Factors Determination that Influence Food Insecurity in Central Java Using Spatial Panel Data Analysis

FACTORS DETERMINATION THAT INFLUENCE FOOD INSECURITY
IN CENTRAL JAVA USING SPATIAL PANEL DATA ANALYSIS

LIA RATIH KUSUMA DEWI

DEPARTMENT OF STATISTICS
FACULTY OF MATHEMATICS AND NATURAL SCIENCES
BOGOR AGRICULTURAL UNIVERSITY
BOGOR
2012

ABSTRACT
LIA RATIH KUSUMA DEWI. Factors Determination that Influence Food Insecurity in Central
Java Using Spatial Panel Data Analysis. Advised by ASEP SAEFUDDIN dan YENNI
ANGRAINI.
Food insecurity refers to the consequence of inadequate consumption of nutritious food at
region, society or household, considering the physiological use of food by the body as being
within the domain of nutrition and health. Sutawi (2008) explained that availability and
achievability on aggregate scale, Indonesia citizen is appertained food secure. However, household
with food insecure still found in almost whole provinces with high proportion. So, it is necessary
to do a research to determine factors that influence food insecurity in a province by calculating

spatial effect of inter-regency or municipality. In this research, food insecurity that will be
analyzed is food insecurity in Central Java using spatial panel data analysis. Cross-section unit in
this research is 35 regencies or municipalities in Central Java province which was observed for 4
years (2007-2010) as time series unit.The analysis result in this research show that fixed effect
model with SAR are better used for modelling food insecuity in Central Java. This model show
that production of paddy (X2) and local government original receipt of regency or municipality
(X3) influence percentage of citizen with food insecure that consume calorie under basic
requirement 2100 kkal/capita/day (Y) with R2 95.88%. Coefficient of λ indicates that spatial
autoregressive effect significant in influencing percentage of citizen with food insecure in Central
Java.
.
Keywords : food insecurity, spatial panel data analysis, fixed effect model, SAR

FACTORS DETERMINATION THAT INFLUENCE FOOD INSECURITY
IN CENTRAL JAVA USING SPATIAL PANEL DATA ANALYSIS

LIA RATIH KUSUMA DEWI

Minithesis
to complete the requirement for graduation of Bachelor Degree in Statistics

at Department of Statistics

DEPARTMENT OF STATISTICS
FACULTY OF MATHEMATICS AND NATURAL SCIENCES
BOGOR AGRICULTURAL UNIVERSITY
BOGOR
2012

Title
Name
NRP

: Factors Determination that Influence Food Insecurity in Central Java Using Spatial
Panel Data Analysis
: Lia Ratih Kusuma Dewi
: G14080043

Approved by

Advisor I,

Advisor II,

Dr. Ir. Asep Saefuddin, M.Sc
NIP. 195703161981031004

Yenni Angraini, S.Si, M.Si
NIP. 197805112007012001

Acknowledged by:
Head of Department of Statistics
Faculty of Mathematics and Natural Sciences
Bogor Agricultural University

Dr. Ir. Hari Wijayanto, M.Si
NIP. 196504211990021001

Graduate date :

ACKNOWLEDGEMENTS

The author felt deeply grateful Alhamdulillah to Allah SWT for deliverancing and blessing.
Especially in completing this minithesis with title “Factors Determination That Influence Food
Insecurity in Central Java Using Spatial Panel Data Analysis” as the requirement for
graduation of Bachelor Degree in Statistics at Department of Statistics, Faculty of Mathematics
and Natural Sciences, Bogor Agricultural University.
I recognized that the completion of this minithesis would not be done without invaluable help
from other people. I am very appreciating and really thank you for their helps, ideas, critics,
advices and improvement my minithesis started from begining during the progress until it was
done. Therefore, I would like to express my graceful to:
1. Dr. Ir. Asep Saefuddin, M.Sc, Yenni Angraini, S.Si, M.Si, and Dr. Anang Kurnia for their
great advice, support, knowledge and patience while finished this research.
2. All the lectures, administration, and library staffs in Department of Statistics, who had
patiently taught and served very well.
3. POM, Karya Salemba Empat, and P.T Perfetti Van Melle for schoolarships that had been given
and could help me on finished my study.
4. My beloved parents Sugiyat and Teliah, S.Pd, my lovely brothers , Deni Wahyu Kusuma Jati,
and Aziz Kusuma Wardana, who never stopped supporting, advising, and praying for me until
the end of my study.
5. Diah Kartika Pratiwi, my beloved same age cousin, for your cheering up and Rodli Abdul
Latif, my adviser, for your advised, supported and cheered up my life, thanks for everything

