Introduction
The lackluster condition of the Hawaiian economy when compared
with the economic expansion in the mainland state economies
since late 1991 led the Hawaiian legislature to reassess the
economy's traditional sole dependence on the tourism industry.
To help revive the economy, the state government focused on
educational reform as one of their priorities. Hawaii needs to
build its human capital stock to be an active player in the new
information or knowledge-based global economy. To help ensure
the availability of educated and skilled human resources, the
presence of dynamic research and teaching institutions is
eminent. However, despite the pronounced good intentions and
plans made by the state government, a growing number of Hawaii
residents realize that not enough is being done. Based on a
statewide survey, residents are generally disappointed about the
economy and the condition of education. In fact, with the dreary
statewide economic performance comes difficult choices and
the need for re-allocation of resources. So, where does public
and private education stand in all this?
In this
study, an empirical investigation is done to assess and compare
the relative contribution of public and private schools to
Hawaii's economy. This paper presents a time-series
evidence on the timing and degree of feedback relationship
between participation in education and income growth in Hawaii.
The empirical investigation uses two feedback methods to measure
the degree of dependence or the extent of feedback between data
series and a related measure to distinguish between short-run and
long-run effects of a given innovation or shock. This study is
intended to contribute to a better understanding of the condition
and quality of the educational system in Hawaii. Also, the
findings of this study may have important implications for
directing resources or investment in education and shaping of
Hawaii's educational policy in the future.
Education in Hawaii:
An Overview
The
establishment of early schools in Hawaii was due to the efforts
of missionaries in the 1840s. Public education was first
instituted on October 15, 1840 with mandatory attendance of
children from ages four to fourteen. The upkeep of earlier
statistics on education in Hawaii was difficult because of
numerous changes on its classifications. For instance, the
compulsory age for school attendance went through six changes:
ages four to fourteen in 1840, six to sixteen in 1859, six to
fifteen in 1865, six to fourteen in 1923, six to sixteen in 1937
and finally six to eighteen in 1965. Secondary education during
the early monarchy years in Hawaii was also limited and left
largely to government-subsidized private schools while, higher
education was developed only in the twentieth century.
Hawaii became the
50th state on Aug 21, 1959. In 1960, 46% of the
population had four years or more of high school training while
only 9% had four years or more of college training. As of 1998,
84% of the population are high school graduates while 24% have
bachelor's or advanced degree.
Overview of School
Enrollment and Educational Resources
As
summarized in Table 1, the participation in Hawaii's formal
public education at the level of kindergarten to grade 12 had its
biggest growth increase in the 1960s; while private schools had
its biggest increase in enrollment in the following decade.
Enrollment in K-12 exhibited contrasting trend for public and
private schools, i.e., when public institutions experienced
positive growth, the private institutions suffered a negative
growth and vice versa.
Table 1
Average Growth
Rate in K-12 and Tertiary Enrollment,
Number of Schools and
Teachers
|
|
1960-69 | 1970-79 | 1980-89 |
1990-99
|
|
Public K-12
Institutions
|
|
Enrollment | 2.42 | -0.58 |
0.095 | 0.91
|
|
Schools | 0.44 |
0.59 | 0.389 | 0.669*
|
|
Teachers | 4.49 |
1.05 | 1.34 | 2.051*
|
|
Private K-12
Institutions
|
|
Enrollment | 1.12 |
1.32 | -0.403 | 0.18
|
|
Schools | 2.63 |
1.38 | -0.25 | -1.064**
|
|
Teachers | 3.36 |
3.03 | 2.62 | 0.177**
|
|
Tertiary
Enrollment
|
|
Public | 10.37 | 1.31
| -1.13 | -0.455
|
|
Private | 9.43 | 9.65
| 5.59 | 2.60
|
Note: Figures indicated
with * refer only to 1990-97 while those with ** refer only to
1990-96.
For some years, the
number of K-12 schools established does not seem to follow the
enrollment trend. In particular, the number of public schools in
the island posted an increase of 0.6% in the 1970s at a time when
it experienced a comparable 0.6% decline in enrollment.
