k , ( p, pp)  h( p, pp)
(8)
1  s d ,k , pe,t  0  k , d , pe, t
(9)
Three further notes with respect to the estimator bear mentioning. First, the
formulation listed above is non-linear in the transition equation. To make the problem
linear, one can substitute valkj , pp,t for estvalkj , pp,t on the right hand side of equation (2).
Second, error bounds, vd,pe,t, must be specified prior to estimation. Golan, Judge, and
Miller (1996) provide guidelines on setting error bounds. An attractive option in the
context of the above formulation is to set upper and lower limits for error bounds as a
proportion of observed enrollments. Finally, prior values on transition probabilities, qp,pp,
must be set. For the estimation of the national transition matrix, simple priors were
employed. Specifically, the prior probability of remaining at level (qp,pp), moving to the
next level (qp,pp+1), and exiting (qp,’exit’) were 1%, 95%, and 4% 3 respectively for the
entire matrix. These particular priors convey to the estimator the very strong prior
3
These priors were derived from an analysis of the data set for the years 2000-06.
12
expectation that the probability of transitioning to a higher level (qp,pp+1) is greater than
the probability of staying in level (qp,pp) for most grade levels.
3.3
Incorporating Migration
As Vietnam has developed since the reforms of the mid-1980s, levels of internal
migration have been increasing. Available evidence suggests that about 1% of the
population changes its place of residence every year (in the five years leading up to the
1999 Migration Census, 6.5% of the population were estimated to have migrated), though
it is likely that such a figure underestimates the true level of movement. There is strong
evidence that there are high levels of seasonal and temporary migration. In addition, a
significant proportion of long-term migrants do not register with the authorities in their
new area of residence.
There are two persistent patterns relating to migration. Firstly, there is a clear
rural to urban movement, with the urban centres of Ho Chi Minh City (HCMC) and
Hanoi in particular experiencing significant in-migration. Secondly, migrants tend to stay
close to their region of origin- migrants to Hanoi are drawn overwhelmingly from the
North, while HCMC sees the majority of its migrants come from the southern provinces.
People in Vietnam migrate for various reasons, and education of themselves and
of their children represents an important motivation among these. The most recent survey
of migrants in Vietnam found that over one fifth of migrants cite family and education as
the key motivating factor for their move. More specifically, over 10% of migrants living
in Hanoi say they moved to the capital for the children’s future.
13
It is possible that administrative data on education enrolments by region can shed
some light on migration pattern if migration is incorporated into the transition matrix
estimation procedure. Perhaps more relevant for our purposes here, explicit inclusion of
migration may substantially improve the quality of regional transition matrix estimates.
For example, without accounting for migration, dropout probabilities in regions
characterized by significant out (in) migration are likely to be over (under) estimated. The
modified estimator is presented below.
Sets /set elements/:
t and te /1, 2, …,T/
d /lower,…, middle, …, upper/
p and pp / grade1, grade2, …, gradeN, exit /
pe(p) / grade2,…,gradeN /
h(p,pp) /(grade1,grade2) ... (gradeN, exit)/
k and kp /region1, region2, …, regionK/
Time periods used in estimation
Discrete distribution points
All scholastic levels and exit
All scholastic levels but grade 1
Non-zero elements of R
Regions
Parameters:
q p , pp
Prior probabilities for transition matrix
qm k , kp
Prior probabilities for the migration matrix
valk , p ,t
Enrollments (data for vector St)
v d , k , p ,t
Prior bounds on estimated values
E k , p ,t
Students in grade 1 and zeros elsewhere
Variables:
Z
rk , p , pp
Objective value
Posterior probabilities for transition matrix R
M k , kp
Posterior probabilities for migration matrix M
