jaya latentvar models examples
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Multivariate Analysis MSE 2010 1
Krishnakumar (JHD, 2007)
A SEM is estimated using national (aggregate) data.
Based on the availability of data, three fundamentalcapability dimensions namely knowledge (education),
health and political freedom, are considered.
Data relate to a cross section of middle and low incomecountries across the world for the year 2000 (or the year
closest to it i.e. 1999 or 1998 for a few variables).
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Multivariate Analysis MSE 2010 3
Possible exogenous variables (observed)
For the structural part
x1: Government Effectiveness
x2: Regulatory Quality
x3: Population using improved water sources (%)x4: Cellular mobile subscribers (per 1000 people)
x5: Public expenditure on health ({\%} of GDP)
x6: Total debt service (% of GDP)
x7: Density (persons per sq.km.)
x8: Political Stability
x9: Population Growth Rate (Annual %)
x10: Urban Population Growth Rate (Annual %)x11: Youth Bulge (Pop. Aged 0-14 as a % of Total)
x12: Physicians (per 100,000 people)
x13: Press Freedom
x14: Democracy - Autocracy Index
x15: Total fertility rate (per woman)
x16: Foreign direct investment (PPP USD)
x17: Gross fixed capital formation (PPP USD)x18: Trade (PPP USD)
For the measurement part
w1: Control of Corruption
w2: Rule of Law
w3: Population with access to essential drugs (%)
w4: Population using adequate sanitation facilities (%)
w5: Public expenditure on education (% of GDP)
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Multivariate Analysis MSE 2010 4
Measurement Model
Dependentvariable
Explanatoryvariable
Political
Rights
Civil
Liberties
Voice
and
Accountability
Adult
Literacyrate
Combined
Enrolment
Ratio
Life
Expectancy
Infantmortality
Knowledgecapability
- - - 1
(0)
0.71
(0.06)
- -
Healthcapability
- - - - - 1
(0)
-3.87
(0.34)
Politicalfreedomcapability
1
(0)
0.66
(0.04)
0.40
(0.02)
- - - -
Access to
essentialdrugs
- - - - - 0.04
(0.03)
-0.10
(0.09)
Public
spending oneducation
- - - 1.72
(0.82)
1.58
(0.83)
- -
R2 0.92 0.88 0.95 0.83 0.87 0.80 0.97
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Multivariate Analysis MSE 2010 5
Krishnakumar (JHD, 2007)
Results of the Measurement Model:
The coefficient of knowledge is positiveand highly significant for adult literacy rate
and combined primary, secondary andtertiary gross enrolment ratio.
The situation is similar for life expectancyat birth and infant mortality rate asindicators for health (the second one witha negative health coefficient) and thefour political freedom indicators.
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Multivariate Analysis MSE 2010 6
Structural ModelDependent variable
Explanatory variable
Knowledgecapability
Health capability Political freedom capability
Knowledge capability - - 0.01
(0.00)
Health capability 1.37
(0.27)
- -
Political freedom capability 0.28
(0.31)
Control of corruption - - 0.61
(0.18)
Access to adequate sanitation - 0.07
(0.02)
-
Population density -0.03
(0.01)
Youth bulge -64.39
(30.55)
Press Freedom 0.08
(0.01)
Fertility rate -4.00
(0.48)
R2 0.82 0.80 0.89
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Multivariate Analysis MSE 2010 7
Krishnakumar (JHD, 2007)
Results of the Structural Model:
These results confirm the interdependent nature
of the three dimensions.
The positive and significant impact of health oneducation shows that better health is definitely
an asset for better performance in education,
which is in turn an important factor in achieving
political rights. Furthermore, greater political freedom leads to
better health status thus completing the loop.
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Multivariate Analysis MSE 2010 8
Krishnakumar (JHD, 2007)
The results also show the importance of certain
supply side (exogenous) factors.
The population with access to essential drugs
has a significant positive impact on lifeexpectancy at birth whereas it has a negative
though not significant effect on the infant
mortality rate.
Public expenditure on education has a positiveand significant effect on adult literacy rate and
combined primary, secondary and tertiary gross
enrolment ratio.
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Multivariate Analysis MSE 2010 9
Krishnakumar (JHD, 2007) Percentage of population using improved water
sources and number of physicians per 100000people have a positive and significant effect onhealth whereas fertility has a negative effect asexpected.