that you have done during this seven years.
6. All my friends in “Statistics 45th”, especially for “Empat Sekawan” Gusti Andhika P, Umi Nur
Chasanah, Nur Hikmah, and Astri Fitriani, thank you for our beautiful friendship and also for
Yulia Anggraeni, Nur Syita P, Ramadiyan F, Didin S who had always helped and supported
me to finished this minithesis.
7. My beloved family in Bogor, “Winning Eleven” (Ubi, Ompu, Choi Young Be, Mba Shin,
Desseh, Mba Na, Idun, Bang Ros, Iza and Etica), Juli S, and all member of Wisma Kompeten
for our great friendship, understood, supported and happiness.
8. Kak Mo, Kak Achi, Hairul, Ermi and all family of Kopma IPB for our great
“UσSHAKEABLE!” experiences.
Hopefully, this research can be useful and able to improved in the future.

Bogor, December 2012

Lia Ratih Kusuma Dewi

BIOGRAPHY
Lia Ratih Kusuma Dewi was born in Klaten on November 21 st 1990 as the middle daughter of
Sugiyat and Teliah, S.Pd from three siblings, Deni Wahyu Kusuma Jati and Aziz Kusuma
Wardana. She finished her education from SD N 1 Jurang Jero at 2002 and graduated from SMP N

1 Karanganom at 2005. She graduated her senior high school at SMA N 1 Karanganom at 2008
and she continued her study in Bogor Agricultural University through USMI and took Statistics as
her major in Department of Statistics and choose Economics and Development Study in
Department of Economics as her minor.
During learning, the author actived in several organizations, such as Koperasi Mahasiswa IPB
as staff of administration, financial and personnel (2008-2011) then as director of administration,
financial and personnel (2011-2012) and Profession Union Gamma Sigma Beta as secretary
(2011). Other than organization, she also actived in several committees, such as Welcome
Ceremony of Statistics as secretary (2011), G-Force 46 as secretary (2010), The 6th Statistika Ria
(2010) as public relations, Pesta Sains 2009 as secretary, The 5th Statistika Ria (2009) as
secretary, MPKMB 46 (2009) as secretary, and TPB Cup as terasurer (2009). Beside in
organization and committes, she also filled her free time to be lecturer assistant (Statistical
Methods (2011 & 2012), Regression Analysis (2011), and Analysis of Categorical Data (2012)),
Consultant of Statistics in Expert (2010), and staff of lecturer in MSCollage Course (2010-2012)
for Basic of Mathematics, Calculus and Statistical Methods .The author did intership at February
13rd until April 6th 2012 in Balai Besar Oraganisme Pengganggu Tumbuhan (BBOPT) Karawang,
West Java.

TABLE OF CONTENTS
Page

LIST OF TABLE ....................................................................................................................... vii
LIST OF FIGURE .................................................................................................................... vii
LIST OF APPENDIX ................................................................................................................ vii
INTRODUCTION
Background…………………………….. ............................................................................. 1
Objective ............................................................................................................................. 1
LITERATUR REVIEW
General Model of Panel Data ............................................................................................... 1
Pooled Model .............................................................................................................. 2
Fixed Effect Model ...................................................................................................... 2
Random Effect Model .................................................................................................. 2
Chow Test ................................................................................................................... 2
Hausman Test .............................................................................................................. 2
Spatial Panel Data Analysis ................................................................................................. 3
Spatial Autoregressive Model (SAR) ........................................................................... 3
Spatial Error Model (SEM) .......................................................................................... 3
Spatial Weight Matrix.................................................................................................. 3
Lagrange Multiplier Test ............................................................................................. 3
METHODOLOGY
Data Sources ....................................................................................................................... 4