Fp
Migration matrix multiplication factor by grade
s d , k , p ,t
Posterior probabilities for error terms
estvalk , p ,t
Estimated enrollments (estimates for vector St)
ehat k , p ,t
Error term on known items
14
Equations:
Minimize Z     rk , pe, pp * ln( rk , pe, pp / q pe, pp ) 
F
k
kp
pe
p
pe
(1M)
k
M k , kp * ln( F p M k , kp / qm k , kp ) 
p

d
pp
t
s d ,k , pe,t * ln( s d ,k , pe,t / 3)
k
subject to:
estvalk , p ,t 1  E k , p ,t   estvalk , pp,t * rk , pp, p   estvalkp , p 1,t * F p 1 M k , kp
pp
valk , pe,t  estvalk , pe,t  ehat k , pe,t
ehat k , pe,t   s d ,k , pe,t * vd ,k , pe,t
kp
 k , pe, t
 k , pe, t
(3M)
(4M)
d
r
k , pe, pp
pp
s
 k , p, t (2M)
  F pe M k , kp  1  k , pe
(5M)
kp
d , k , pe,t
 1  k , pe, t
(6M)
d
1  rk , p , pp  0  k , ( p, pp)  h( p, pp)
(7M)
rk , p , pp = 0  k , ( p, pp)  h( p, pp)
(8M)
1  s d ,k , pe,t  0  k , d , pe, t
(9M)
F pe  0  pe
(10M)
1  M k , kp  0  k , kp
(11M)
The principal modification involves incorporation of a probability to migrate in
equations 1M, 2M, and 5M. Equations 10M and 11M oblige non-negativity. A new
parameter indicating prior migration probabilities, qmk ,kp , is also added. Migration
probabilities are modelled by multiplying a regional matrix, M k ,kp , by a factor, Fpe ,
indexed on grade level. In the actual estimations, the factor, Fpe , is fixed to one for all
grades except five and nine, corresponding to the end of primary and lower secondary
school. The assumption is that the probability to migrate does not vary by grade level
with the exception of grades five and nine.
15
For the estimation of all regional transition probabilities, results from the estimated
national transition matrix were employed as priors, q pe, pp , for all regions.
3.4
Estimation of Enrollments in Grade 1 over the Projection Period
As mentioned above, demographic projections to 2024 are available. However,
these projections are published by five year age cohort (0-4, 5-9, 10-14, etc). Both the
enrollment data and the projections data indicate a fairly rapid rate of demographic
transition with births per woman declining during the 1990s. As a consequence of this
demographic transition, simple assumptions, such as approximately one fifth of children
aged 5-9 enter grade 1, may be incorrect. To account for this, we estimate the population
age structure by year for children aged 0-9 for the period 1999-2024. We use the basic
entropy approach described above. For each year, the sum of our estimated number of
children aged 0, 1, 2, 3, and 4 should be as close as possible to the published aggregate
for children aged 0-4 and similar for children aged 5-9. We also estimate survival
probabilities by yearly age category. Priors on survival probabilities were obtained from
the census.4
Interestingly, the published population projections are not consistent with a detailed
and coherent age structure (e.g., the number of seven year olds in t+1 is less than or equal
to the number of six year olds in year t). The inconsistencies appear to stem from errors
in the declarations of ages of children in the 1999 census. For the periods nearer to 1999,
a coherent age structure can only be produced with some error compared to the projection
aggregates. For the periods closer to 2024, the error declines to practically zero.
4
GAMS code for this procedure is available from the authors upon request.
16
The disaggregated age structure was then compared with actual grade 1 enrollments
by region for the period 2000-2006. Regression analysis indicated that grade 1
enrollments are insignificantly different from the estimated number of seven year olds.
Hence, in the enrollment projections to follow, grade 1 enrollments are assumed to equal
the estimated number of seven year olds. We now turn to estimation results and
projections.
4
4.1
Estimation Results and Projections
National Results
Estimated transition matrices and enrolment projections are presented firstly for the
country as a whole, then for selected regions within Vietnam. Figure 2 illustrates the
stationary transition matrix for all students at the national level.