Conversely, at a time of recovery in enrollment, the number of
public schools established continued to decline. The number of
private schools recorded big increases during the 1960s and 1970s
but was drastically reversed in the 1980s and 1990s. In terms of
school resources, both public and private schools had their
biggest growth increase in hiring teachers during the 1960s.
However, in terms of average number of pupil per teacher, private
schools do a better job than public schools in providing small
classes due in part to private schools continued bigger increases
in hiring teachers. The public school system also continue to be
plagued by other problems or concerns such as low test scores,
aging facilities and low teacher morale.
For tertiary level,
private universities exhibited continuous positive growth in
enrollment from 1960 to 1999. In contrast, the public university
suffered a drastic drop in enrollment in the 1970s relative to
the previous decade, and turned into a negative growth in the
1980s and 1990s. This downward trend in enrollment may not seem
surprising given that the state funding for the public university
system dropped 19% in the past ten years. In fact, a national
survey spotlighted Hawaii as the state with the largest loss in
state support for higher education in 1998-99. Budget cuts have
forced some programs to close or cease operation. A state law
that sets a $352 million floor in state funding for the
University of Hawaii (UH) was amended by the legislature wherein
they are now to provide only for an appropriation ranging from
60-80% of funds required in addition to tuition. Beginning in
1995-1996, UH was allowed to keep tuition fees which formerly go
into state general fund. Despite this change, the state
university system still finds their resources constrained that
they have to resort to increasing tuition fees which took a toll
in their enrollment.
Data and Description
of Methodology
Data on school
enrollment and per capita Gross State Product were taken from The
State of Hawaii Data Book, various issues, Dept. of Planning and
Economic Development. Earliest available data for private
universities were recorded in 1955 and were taken from various
sources such as Historical Statistics of Hawaii by Robert Schmitt
(1977) and Hawaii State Department of Education records. Private
universities in Hawaii primarily consists of Bringham Young
University of Honolulu, Chaminade University and Hawaii Pacific
University. In this study, data on public university account only
for enrollment at the University of Hawaii at Manoa which is the
biggest institution in the state university system. Data on the
number of K-12 schools and teachers for both public and private
institutions were taken from the Hawaii State Department of
Education records. Given the availability of relevant data, this
study covers the period of 1958 to 1999.
Given
that a number of models are consistent with observed correlation
between human capital and income growth, I used the unrestricted
vector autoregression (VAR) approach to model the dynamic
relationship among pertinent variables in order to minimize
specification error. The VAR approach avoids the need for tight
structural modeling by treating variables in a system as a
function of all lagged values of all of the endogenous variables
in the system (Hamilton, 1994). It uses only past regularities
and historical patterns in the data as a basis for forecasting.
In this study, a three-variable autoregressive system is used.
The variables include income growth as proxied by the growth rate
of real gross state product per capita, enrollment figures at
different levels, i.e., K to 12 and higher education from both
public and private schools to serve as proxies for human capital
stock. A lag length of four years is used for all variables as
suggested by the likelihood ratio test done. Also, based on the
unit root tests conducted (Dickey, D. & Fuller, 1979;
Kwiatkowski, D., Phillips, Schmidt & Shin, 1992; Phillips
& Perron, 1988), the stationarity of some data series are
inconclusive. Hence, the empirical investigation uses the data
series in both levels and first differences or in percentage
change.
The details of the two related measures of linear dependence and
feedback used in this study can be found in the Appendix. To
measure the degree of dependence or the extent of various kinds
of feedback between income growth and participation in education
as measured by school enrollment, I used Geweke's (1982)
bi-variate feedback method. The feedback measures are
non-negative and zero only when feedback or causality of the
relevant type is not present. A simple transformation of each
feedback measure gives the reduction in the prediction error
variance. Also, to distinguish between short-run and long-run
effects of a given shock, I decomposed the feedback by frequency
using McGarvey's (1985) methodology. I used this method on
an expanded three-variable VAR system.
Empirical Results and Data
Analysis
The bi-variate feedback results using Geweke's method are
shown in Table 2. The results suggest that both in terms of
levels and first differences, the magnitude of linear feedback
from participation in K-12 private education to income growth to
be about five times greater than the feedback from public
enrollment to income growth. However, in terms of higher
education, the magnitude of feedback from the public university
is bigger than the feedback from participation in private
universities. Also, at all educational levels (i.e., K-12 and
tertiary), the feedback from public education to income growth
remains bigger than the feedback from private education. This
result may suggest that in Hawaii, participation in public
education could be a good predictor of income growth.