Method ................................................................................................................................ 4
RESULT AND DISCUSSION
Exploratory Data ................................................................................................................. 4
Panel Data Analysis ............................................................................................................. 5
Chow Test ................................................................................................................... 5
Hausman Test .............................................................................................................. 5
Spatial Panel Data Analysis ................................................................................................. 6
Lagrange Multiplier Test ............................................................................................. 6
Spatial Autoregressive Model (SAR) ........................................................................... 6
Examination The Assumptions of SAR ........................................................................ 6
CONCLUSION AND RECOMMENDATION ............................................................................. 7
REFERENCE .............................................................................................................................. 7
APPENDIX ................................................................................................................................. 9

vii

LIST OF TABLE
Page
Table 1 The result of pooled model ............................................................................................. 5
Table 2 The result of fixed effect model ...................................................................................... 5

Table 3 The result of random effect model .................................................................................. 5
Table 4 The result of LM-Test..................................................................................................... 6
Table 5 Estimation and examination parameter of SAR model ..................................................... 6
Table 6 The result of Glejser test for SAR ................................................................................... 7
Table 7 The result of multicollinearity test for SAR ..................................................................... 7

LIST OF FIGURE
Page
Figure 1 Probability plot of residual ............................................................................................ 7

LIST OF APPENDIX
Page
Appendix 1 Description of response and explanatory variables .................................................. 10
Appendix 2 Average value of response variable for whole regency or municipality .................... 10
Appendix 3 The result of panel data analysis for pooled model .................................................. 11
Appendix 4 The result of panel data analysis for fixed effect model .......................................... 11
Appendix 5 The result of panel data analysis for random effect model ....................................... 11
Appendix 6 Cross-section effect value (�� ) ................................................................................ 12
Appendix 7 Map of Central Java Province ................................................................................ 13

1

INTRODUCTION

LITERATURE REVIEW

Background
Food is the necessary basic needed for
everybody through physiological, social, and
antrhopological. Food always related with
society effort for living on. If this primary
requirement unfulfilled, then food insecurity
will impact for various life aspect (Maria
2009). Food security refers to a household's
physical and economic access to adequate,
safe, and nutritious food that fulfills the
dietary needs and food preferences of
household for living an active and healthy life.
Food security levels are classified into four
levels: food secure, food less secure, food

vulnerable, and food insecure (Law No.
7/1996).
Food supply in national or regional is
apparently adequate is not assured that
individu or household in food security
condition (Saliem 2001). Sutawi (2008)
explained that availability and achievability on
aggregate scale, Indonesia citizen is
appertained food secure. However, household
with food insecure still found in almost whole
provinces with high proportion. Based on
National Socio-Economic Survey data of
Statistics Indonesia in 2006, the lowest
percentage of citizen with food insecure was at
Bali province (4.8%) and the highest was at
Special District of Yogyakarta (20%). Even in
whole provinces which well known as central
location of food production like South
Sumatera, South Sulawesi, East Java, West
Java, and Central Java, had high proportion of
food insecure citizen over 10%.
Based on the above informations, it is
necessary to do a research to determine factors
that influence food insecurity in a province by
calculating spatial effect of inter-regency or
municipality. In this research, food insecurity
that will be analyzed is food insecurity in
Central Java, province with the lowest average
expenditure per capita for food in Java island
based on Statistics Indonesia in 2008. The data
from this research is spatial panel data built by
cross-section and time series data that have
specific interaction between spatial units. So,
the analysis that can be used for this data type
is spatial panel data analysis.

Food Insecurity
Food insecurity refers to the consequence
of inadequate consumption of nutritious food
at region, society or household, considering
the physiological use of food by the body as
being within the domain of nutrition and
health. Those are two form of food insecurity,
first, chronic food insecurity, that can be
happened repeatedly in certain of time because
of low purchasing power and low quality of
resource. Second, transient food insecurity is
happened because of urgen situation like
nature or social disaster (Food Security
Council 2006).
Maria et al (2009) explained that food
insecurity can be influenced by production of
paddy, rice aid, rice suply, and rice
purchasing. This research used regression
analysis. Laelati (2012) explained that food
insecurity a province can be influenced by
food insecurity from each regency or
municipality in that province. This research
result explained that factors that influence
food insecurity using panel data analysis are
general allocation fund, local government
original receipt, income percapita, harvested
area of paddy, and production of paddy.