The matrix clearly reflects some of the discussion above. Progression rates are
high, with near to or above 90% of pupils passing to a higher grade at the end of nearly
any given school year. Correspondingly, repeat rates are low, while the probability of a
pupil exiting the school system is, with one exception, also consistently under 10%. The
row of the matrix corresponding to grade 7, for example, shows that if 1,000 pupils are
enrolled in grade 7 this year, then next year 921 will progress to grade 8, 16 will repeat
grade 7, and 63 pupils will exit the schooling system and presumably enter the labour
force. As an illustration of the health of the education system in Vietnam, we see that
over 97% of pupils progress from primary school (grade 5) to lower secondary school
17
(grade 6). Notably, the repeat rate in grade 6 is somewhat higher than in the previous five
grades, perhaps reflecting an increased level of difficulty after primary school.
As noted, the exception to this is grade 9, where we observe a significant increase
in the probability of repeating the year and of exiting the school system. Only 70% of
pupils finishing grade 9 currently progress to upper secondary school.
Turning attention now to school enrollment trends over time, Figure 3 presents
the projections by level of schooling for the country as a whole. Some interesting trends
emerge from the data. Firstly, enrollments for all levels of schooling have already peaked
(primary before 2000, lower secondary in 2004, and upper secondary in 2006). In the
case of primary school, enrollments are projected to have troughed in 2007, before
gradually rising thereafter, while for lower and upper secondary, the trough comes in
2012 and 2015 respectively.
The implication of this for total enrollments is a decline until 2012, followed by a
gradual increase thereafter. Total enrollments will remain below the levels seen in the
early 2000s for a long time (well beyond the projection period). The proportion of total
enrollments represented by each level of school is projected to stay roughly the same,
with primary, lower secondary and upper secondary accounting for approximately 50%,
35% and 15% respectively.
Grade 9 aside, attrition of pupils from grade to grade is small. Nevertheless,
enrollments across grades for any given year are actually declining- in some cases, by a
significant amount. In a scenario of high population growth and attrition (such as in the
African context for example) this is to be expected, but even here with relatively low
exits and repeats, and a falling school entry age population, the magnitude of the impact
18
on enrollment numbers is noteworthy- in 2010, for instance, there are projected to be 46%
fewer pupils (representing 759,281 children) in grade 12 than in grade 1. An alternative
way to consider this is to examine the progression of pupils in a given grade and year to
the next grade in the following year. Due to attrition, in the overwhelming majority of
cases, the pupil population in the latter case is lower than in the former. This is with the
exception of grade 6, where the impact of the higher than average repeat rate means that
grade 6 enrollments are actually above those of grade 5.5
4.2
Regional Results
Turning now to the sub-national level, transition matrices were estimated for
twelve regions within Vietnam. 6 As mentioned above, the added dimension of interregional migration is introduced here. In this section, we present detailed findings for two
regions: the urban area of Hanoi and the more rural area of the Mekong Delta. Figure 4
illustrates the stationary transition matrix for all students in Hanoi.
In general, similar trends to those at the national level are found, with the large
majority of pupils progressing to higher school grades. Perhaps unsurprisingly, given the
more urban and wealthy environment, the probability of exiting at the end of lower
secondary school is roughly seven percentage points lower than the national average.
Finally, migration probabilities are low, at just 0.3%, rising to 1.0% at the end of grade
5
As will be seen below, inter-regional migration may also influence this at the sub-national level.
6
Vietnam consists of 63 provinces, which are commonly grouped into 8 regions, namely Red River Delta,
North East, North West, North Central, Coastal Central, Central Highlands, South East and Mekong Delta.
The analysis here makes use of provincial-level data to disaggregate Vietnam’s four most populous cities of
Hanoi, HCMC, Hai Phong and Da Nang, thus giving a total of 12 regions for the analysis here.
19
97- Migration of school pupils away from Hanoi to other regions within Vietnam would
appear to be quite rare.8
The rural area of the Mekong Delta provides an interesting comparison with the
above findings. Figure 5 presents the transition matrix. For the Mekong Delta, we see exit
probabilities far higher than in Hanoi and the national average. This is particularly
marked in lower secondary school. Propensity to migrate to other regions in Vietnam is
also higher than in Hanoi, and again we see a higher percentage of pupils leaving at the
end of lower secondary school to either enter the labour force (22.8%) or pursue their
studies elsewhere (2.1%). Interestingly, and in contrast to all other grades in Mekong
Delta schools, the exit probability at the end of lower secondary school, grade 9, is
actually lower than the national average: A fact that is possibly explained by very high
exit rates in the prior grades, meaning that much of the attrition has already taken place.