Finally, press freedom and control of corruptionhave a significant and positive effect on politicalfreedom, the effects of regulatory quality,government effectiveness and political stability
not being significant. Lack of corruption definitelyimplies more freedom and the more thecollective voice in terms of press freedom thebetter the political rights atmosphere.
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Multivariate Analysis MSE 2010 10
Krishnakumar (JHD, 2007)
Finally, the relevance of political, demographic,socio-economic and environmental factors in thedetermination of capabilities is also confirmed byour results.
The democracy-autocracy index has an important
positive effect on education (that is a moredemocratic regime seems to favour higherachievement in education).
Population growth rate and population density havean important negative effect on education. This can
be explained by the increased pressure exerted bya higher growth rate and density of population, onexisting educational services and governmentresources thereby affecting the overall achievementin this field.
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Multivariate Analysis MSE 2010 11
Krishnakumar (JHD, 2007)
A key message of this paper is that a better social and
political environment not only implies a better conversion
of capabilities into achievements but also enhances the
capabilities themselves. This emphasizes the powerful
role that a State can and should play in terms of
providing better infrastructure and governance.
The paper also constructs capability indices from the
latent variable scores and ranks countries according to
them.
These rankings are compared with those obtained with
the commonly used HDI or GDP per capita.
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Multivariate Analysis MSE 2010 12
Argentina 1 10 2 3 7 15
Hungary 2 1 1 1 2 3
Slovakia 3 4 3 5 1 6
Chile 4 5 7 6 3 10Uruguay 5 3 8 2 4 5
Costa Rica 6 2 5 15 5 1
Mexico 7 18 9 17 16 23
Panama 8 7 17 12 11 9
Bulgaria 9 8 13 4 6 11
Romania 10 11 21 7 12 13
Colombia 11 24 11 13 17 34
Mauritius 12 6 6 32 8 2
Venezuela 13 20 20 24 14 27Thailand 14 15 15 20 18 18
Brazil 15 16 10 16 19 19
Philippines 16 13 27 8 20 16
Kazakhstan 17 36 18 10 37 44
Peru 18 25 23 9 28 28
Jamaica 19 9 29 33 10 8
Turkey 20 29 14 27 30 37
Sri Lanka 21 19 32 14 9 31Paraguay 22 22 22 22 15 32Dominican Republic 23 12 12 10 13 14
Uzbekistan 24 43 38 28 32 53
China 25 38 28 19 23 52
Iran 26 34 18 29 29 45
Jordan 27 26 26 35 25 29
Country rankhdi rankhhat rgdpn ry*1 ry*2 ry*3
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Multivariate Analysis MSE 2010 13
Kyrgyzstan 28 33 36 25 34 38
Guyana 29 14 24 18 33 7
Algeria 30 42 16 37 36 50
South Africa 31 17 4 23 40 4
Syrian Arab Republic 32 41 33 36 21 54Vietnam 33 40 41 26 22 55
Indonesia 34 27 34 21 27 33
Bolivia 35 23 39 31 41 12
Egypt 36 32 30 30 26 41
Honduras 37 21 35 34 24 22
Guatemala 38 28 25 39 35 26
Morocco 39 31 31 45 31 35
Zimbabwe 40 46 37 38 43 47
Ghana 41 30 40 43 39 24Cambodia 42 47 46 40 47 39
Kenya 43 45 51 41 42 43
Pakistan 44 51 44 47 46 51
Togo 45 48 47 46 44 42
Bangladesh 46 37 48 50 38 30
Madagascar 47 35 53 44 48 21
Mauritania 48 53 44 54 54 40
Zambia 49 49 55 42 51 36
Senegal 50 44 49 49 45 25Benin 51 39 52 48 50 17
Guinea 52 55 43 53 52 48
Gambia 53 52 41 51 49 49
Mali 54 50 54 55 55 20
Chad 55 54 50 52 53 46
Country rankhdi rankhhat rgdpn ry*1 ry*2 ry*3
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Multivariate Analysis MSE 2010 14Access to electricity
Access to radio, TV,
phone
LivingConditions
Capability
Schooling for
Age
(SAGE)
Level of
Education
Basic services
conditions
Water coverage
Habitability
conditions
Dwelling
conditions
Knowledge
Capability
Social investment
Number of
classrooms
Belongs to the urban
area
Number of individuals
Age
Number of siblings aged
7-14
To be poor
To be indigenous
Number of female/male
adults
Number of schools
Presence of a school
%of agricultural
population in the
active population
Belongs to maincities
Parental education
Use of medical
services
Literacy
Gender
Working status
Number of siblings
# of siblings aged 7-14
enrolled
Number of children
Male household head
Belongs to the urban
area
To be the oldest
Monthly per
capita expenditure
Belongs to main cities
Krishnakumar and
Ballon (2007, WD)
Basic Capabilities for
Bolivian Children
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Multivariate Analysis MSE 2010 15
Structural Model
oeff.Sta ar .