Objective
The aim of this research is to determining
factors that influence food insecurity in
Central Java using spatial panel data analysis.

General Model of Panel Data
If the same units of observation in a crosssectional sample are surveyed two or more
times, the resulting observations are described
as panel data set. Cross-section data refers to
data that are collected from many units or
subjects at one point in time. Time series data
is a set of observations on the values that a
variable takes at different times. There are
another names for panel data, such as pooled
data (pooling of time series and cross-sectional
observations), combination of time series and
cross-section
data,
micropanel
data,
longitudinal data (a study over time of a
variable or group of subject), event history
analysis and cohort analysis.
If each unit cross-section has the same
number of time series observation, it is called
balance panel data. Otherwise, if each unit
crosssection has a different number of time
series observation, it is called unbalance panel
data. In panel data also come across the terms
short panel and long panel. In short panel the
number of cross-sectional subject, N, is greater
than the number of time periods, T. Then in a
long panel, T is greater than N (Gujarati
2009). The structure of panel data is sorted

2

first by spatial units then by time (Elhorst
2010).
A panel data regression differs from a
regular time-series or cross-section regression,
in that it has a double subscript on its
variables, i.e.
yit = α + �′it � + uit

[1]

i = 1,2, …, σ ; t = 1,2, …, T
with i denoting unit cross section or
individuals and t denotes the time series
dimension. yit denotes response for i
observation and t time period. α is a scalar, β
is a vector that have measure K x 1, xit is a
vector which have measure K x 1 for i
observation and t time period and uit denotes
error.
Most of the panel data applications utilize
a one-way error component model for the
disturbances, with

uit = τi + εit

[2]

where τi denotes the unobservable individualspecific effect and ɛit denotes error for i
observation and t time period. (Baltagi 2005).
Pooled Model
Pooled model is one of the models panel
data analysis. Assumption in this model is the
regression coefficient (constanta or slope)
between cross-section unit and time series unit
is the same. Then, to estimate the parameters
used ordinary least square (OLS) (Gujarati
2009).
Fixed Effect Model
The fixed effect model is an appropriate
specification if we are focusing on a specific
set of N. The assumptions for this model are
(1) τi is assumed to be fixed parameters to be
estimated, (2) εit disturbances stochastic
independent and identically distributed IDD
(0, 2ε ), (3) E(Xit, εit) = 0, Xit are assumed
independent with εit for all i and t (Baltagi
2005).
Parameters estimation in fixed effext
model is estimated by within estimator, can be
explained as follows :
For the panel data regression,
yit = α + � ′ it � + τi + ���

[4]

these equation are averaged for over time
gives:
�

= �+

′
�. �

+ τi + ��.

[5]

therefore, subtracting equation [5] from [4]
equation gives
yit −

�

= � ′ it −

′
�.

� + ( ��� − ��. )

[6]

these [6] equation is called within
transformation (Elhorst 2010).
Model above is estimated with OLS
method. This fixed effects least squares, also
known as least squares dummy variables
(LSDV) (Baltagi 2005).
Random Effect Model
The random effects model is an
appropriate specification if we are drawing N
individuals randomly from a large population.
The assumptions for this model are (1) τi is
normal distribution (0, 2 ), ) εit disturbances
stochastic independent and identically
distributed IDD (0, 2ε ), (2) E(Xit, τi ) = 0 and
E(Xit, εit) = 0, Xit are assumed independent
with εit for all i and t.
Consistent estimator obtained by OLS,
but this case can make unbiased standart error.
Therefore, Generalize Least Square (GLS) is
better used for this model. (Baltagi 2005).
Chow Test
Chow test is used for examining the
significant between pooled model and fixed
effect model. The hypothesis for this test is:
H0 : τ1 = τ2 = ... = τN-1 = 0 (the model
followed pooled model)
H1 : There is one minimum i so τi ≠ 0 (the
model followed fixed effect
model)
The test statistic for Chow test is:

F0 =

(RRSS −URSS )/(N−1)
URSS /(NT −N−K)