To put these two regions into context, the Figure 6 presents enrollment ratios of
grade 6 in 2009 to grade 5 in 2008, and grade 10 in 2009 to grade 9 in 2008. The table
therefore examines the transition of pupils from primary to lower secondary school, and
from lower to upper secondary school. A number greater than one indicates higher
enrollments in the more senior grade.
With the exception of two regions, enrollments rise in grade 6. For the country as
a whole, this slight increase can be explained by the higher repeat rate in grade 6 that was
noted above. For the individual regions too, grade 6 repeat rates are in general relatively
7
This is possibly explained by pupils who, having migrated to Hanoi in earlier grades, are forced to return
to their homes having failed to secure a place in upper secondary school in Hanoi.
8
This is in-line with the findings from the 2004 Vietnam Migration Survey (GSO, UNFPA) which shows
high inward migration to Hanoi.
20
high, explaining some of the rise. But there is one other factor at play here- namely
migration. We see that both Hanoi and Da Nang show large increases perhaps indicating
the presence of in-migration into these urban areas at the start of lower secondary school.
For HCMC and Hai Phong, the increase is less-pronounced, though their repeater rates
are quite low, perhaps offsetting some of the impact.
The transition from lower to upper secondary school exhibits a somewhat
different pattern, with the sharp drop-off in enrollments evident in the numbers. Again
here, the ratios would point toward some impact of in-migration, particularly to the urban
areas of Hanoi and HCMC, where upper secondary schools are more prevalent and of
better quality.
4.3
Projections Using Dynamic Matrices
It may be unrealistic to project to 2024 on the basis of static transition matrices.
Over time, one would logically expect transition probabilities to evolve. For example,
one might expect the high exit probability between lower and upper secondary school to
decline with time. In the dynamic matrices, we assume that exit probabilities decline
linearly over the projection period to a level equal to half of the value estimated in the
static transition matrices. The decline in exit probability is attributed to an increased pass
probability. To take our two earlier examples, the grade 9 exit probability in Hanoi for
the final year of our projection period, 2024, falls to 9%, with 85% progressing to upper
secondary school. For the Mekong Delta, the probabilities become 11% and 84%
respectively.
21
In order to clearly illustrate the different impacts on enrollment numbers, Figure 7
provides a comparison of total enrollments in three years, as estimated by the static and
dynamic matrix. Enrollments, therefore, fall off less dramatically when estimated by the
dynamic matrices: In 2024, there are forecast to be 7% more pupils in grade 6, and 41%
more in grade 9. Nevertheless, projected total enrollments at the national level in 2024
remain below the peak attained in 2000.
5
Discussion and Policy Implications
The development of human capital through education is seen as a key priority for
industrialization and sustainable economic development by Vietnamese policymakers.
Ensuring equal opportunities for all to study, and a focus on improving the quality of
teaching and educational facilities are firmly embedded in the national education
development strategy9.
In recent years, Vietnam has accomplished significant progress in this area. As the
World Bank notes, ‘the education and training system of Vietnam is already confronting
some of the challenges typically faced by middle-income countries’.10 This is particularly
the case for primary schooling, where net enrollment of 97% in 2008 (estimated in SEDP
Review) falls just short of the ambitious target set in the early 2000s of 99% by 2010. 11
Targets for secondary school are also ambitious, with a 90% and 50% net enrollment rate
9
MOET (2001) National Education Strategic Plan
10
World Bank, 2006
11
MPI (2005) Socio-Economic Development Plan
22
targeted for lower and upper secondary school respectively. Currently, net enrollment
rates are estimated at 79% and 65%.
