average index of 9.55, followed by Southeast
Sulawesi with an index of 8.03, and then by West
Sulawesi with an index of 7.96. The province with
the lowest index was East Kalimantan with an index
of 2.44, followed by Aceh with a 2.58 of index, and
then Riau 2.81.
HDI is a comparison of life expectancy, literacy,
education, and living standards for all countries
throughout the world. The HDI is used to classify
whether a country is a developed country, a
developing country, or a backward country and also
to measure the influence of economic policies on
quality of life of people in a country. From the data,
it can be seen that the highest human development
index is owned by DKI Jakarta province, followed
by DI Yogyakarta, and the province of Riau Islands.
The lowest of human development index occurs in
the provinces of North Kalimantan, Papua, and West
Papua.
From the data (Table 3), it can be seen that the
greatest local government capital expenditures
(average) is held by DKI Jakarta province, followed
by East Kalimantan, and Papua. While the lowest
local government capital expenditures (average) is
held by Bangka Belitung province, and then
followed by Gorontalo, and Bengkulu.
The statistical analysis obtained the results for
the three panel data models, namely: Common
Effect Model (CEM), Fixed Effect Model (FEM),
and Random Effect Model (REM). The three panel
data models are then tested to get the best model
through these 3 following tests: 1) Chow Test , 2)
Hausman Test, and 3) Lagrange Multiplier Test (LM
Test)
Chow test is a test to determine whether the
Common Effect or FEM is the most appropriate to
be used in estimating the research panel data. Model
selection is done by comparing the value of F-
statistics (F
stat
) with F-table. If the F-statistics result
is greater (>) than F-table, the selected model is
FEM. If F-statistics is smaller (<) than F-table, the
selected model is CEM. The Cross-section F-value
of the Chow test above obtained a value of
437.5378. F-table values from numerator (dF-1) and
denumenator (dF-2) at ⍺: 5%, is 1.5464. From the
results of the Chow Test above it can be concluded
that F-stat is greater than F-table (437.5378 >
1.5464), so the model chosen from this Chow test is
FEM.
The Hausman test was conducted to test whether
the selected model for analyse research data using
the FEM or REM. If value of Chi Square statistics >
Chi Square table then the model used is FEM.
Whereas if Chi Square statistic < Chi Square table
then the chosen model is REM. In this study the
value of Chi Square calculated/statistic was obtained
at 5.5711. While the Chi Square table (df = 2, α =
0.05) is 5.9915. Based on the Hausman test, the Chi
Square statistics (5.5711) shows that the value is
smaller than the Chi Square table (5.9915), then the
best model for Hausman test is REM.
Lagrange Multiplier (LM) is a test to find out
whether the REM or the Common Effect (OLS)
model is the most appropriate to use. The basis of
the selection is to use a calculated Chi
Square/statistical value compared to the calculated
LM value. If LM counts > the critical value of chi-
squares statistics, the model used is the Random
Effect, and vice versa if LM counts < critical value
of chi-squares statistics, then the right model for
panel data regression is the CEM.
Based on LM statistics obtained that is 282.8001,
greater than Chi Square statistic of 5.5711 then the
selected model of the LM test is REM.
From the results of the 3 above tests, it can be
conclude that the best model is REM.
Estimation Equation from REM:
HDI = α + β
1
LNGE + β
2
EG + ε
HDI = 27.8466288389 + 1.47011327607 * LN_GE
- 0.0104448476419 * ED + e
From the above equation can be stated as
follows. In general, government capital expenditure
variables (X1) have a significant positive effect
(coefficient = 1.4701) on public welfare which is
represented by human development index (Y) with
p-value of 0.0000. This means that every increase of
1 unit (one hundred billion IDR) in government
capital expenditure will increase 1.4701 points of the
human development index. For other variables,
economic growth (X2) does not affect the human
development index. However, together all variables,
namely government capital expenditure and
economic growth affect the human development
index. This can be seen from the p-value of F-
statistic of 0.0000, which is smaller than α (5%).
In this study, the result of the coefficient of
determination (R2) is 0.2976 or 29.76%. The
coefficient of determination (R2) reflects 0.2976 or
29.76% of the human development index can be
explained by the variable government capital
expenditure, while the remaining 70.24% is
explained by other variables outside this study.
From the results of the selected output model can
be calculated and interpreted the individual effect
value (Ci) of the selected model (Random Effect
Model). This individual effect value shows the
sensitivity of each regional (provincial) government.