[7]

with the restricted residual sums of squares
(RRSS) being that of OLS on the pooled
model, the unrestricted residual sums of
squares (URSS) being that of the LSDV
regression, N denotes quantity of observations
and K denotes quantity of variables. The
decision for reject H0 if F0 > FN-1,N(T-1)-K,α or if
p-value < α (Baltagi 2005).
Hausman Test
Hausman test is used for examining the
significant between fixed effect model and
random effect model. The hypothesis in a
population, if the individual is taken at random
an a sampel, the panel data model supposition
is random effect model, but if the individual
who used from the whole of the population,

3

then tend to use fixed effect model. The
hypothesis for this test is:
H0 : E(τi |Xit) = 0 (the model followed
random effect model)
H1 : E(τi |Xit) ≠ 0 (the model followed fixed
effect model)
The test statistic for Hausman test :
�2hit = �′ [Var(�)]−1 �

[8]

where � = �random − �fixed
�random = coefficient vector of independent
variable from random effect
model
�fixed = coefficient vector of independent
variable from fixed effect model
The decision for reject H0 if �2hit > �2(k,α) with
k is dimension vector of β or if p-value < α
(Baltagi 2005).
Spatial Panel Data Analysis
Panel data model with spatial specific
effect will have specifying interaction between
spatial units. The model may contain a
spatially lagged dependent variable or spatial
autoregressive process in the error term, it is
called spatial autoregressive model (SAR) and
spatial error model (SEM) (Elhorst 2010).
SAR focus on spatial correlation of
explanatory variable, while the SEM focus on
the shape of error (Anselin 2009). The
structure of spatial panel data is sorted first by
time and then by spatial units (Elhorst 2010).
Spatial Autoregressive Model (SAR)
The
spatial
autoregressive
model
expressed by the following equation:
yit = λ

N
j=1 wij yjt

+ �′it � + τi + εit

[9]

where λ is called the spatial autoregressive
coefficient and wij is an element of a spatial
weights matrix (W) describing the spatial
arrangement of the units in the sample and i ≠
j. Estimation for parameters in this model
using Maximum Likelihood Estimator (MLE)
(Elhorst 2010).
Spatial Error Model (SEM)
The spatial error model expressed by the
equation :
yit = �′it � + τi + ϕit ;
[10]
ϕit = ρ

N
j=1 wij ϕit

+ εit ;

[11]

where ϕ reflects the spatially autocorrelated
error term and ρ is called the spatial
autocorrelation coefficient. Estimation for

parameters in this model using MLE (Elhorst
2010).
Spatial Weight Matrix
Spatial weight matrix is a weight matrix
summarizes the spatial reliationship in the
data. The main diagonal from this matrix
consists of zeros. Because weight matrix
shows the reliationships between all of the
observation, its dimention is always NxN,
where N is te number of observation.
The most natural way to represent the
spatial relationships with area data is through
the concept of contiguity.
1 , if i and j are neighbours
wij =
0, otherwise
There are three types of contiguity that are
commonly considered :
1. Rook Contiguity
A spatial unit is a neighbour of another
unit if both areas share a common edge
(side).
2. Bishop Contiguity
A spatial unit is a neighbour of another
unit if both areas share a common vertex
(region that tangent corner from another
region that being observed).
3. Queen Contiguity
A spatial unit is a neighbour of another
unit if both areas share a common edge or
vertex.
After determining spatial weight matrix that
will be used, then do normalization. This
means that matrix is transformed so that each
of the rows/collumn sums to one. It is
common, but not necessary for normalization
matrix is used row-normalizing. Columnnormalizing is the other method for
normalization, otherwise also can do with
divide the element of matrix with the biggest
character root from that matrix (Dubin 2009;
Elhorst 2010).
Lagrange Multiplier Test
The examining of spatial interaction
effects in
cross-sectional data developed
Lagrange Multiplier (LM) tests for a spatially
lagged dependent variable and a spatial error
correlation. The hypothesis for this test is :
a. Spatial autoregressive model
H0 : λ = 0 (there is no dependence of
spatial autoregressive)
H1 : λ ≠ 0 (there is dependence of spatial
autoregressive)

4

b. Spatial error model
H0 : ρ = 0 (there is no dependence of
spatial error)
H1 : ρ ≠ 0 (there is dependence of spatial
error)
The test statistic for LM used:

LMλ =
LMρ =

[�′ �� ⊗
[�′ �� ⊗

/σ 2 ]2

[14]

J
�/σ 2 ]2

[15]