In-line with these impressive enrollment rates, the number of classrooms and
teachers has been rising steadily for many years. This, combined with a falling school
population, makes for healthy comparisons with the number of pupils. Figure 8 shows
2006 classroom and teacher numbers by level of schooling and region as compared to the
projected enrollment numbers from the static transition matrix presented above.
Focusing firstly at the national level, it is clear that ratios are comparable to those
one might associate with international best-practice. This is particularly so for the number
of teachers, where ratios for the Whole Country of 20.4, 20.0 and 24.8 for primary, lower
and upper secondary respectively are impressive. Moreover, with enrollment numbers in
lower and upper secondary school projected to fall over the coming years (relative to
2006 levels), the ratios will naturally improve without any new classroom construction or
net teacher recruitment. Indeed, if one assumes a constant pupil:teacher ratio, for example,
and the enrollment projections as detailed above, the number of teachers required in 2024,
in lower and upper secondary school fall by approximately 46,000 (-15%) and 34,000 (27%) respectively. Applying the same assumptions to primary school yields a required
increase of approximately 50,000 new teachers (+15%). In many ways, of course, the
calculation of such numbers oversimplifies the situation. Nevertheless, they do help to
emphasize the extent of the structural shift currently underway in the total education
system. If teachers’ skills were fungible across school levels, then the analysis would call
for a redistribution of teachers from secondary to primary school over the next 5-7 years12.
12
More realistically, the analysis provides a useful tool to examine the allocation of public spending on
teacher training by scholastic level.
23
At the regional level, the picture is evidently more mixed, with certain inequalities
immediately apparent. Firstly, we see that those regions that have a relatively high
number of classrooms also have more teachers. Primary and lower secondary schools in
the North East and West are good examples of this13. Secondly, there is somewhat of an
urban/rural split in the number of classrooms. Densely populated cities such as Hanoi and
HCMC have less space in which to build new facilities. Finally, the picture for upper
secondary school is more even across regions than for other school levels.
The analysis therefore points to the need to target accurately where new
investment is made. Clearly there are regions that would benefit from an increase in
resources, and at the provincial, district and commune level, one can reasonably expect
these differences to be more pronounced.14 Nevertheless, quantity, in terms of the number
of classrooms and teachers at the national level, is not the key problem, and given the
projections presented above, will not be a problem for many years to come.
Over the past few years, the focus of the educational reform agenda in Vietnam
has shifted toward improving the quality of education services- and the above analysis
would certainly endorse this. Supply, of schools and teachers has been rising steadily as
public spending on education has climbed to represent more than 18% of the state budget.
However, concerns do remain surrounding the standard of teaching, the relevance of the
13
The reader should note that certain areas (such as the Northern regions) may still be in need of more
classrooms and teachers given their low population densities and poor infrastructure.
14
There are certainly many areas (at the sub-regional level) where access to schools is limited. This is
particularly so in the case of upper secondary schools. The Strategic Education Plan (MOET, 2001) targets
having a national standard primary and lower secondary school in every commune, though no timeline is
given.
24
curriculum, the physical state of classrooms, and most importantly, the low number of
hours of teaching currently administered in the education system.15
Indeed, the low time of instruction in schools has become one of the key
perceived shortcomings of education in Vietnam. And, while in the case of primary
schools all day lessons have now been implemented, the financing that has made this
possible has come from fees that parents have been paying, with minimal government
subsidization. Moreover, despite efforts to alleviate some of this burden, for example
through the targeted fee exemption policies, such fees are widely acknowledged to be a
significant source of inequality in access to primary education. With this in mind, the
enrollment trends and transition probabilities as outlined above indicate that Vietnam
faces a clear window of opportunity to implement measures to address issues of quality
and equity.
15
World Bank (2006).
25
6
Conclusions and Suggestions for Future Research
In this paper, an information theoretic approach has been applied to administrative
education data, allowing the estimation of education transition matrices for Vietnam as a
whole and twelve regions within the country. The incorporation of migration into the
transition matrices is an innovation that enables a more accurate representation of pupil
movement through the school system and between regions. A clear picture of transition
probabilities and scholastic trends emerges from the exercise, yielding some policyrelevant findings.