Table 2
Feedback from
Participation in Education to Income Growth
|
K to
12
|
In levels
|
In Percentage
Change
|
|
Public
|
0.0852
(8.17%)
|
0.0994
(9.46%)
|
|
Private
|
0.4997
(39.33%)
|
0.5033
(39.55%)
|
|
Higher
Education
|
|
Public
|
0.2477
(21.94%)
|
0.0743
(7.16%)
|
|
Private
|
0.0496
(4.84%)
|
0.0459
(4.49%)
|
|
All educational
Levels
|
|
Public
|
0.1683
(15.49%)
|
0.0832
(7.98%)
|
|
Private
|
0.0788
(7.57%)
|
0.0782
(7.52%)
|
In order to have a better idea of an innovation's short-run
versus long-run effects, the feedback measure is decomposed by
frequency bands. Also, the bi-variate system is extended to a
three-variable system and uses the ordering of 'growth prior to
public education prior to private education' in the Choleski
decomposition. Although the feedback measure is consistent,
McGarvey showed that, in small samples, the feedback measure is
biased upward. Hence, the Monte Carlo simulation method is used
to derive bias-adjusted feedback estimates. Table 3 summarizes
the adjusted estimates and figures enclosed in parentheses
pertain to the proportion of variance explained by a
corresponding shock to a series.
Table 3
Feedback from
Participation in
Education to Growth by Frequency
Levels
|
In
levels
|
Private K-12
|
Public K-12
|
|
Permanent
|
0.0002
(0.02%)
|
0.0015
(0.15%)
|
|
Long-run
|
0.024 (2.36%)
|
0.132
(12.40%)
|
|
Medium-run
|
0.174
(15.97%)
|
0.056 (5.49%)
|
|
Short-run
|
0.832
(56.48%)
|
0.043 (4.24%)
|
|
Overall
|
0.271
(23.74%)
|
0.061 (5.90%)
|
|
In
Percentage Change
|
Private K-12
|
Public K-12
|
|
Permanent
|
0.222
(19.91%)
|
1.124
(67.51%)
|
|
Long-run
|
0.1281
(12.03%)
|
0.376
(31.32%)
|
|
Medium-run
|
0.4108
(33.69%)
|
0.0068
(0.68%)
|
|
Short-run
|
0.8790
(58.48%)
|
0.0893
(8.54%)
|
|
Overall
|
0.516
(40.29%)
|
0.045 (4.40%)
|
|
In Levels
|
Private Universities
|
Public University
|
|
|
Permanent
|
0.0966
(9.21%)
|
0.0492
(4.79%)
|
|
|
Long-run
|
0.0547
(5.32%)
|
0.2792
(24.36%)
|
|
|
Medium-run
|
0.0104
(1.03%)
|
0.1525
(14.15%)
|
|
|
Short-run
|
0.0114
(1.13%)
|
0.1087
(10.30%)
|
|
|
Overall
|
0.0161
(1.59%)
|
0.1526
(14.15%)
|
|
|
In
Percentage Change
|
Private Universities
|
Public University
|
|
|
Permanent
|
0.0379
(3.72%)
|
0.0028
(0.28%)
|
|
|
Long-run
|
0.0417
(4.08%)
|
0.0123
(1.22%)
|
|
|
Medium-run
|
0.0612
(5.94%)
|
0.0797
(7.66%)
|
|
|
Short-run
|
0.0078
(0.78%)
|
0.0709
(6.85%)
|
|
|
Overall
|
0.0405
(3.96%)
|
0.0664
(6.43%)
|
|
|
In
Levels
|
Private
|
Public
|
|
Permanent
|
0.00012
(0.012%)
|
0.1537
(14.24%)
|
|
Long-run
|
0.0230
(2.28%)
|
0.1461
(13.60%)
|
|
Medium-run
|
0.0048
(0.48%)
|
0.1256
(11.80%)
|
|
Short-run
|
0.0568
(5.52%)
|
0.0564
(5.48%)
|
|
Overall
|
0.024 (2.41%)
|
0.1038
(9.86%)
|
|
In
Percentage Change
|
Private
|
Public
|
|
Permanent
|
0.0081
(0.81%)
|
0.0072
(0.72%)
|
|
Long-run
|
0.0137
(1.36%)
|
0.0201
(1.99%)
|
|
Medium-run
|
0.0256
(2.52%)
|
0.055 (5.37%)
|
|
Short-run
|
0.0791
(7.60%)
|
0.064 (6.22%)
|
|
Overall
|
0.0396
(3.88%)
|
0.055 (5.35%)
|
In terms of K-12 enrollment, the results suggest that private
schools exhibit bigger overall effect on Hawaii's income
growth relative to that of public schools, confirming the
previous result under the bi-variate feedback method. However,
the feedback effect is concentrated mainly in the short-run (2-3
years) to medium-run (4-12 years). Conversely, participation in
K-12 public education exhibited a significant long-run to
permanent effect on Hawaii's income growth relative to that of
private education. This result may be explained by the growing
number of high school graduates migrating out of the state. For
example in 1992, the net out-migration of high school graduates