T×T W

denotes the Kronecker
where the symbol
product, IT denotes the identity matrix and it is
subscript the order of this matrix, � 2 denotes
mean square error of panel data model, W
denotes spatial weights matrix which have
been normalized and e denotes the residual
vector of a pooled regression model without
any spatial or timespecific effects or residual
vector of panel data with fixed/random effect
with spatial and/or time period. Finally, J and
Tw are defined by :
J=

1
2

�′ � �

+ TTW
′

TW = tr

+

� = (�� ⊗

) �

2

[16]
[17]

where,
� = ��� − (

′

)−1 ′

Method
Methodologies of this research are
summarized as follows:
1. Exploration of
data to observe the
characteristic of data.
2. Perform panel data analysis :
a. Estimate the parameter of pooled
model.
b. Estimate the parameter of fixed effect
model.
c. Examine the influence of individual to
establish a model that is used through
the Chow test. If H0 is accepted, the
pooled model is used, but if H0 rejected
then go to step (d).
d. Estimate the parameter of random effect
model.
e. Examine the significance of random
effect model or fixed effect model by
using the Hausman test. If H0 is
accepted, the random effect model is
used, but if H0 rejected then fixed effect
model is used.
3. Determine the spatial weights matrix (W).
4. Examine the effect of spatial interaction by
using Lagrange Multiplier (LM) test.
5. Estimate the parameters for the equation of
spatial panel data model.
6. Examine the assumptions

[18]
[19]

where INT denotes identity matrix and "tr"
denotes the trace of a matrix. The decision for
reject H0 if the value of LM statistic greater
than χ2(q) value with q=1 (q is the number of
spatial parameters) or if p-value < α (Anselin
2009; Elhorst 2010).

METHODOLOGY
Data Sources
The data that is used in this research is
secondary data. The data derived from three
sources: National Sosio-Economic Survey,
Data and Proverty Information, and Central
Java in Figure. Response variable of this
research is percentage of citizen with food
insecure in each regency or municipality. The
number of explanatory variables are five
variables. Cross-section unit in this research is
35 regencies or municipalities in Central Java
province which was observed for four years
(2007-2010) as time series unit. Description of
the variables can be seen in Appendix 1.

RESULT AND DISCUSSION
Data Exploration
Average value for over time of response
variable for whole regency or municipality can
be seen in Appendix 2. From this exploration
is gotten information that Wonosobo is a
regency with the highest average value of
citizen percentage with food insecure with
27.1%. Wonosobo has the lowest total of local
government original receipt and actual receipt
of region when compared with another
regencies with characterictic similarity of
agricultural
(Kudus,
Banjarnegara,
Purbalingga, and Temanggung).
Regency or municipality with the lowest
average value of citizen percentage with food
insecure is Semarang Municipality (5.3%).
Although Semarang Municipality is not
included municipality where became central of
food production, but when compared with
another regency or municipality in Central
Java province, total of local government
original receipt and actual receipt of region is
the highest. And Semarang Municipality is
capital of Central Java province.

5

Another information from this exploration
is found some groups of regencies or
municipalities that neighboring with average
value of citizen precentage with food insecure
almost same. The first group consist of
Purbalingga, Banjarnegara, Kebumen, and
Wonosobo with average value of citizen
precentage with food insecure revolve 26%.
The second group consist of Grobogan and
Sragen revolve 20%. The third group consist
of Boyolali, Sukoharjo, and Karanganyar
revolve 15%. And the last group consist of
Magelang, Purworejo, and Temanggung with
average value of citizen precentage with food
insecure revolve 16%.
Based on that information it has possibility
that food insecure could be influenced by
closeness inter region or municipality. It can
be happened because of characteristic
similarity
from
those
regencies
or
municipalities.
According to the data, can be seen that
percentage of citizen with food insecure that
consume calorie under basic requirement 2100
kkal/capita/day (Y) and percentage of
expenditure percapita for food (X5) have high
stretches of value as compared to the other
variables. To solve this problem, natural
logarithm transformation is taken for whole
variables.
Panel Data Analysis
This research used alpha 5%. The result for
estimating parameter of panel data analysis
for pooled model, fixed effect model and
random effect model are presented in Table 1,
Table 2 and Table 3. From Table 1,
explanatory variables that significant for
pooled model are local government original
receipt of regency or city (X3) and percentage
of expenditure per capita of regency or city for
food (X5) with R2 value is 41.34%.
Tabel 1 The result of pooled model
Variable
Coefficient
C
1.097
X1
0.128
X2
-0.014
X3
-0.241
X4
0.043
X5
1.375
R2
0.4133