First, the probability of a given pupil in a given grade progressing to the next
grade is high. This is true across all grades with the exception of grade 9, where
approximately one in four pupils do not progress to upper secondary school. Net
enrollment rates are high, especially in primary school, and the educational apparatus
thus appears to be functioning well in supporting the progression of pupils through the
system.
Second, noteworthy changes in the composition of enrollments across the school
system will be observed in the short to medium term. Specifically, primary enrollments
have already troughed and will slowly rise for the near future. Lower and upper
secondary enrollments, on the other hand, are falling, and are forecast to trough in 2012
and 2015, respectively. As a result, total enrollments, for all grades, have peaked and will
decline until 2012 before slowly rising thereafter. Therefore, in a break with the past,
expanding the quantity of education services will not represent the sector’s largest
challenge. Principal challenges lie in quality and equity.
26
Third, relating particularly to equity, there are significant differences in some of
the key trends across regions. The probability of leaving the school system at a given age
is much higher in some regions, lower in others.
As discussed above, the results have strong implications for the allocation of
educational resources- among scholastic levels, and geographical regions. The analysis
can certainly help to provide information for a more equitable and efficient distribution of
educational services in Vietnam.
Further work should focus on repeating the analysis at the provincial level.
Decentralisation in Vietnam has given provincial authorities increasing levels of
autonomy, and planning at the central level uses as its primary sub-national unit, the
province. As a result, a more disaggregated analysis would certainly prove highly
relevant.
Moreover, a close examination of the current distribution of educational resources,
in terms of teachers, classrooms and other school material, as well as an analysis of the
criteria used for their allocation, would be highly complementary. Further work using the
dynamic matrices, in conjunction with the Educational Authorities’ own projections for
teacher number requirements, would also be informative.
Finally, the innovative step of incorporating migration into the analysis is
something that could be elaborated upon. As noted above, the inclusion of migration was
a first step, and the analysis would certainly benefit from a more detailed examination of
this area- in particular to refine the prior probabilities.
27
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7
Tables and Figures
Figure 1: Education Transition Matrix.
rg1g1
rg1g2
rg2g2
rg1exit
rg2g3
rg3g3
rg2exit
rg3g4
rg4g4
R=
rg3exit
rg4g5
rg5g5
rg4exit
rg5g6
rg6g6
rg5exit
rg6g7
rg7g7
rg6exit
rg7g8
rg8g8
rg7exit
rg8g9
rg9g9
rg8exit
rg9g10
rg10g10
rg9exit
rg10g11
rg11g11
rg10exit
rg11g12
rg11exit
rg12g12
rg12exit
0
Figure 2: Stationary transition matrix for all students at national level (%)