was recorded to be around 690 and increased to 958 four years
after. Apparently, families who could afford to send their
children to private schools are willing to spend a little more to
send them out of state in anticipation of more and better choices
in education available in the mainland.
In terms of tertiary level, the overall contribution of public
school enrollment to Hawaii's income growth is bigger than that
of private universities. However, decomposing the feedback effect
by frequency suggest that this dominance of public enrollment in
explaining the variation in income growth seem to be concentrated
mainly in the short-run to medium-run. Conversely, private
universities exhibit a permanent and long-run effect in
explaining the variance in Hawaii's income growth relative to
that of the public university. This finding might suggests that
private tertiary education may be the key to promoting long-run
growth in Hawaii. Similarly, one cannot ignore the significant
contribution of the public university in building Hawaii's human
capital stock in the short to medium-run.
In terms of all educational levels, i.e. primary, secondary and
tertiary level combined, participation in public education tend
to explain a greater proportion of variance in Hawaii's
income growth relative to private education across almost all
frequency levels. Again, this finding confirms the previous
result found in the bi-variate feedback method.
Concluding
Remarks
In this
study, an empirical investigation is done to assess and compare
the relative contribution of public and private schools to
Hawaii' economy. I employed the unrestricted vector
autoregression (VAR) model that uses only past regularities and
historical patterns in the data to examine the dynamic feedback
relationship between participation in education and income
growth. The results suggest that across all educational levels,
i.e., K-12 and tertiary, participation in public education could
be a good predictor of income growth in Hawaii. However,
decomposing the feedback effect by frequency suggests that the
dominance of public education in explaining the variation in
income growth to be concentrated mainly on the short-run to
medium-run for tertiary level and long-run to permanent effect
for K-12 level. Hawaii state legislature and educators should
perhaps take these results as a motivation not to ignore the
problems plaguing Hawaii's public schools but should work
towards greater improvement and support for public education
given its predicted significant overall contribution to the
economy. Similarly, the presence of significant contribution of
K-12 private schools in the short-run to medium-run and private
universities' long-run to permanent effect on
Hawaii's income growth should serve as a driving force that
could help bring about healthy competition and greater efficiency
in the provision of educational services in Hawaii.
References
Dickey, D. and W.A. Fuller. (1979). Distribution of the
estimators for time series regressions with a unit root.
Journal of the American Statistical Association,74,
427-431.
Geweke, John. (1982). Measurement of linear dependence and
feedback between multiple time series. Journal of the American
Statistical Association, 77, no.378, 304-313.
Hamilton, James.(1994). Time Series Analysis. Princeton
University Press.
Hawaii State Department of Business, Economic Development and
Tourism. Hawaii Data Book. Various issues.
Kwiatkowski, D., P.C. Phillips, P. Schmidt and Y. Shin.
(1992).Testing the null hypothesis of stationarity against the
alternative of a unit root: How sure are we that economic time
series have a unit root ?. Journal of Econometrics, 54,
159-78.