P-Value
0.491
0.735
0.970
0.003
0.578
0.031

Then from Table 2, explanatory variables
that significant for fixed effect model are
production of paddy (X2) and local
government original receipt of regency or

municipality (X3). R2 value for this model is
95.13%.
Tabel 2 The result of fixed effect model
Variable
Coefficient
P-Value
C
10.251
0.000
X1
0.137
0.640
X2
-0.622
0.013
X3
-0.359
0.000
X4
0.021
0.502
X5
0.045
0.871
R2
0.9513
And explanatory variables that significant
for random effect model are harvested area of
paddy (X1), production of paddy (X2) and
local government original receipt of regency
or municipality (X3) that can be seen in Table
3. R2 value for this model is 95.17%.
Tabel 3 The result of random effect model
Variable
Coefficient
P-Value
C
5.544
0.000
X1
0.768
0.002
X2
-0.647
0.006
X3
-0.416
0.000
X4
-0.001
0.979
X5
0.048
0.860
R2
0.9517
The complete result for estimating
parameter of panel data model can be seen at
Appendix 3, Appendix 4 and Appendix 5.
Furthermore, will be done examine the
influence of individual to establish a model
that is used through the Chow and Hausman
Test.
Chow Test
Chow Test is used to choose appropriate
model betwen pooled model and fixed effect
model. Statistic value of cross-section F that is
goten is 32.457 with p-value 0.000, where pvalue (0.000) < alpha (0.05), so H0 is rejected.
It shows that appropriate model that is used for
temporary is fixed effect model. The complete
result of calculation for this test can be seen at
Appendix 6. Furthermore will be done
Hausman Test.
Hausman Test
Hausman test is used to choose appropriate
model betwen fixed effect model and random
effect model. Statistic value of cross-section
random that is gotten is 27.752 and p-value
0.000 where p-value (0.000) < alpha (0.05), H0
is rejected. So the model that is used is fixed

6

effect model. The complete of calculation
result for Hausman test can be seen at
Appendix 7.

influenced or have interact with regencies or
municipalities nearby. So the model that will
be estimates is SAR.

Spatial Panel Data Analysis
The method that can be used to detected
spatial effect is Lagrange Multiplier Test (LMTest). Before analyze spatial effect with LMTest, it is required determination spatial
weight matrix. The most natural way to
represent the spatial relationships with area
data is through the concept of contiguity.
Contiguity concept that is used in this research
is queen contiguity because this concept more
reguler to used and from data exploration is
estimated that food insecure could be
influenced by closeness inter region or
municipality. And from the map could be seen
that neighborhood position be in edge (side)
and corner (vertex).
After determining spatial weight matrix
then next step is normalization. This means
that matrix is transformed so that each of the
rows or column sums to one. Normalization
that is used in this research is rownormalitation.

Spatial Autoregressive Model (SAR)
Variables that significant in fixed effect
model are production of paddy (X2) and local
government original receipt of regency or
municipality (X3). Two of those variables are
used to build SAR model. The estimation and
examine result of the parameter can be seen in
Table 5. Variables production of paddy (X2),
local government original receipt of regency
or municipality (X3), and λ significant at α =
5%, that can be seen from p-value < α (0.05)
with R2 95.88%.

Lagrange Multiplier Test
Spatial effect can be detected by Lagrange
Multiplier (LM) tests for spatial autoregressive
model (SAR) and spatial error model (SEM).
The calculation result can be seen in Table 4.
LM-value for SAR is 63.956 bigger than χ2(1)
(3.841) at α =5% or p-value (0.000) < α
(0.05). And LM-value for coefficient SEM is
937.211, bigger than χ2(1) (3.841) at α =5% or
p-value (0.000) < α (0.05). So for both test H0
is rejected. It means that those are dependence
of spatial autoregressive and spatial error.
Tabel 4 The result of LM-Test
LM-Value
χ2(1)
SAR
63.9561
3.841
SEM
937.211
3.841