g1
0.0
g1
g2
g3
g4
g5
g6
g7
g8
g9
g10
g11
g12
g2
94.7
0.7
g3
96.1
0.9
g4
g5
96.7
1.4
g6
95.3
0.6
g7
97.4
3.0
g8
89.7
1.6
g9
92.1
2.1
g10
89.6
4.1
g11
70.3
1.0
89.5
0.9
g12
Exit
5.3
3.3
2.4
3.3
1.9
7.3
6.3
8.4
25.6
9.5
5.6
99.4
93.5
0.6
Figure 3: Enrolment projections by level of schooling at national level
12000
Enrolments '000 pupils
10000
8000
Primary
6000
Lower Secondary
Upper Secondary
4000
2000
0
Figure 4: Stationary transition matrix for all students in Hanoi (%)
g1
g2
g3
g4
g5
g6
g7
g8
g9
g10
g11
g12
g1
0.0
g2
95.0
0.8
g3
95.6
1.1
g4
95.6
1.0
g5
95.7
0.5
g6
97.7
4.4
g7
87.1
2.1
g8
91.3
2.3
g9
90.5
4.2
g10
76.2
1.3
g11
90.5
1.2
g12
93.3
0.8
Exit
4.7
3.3
3.0
3.0
1.4
8.3
6.3
6.9
18.6
7.9
5.2
98.9
Migrate
0.3
0.3
0.3
0.3
0.4
0.3
0.3
0.3
1.0
0.3
0.3
0.3
0
Figure 5: Stationary transition matrix for all students in Mekong Delta (%)
g1
g2
g3
g4
g5
g6
g7
g8
g9
g10
g11
g12
g1
0.0
g2
89.9
0.7
g3
g4
93.6
1.0
95.0
1.8
g5
91.7
0.7
g6
94.6
2.6
g7
83.1
1.7
g8
87.3
2.0
g9
85.1
2.5
g10
g11
72.6
1.8
82.8
0.9
g12
90.2
0.4
Exit
9.5
5.0
3.3
5.9
3.9
13.7
10.3
12.2
22.8
14.8
8.3
99.0
Migrate
0.6
0.6
0.6
0.6
0.8
0.6
0.6
0.6
2.1
0.6
0.6
0.6
Fiigure 6: Ratios of projected enrollments in for selected grades in 2008 and 2009
Whole Country
Hanoi
Hai Phong
North East
North West
North Central
Da Nang
Central Highlands
HCMC
Mekong Delta
Red River ex-Hanoi & Hai Phong
Coastal Central ex-Da Nang
South East ex-HCMC
g6 2009 /
g5 2008
g10 2009 /
g9 2008
1.01
1.07
1.03
1.01
0.98
1.01
1.10
1.01
1.02
0.98
1.03
1.05
1.02
0.71
0.88
0.72
0.66
0.65
0.64
0.79
0.78
0.84
0.75
0.64
0.75
0.77
Figure 7: Enrolment numbers at national level (‘000 pupils)
2008
g1
g2
g3
g4
g5
g6
g7
g8
g9
g10
g11
g12
TOTAL
Static
1,599
1,444
1,368
1,256
1,237
1,394
1,359
1,385
1,365
1,052
944
968
15,373
2015
Dynamic
1,599
1,447
1,370
1,257
1,238
1,395
1,362
1,387
1,369
1,062
947
970
15,403
Static
1,661
1,604
1,549
1,492
1,420
1,431
1,293
1,178
1,047
731
623
609
14,637
2024
Dynamic
1,661
1,626
1,580
1,525
1,459
1,470
1,348
1,236
1,112
827
708
687
15,238
Static
1,753
1,692
1,614
1,594
1,519
1,548
1,386
1,254
1,148
823
744
691
15,767
Dynamic
1,753
1,740
1,685
1,678
1,623
1,662
1,542
1,431
1,357
1,119
1,044
977
17,611
1
Figure 8: Classroom and Teacher to Pupil Ratios, 2006
Pupil : Classroom
Primary
Whole Country
Hanoi
Hai Phong
North East
North West
North Central
Da Nang
Central Highlands
HCMC
Mekong Delta
Red River ex-Hanoi & Hai Phong
Coastal Central ex-Da Nang
South East ex-HCMC
26.1
35.2
30.3
19.7
18.1
25.4
32.1
27.0
37.0
26.3
29.0
26.6
28.1
Low
Upper
Secondary Secondary
38.0
39.3
37.3
33.8
30.9
38.2
42.4
38.0
43.4
38.6
38.0
40.0
40.3
46.4
44.8
49.5
46.5
44.5
47.6
49.1
44.4
44.4
42.6
50.4
47.9
44.8
Pupil : Teacher
TOTAL
Primary
32.7
38.6
36.4
27.3
23.9
33.3
38.7
32.4
40.4
31.8
35.6
34.0
34.1
20.4
23.3
19.7
15.7
14.5
18.9
22.3
23.7
29.3
21.1
21.4
21.6
22.5
Low
Upper
Secondary Secondary
20.0
18.4
17.8
17.6
15.2
20.4
21.7
22.9
24.0
19.9
18.6
23.0
23.0
24.8
20.7
21.4
25.9
26.6
26.6
24.4
25.0
22.7
22.7
24.2
29.4
25.8
2
TOTAL
21.0
20.7
19.3
17.8
15.9
20.8
22.5
23.6
25.9
20.9
20.8
23.3
23.2