McGarvey, Mary. (1985). US evidence on linear feedback from money
growth shocks to relative price changes, 1954 to 1979. The
Review of Economics and Statistics, 67, no.4,
675-680.
National Center for Education Statistics. Education in
States & Nations: Indicators Comparing US with the other
Industrialized Countries. Various issues.
National Center for Education Statistics.
The Digest of Education Statistics. Various
issues.
National Center for Education Statistics.
The Condition of Education. Various issues.
Phillips, P.C. and P. Perron. (1988).Testing for a unit root in
time series regression. Biometrika, 65,
335-346.
Schmitt, R. (1977). Historical Statistics of Hawaii.
University Press of Hawaii.
About the
Author
Antonina Espiritu, Ph.D.
Hawaii Pacific
University
1060 Bishop St. LB
402A
Honolulu, HI
96813
Phone: (808)
544-0892
Fax: (808)
544-0862
Email:
aespirit@hpu.edu
Antonina Espiritu is an
Assistant Professor of Economics at Hawaii Pacific University.
She earned her PhD in Economics at the University of
Nebraska-Lincoln under the NSF Economic Education Scholarship and
her MA in Economics at the University of Hawaii at Manoa under
the East-West Center Scholarship. Her current educational
research interests include learning assessment of undergraduate
and graduate economics students and the role of education to
productivity growth.
Appendix
Two Related Linear
Dependence and Feedback Measures
A. Geweke's (1982)
method is used to measure the degree of dependence or the extent
of various kinds of feedback between data series. He defined the
measures of linear dependence between say, X and Y wide-sense
stationary series in terms of the following linear
projections,
(1)
Yt = S¥s=1a1sYt-s+ S¥s=1a2sXt-s + u1t
(2) Yt = S¥s=1 b1sYt-s+ S¥s=0 b2sXt-s + u2t
(3) Yt = S¥s=1g1sYt-s + u3t
where the linear feedback
measure from X to Y is defined as
FX ®Y = log [var (u3t)/
var(u1t)]
while the measure of
contemporaneous feedback between X and Y is defined as
FX°Y = log [var (u1t)/
var(u2t)].
So, the measure of
linear dependence between X and Y or FX,Y is the sum
of linear feedback from X to Y, FX ®Y , linear feedback from Y to X,
FY®X and instantaneous linear feedback F
X°Y.
FX,Y =
FX®Y + F Y®X + F X°Y
where
FY ®X is found by switching X and Y in equations (1)
and (3) and in the definition of directional feedback.
B. Building on
Geweke's feedback measure, McGarvey(1985) developed a
useful alternative summary measure by decomposing the feedback by
frequency in order to distinguish between short-run and long-run
effects of a given innovation or shock.
In the context of this
study, the MA representation of the 3-variable orthogonalized
autoregressive system is as follows:
éXt ù éC11(L)
C12(L) C13(L) ù éut ù
êYtú
= êC21(L)
C22(L) C23(L) ê êwt ê
ëZt û
ëC31(L)
C32(L) C33(L) û ëht û
where for example,
C21(L) gives the response of Yt to
innovations in Xt and, the overall feedback from X to
Y is defined as
FX ®Y = log [var (Yt) /
var(Yt) - S¥s=0 c21 (s)2var(ut)]
The transformation (
1-exp[-FX ®Y]) gives the proportion of Y's variance
explained by shocks to X.
To distinguish between
short-run and long-run effects, the overall feedback is
decomposed frequency bands. Feedback from X to Y over the
interval ( l1 , l2) is defined as
fX ®Y(l1 , l2) = log [( Il1 l2 SY(l)dl) /
( Il1 l2 SY(l)
- C 21(l)2 su2) dl)]
since var(Y) =
(1/2 p) Ip-pSY(l)dl and
SY( l) = C
21(l)2 su2+ C 22(l)2 sw2+ C 22(l)2 sh2. So, if ut contributes nothing to the variance of Y at frequency
l, the ratio
will be one and the feedback measure will be zero. Note that a
period of a cycle is defined as the ratio of 2p to the
frequency.
|
times since October 22, 2001