oeff.Sig if. oeff.
Sta ar .
oeff.Sig if.
y1*
Kno ledge capabil ity - - - 0.078 0.129 ***y2 iving conditions capability 0.124 0.075 *** - - -
x9 Father's level o education 0.074 0.160 ***
x10 other's level o education 0.141 0.171 *** 0.067 0.134 ***
x14 elongs to main cities 0.109 0.044 *** 0.128 0.085 ***
x11 se o medical services 0.170 0.023 * ***
x1 umber o schools 0.001 0.200 *** ***
x2 umber o classrooms 0.000 -0.273 *** ***
x4 gricultural population/ -0.045 -0.016
x12 onthly per capita expenditure 1.275 0.457 ***
R2 0.065 0.441
***,* denote signi icance at 1 and 10 levels respect ively.
ivi g co itio s
ca a ility equatio
y2*
Varia le
o le ge ca a ility
equatio
y1*
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Multivariate Analysis MSE 2010 16
Knowledge Measurement Model
Standardized
coefficientSignificance
Standardized
coefficientSignificance
Standardized
coefficientSignificance
y1*
Knowledge capability 0.609 - 0.599 *** 0.655 ***
w7 Number of siblings -0.106 *** -0.029 ** -0.068 *
w8 Number of siblings aged 7-14 -0.091 *** -0.045 *** -0.027 ***
w9 Number of siblings aged 7-14 enrolled 0.453 *** 0.166 *** 0.189 ***
w1 Age 0.534 *** 0.447 *** -0.156 ***
w4 Being indigenous -0.041 * -0.029 *** -0.082 ***
w2 Male 0.046 * -0.033 *** -0.028 ***
w14 Male household head -0.228 *** -0.097 *** -0.111 ***
w3 Working status -0.039 *** -0.017 *
R2 0.759 0.567 0.507
***,**,* denote significance at 1%, 5% and 10% levels respectively.
Sage
y3
Variable
Literacy Level of Education
y2y1
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Multivariate Analysis MSE 2010 17
Living Conditions Measurement Model
Standardized
Coefficient Significance
Standardized
Coefficient Significance
Standardized
Coefficient Significance
y2*
Living conditions capability 0.532 - 0.546 *** 0.532 ***
w4 Being indigenous -0.031 ***
w5 Being poor -0.052 *** -0.112 *** -0.065 ***
w14 Male household head -0.048 *** -0.050 *** -0.031 ***
w11 Number of female adults 0.036 *** 0.028 ** 0.076 ***
w13 Number of children -0.080 *** -0.233 *** -0.078 ***
w15 Urban 0.278 *** -0.076 *** 0.436 ***
R2 0.500 0.446 0.695
***,** denote significance at 1% and 5% levels respectively.
Variable
Basic Services
y6y4 y5
Dwelling Habitability
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Multivariate Analysis MSE 2010 18
Normalised Capability Scores
Knowledge Living Conditions
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Multivariate Analysis MSE 2010 19
Some Capability Determinants
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Multivariate Analysis MSE 2010 20
Department rankings
Department ank ank ank ank
(alphabetical order) EduAchiev. Knowledge LC.Achiev. LC.Cap Education LivCond
A1 C1 A2 C2 C1-A1 C2-A2
Beni 8 6 9 8 -2 -1Chuquisaca 3 4 7 5 1 -2
Cochabamba 4 3 4 2 -1 -2
La Paz 7 5 3 3 -2 0
Oruro 2 2 5 4 0 -1
Pando 5 6 8 6 1 -2
Potos 9 5 6 7 -4 1
Santa Cruz 1 1 1 1 0 0
Tarija 6 5 2 3 -1 1
Differences
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