P-value
0.000
0.000

Because both tests are significant, estimate
the specification is appointed by the empirical
literatur. Elhorst (2010) gave example that in
the empirical literatur on strategic interaction
among local government, the situation where
taxation and expenditures on public service
interact with taxation and expenditures on
public services in nearby jurisdiction is follow
theoretically consistent for the spatial
autoregressive model. And from exploration
data was gotten that it has possibility that food
insecure in a regency or municipality could be

Tabel 5 Estimation and examination parameter
of SAR model
Variable
Coefficient
P-value
X2
-0.406
0.000
X3
-0.175
0.004
λ
0.420
0.000
R2
0.9588
So, appropriate models for percentage of
citizen with food insecure that consume
calorie under basic requirement 2100
kkal/capita/day (Y) in 35 regency or
municipality which was observed for 4 years
(2007-2010) are :
N

Ln yit = 0.420
j=1

wij yjt − 0.406Ln x2it

−0.175Ln x3it + Ln τi

The above models have cross-section effect
value (�� ) that can be seen in Appendix 8.

Examination The Assumption of SAR
Assumptions that must be fulfilled are
residual deviation is homogenous, nonautocorrelation inter residual, residual
normality,
and
no
multicollinearity.
Examination
the
first
assumption,
homogeneity of residual deviation can be
detected with Glejser Test. This test is
performed by regression betwen absolute
residual and all explanatory variables. If all
explanatory variables are not significant
influence toward absolute residual, it means
that the model is not happend heterogeneity
problem. Based on result of Glejser Test that
is shown in Table 6, observably that all
explanatory variables are not significant
influence toward absolute residual value at

7

alpha 5%. It provides an explanation that
homogeneity assumption is fulfilled.
Tabel 6 The result of Glejser test for SAR
Variable
Coefficient
P-Value
C
0.4258
0.068
X2
-0.008586
0.100
X3
-0.01510
0.235
Second assumption is non-autocorrelation
inter residual can be detected with DurbinWatson Test. Durbin-Watson value that is
gotten is 2.644 . At k=2, α = 5% and n= 140
are gotten dL= 1.6950 and dU= 1.7529.
Because of dU < DW < 4-dU, it indicates that
residual is interdependent at α = 5%. So nonautocorrelation assumption is fulfilled.

p
e
r
s
e
n
t

P-value=0.116

CONCLUSION AND
RECOMMENDATION
Conclusion
Fixed effect model with SAR are better
used for modelling food insecuity in Central
Java. This model show that production of
paddy (X2) and local government original
receipt of regency or municipality (X3)
influence percentage of citizen with food
insecure that consume calorie under basic
requirement 2100 kkal/capita/day (Y) with R2
95.88%. Coefficient of λ indicates that spatial
autoregressive effect significant in influencing
percentage of citizen with food insecure in
Central Java.
Recommendation
Based on that result, for government it is
suggested to decide foreigh for increasing
production of paddy and local government
original receipt. For the next researcher, it is
suggested to use another contiguity concept
like distance or characteristic similarity of
economic region (local government original
receipt of regency, general allocation fund,
etc).

REFERENCE
Figure 1 Probablity plot of residual
Third assumption is residual normality can
be detected with Kolmogorov-Smirnov Test.
H0 for this test is residual from model has
normal distribution. P-value that is gotten is
0.116, biger than α = 5%. It indicates that
residual from this model is normal
distribution, the assumption is fulfilled.
The last assumption that must fulfilled is
no multicollinearty inter explanatory variables.
For detecting multicollinearity, can be
detected with Variance Inflation Factors (VIF)
value. If for all explanatory variables have
VIF-value < 10, it means that no
multicollinearity inter explanatory variables.
Based on Table 7, all explanatory variables
have VIF-value < 10, it provides an
explanation that no-multicollinaerity assumption is fulfilled.
Tabel 7 The result of multicollinearity test for
SAR
Variable
VIF-value
X2
1.0
X3
1.0

Anselin L. 2009. Spatial Regression.
Fotheringham AS, PA Rogerson, editor,
Handbook of Spatial Analysis.London :
Sage Publications.
Baltagi BH. 2005. Econometrics Analysis of
Panel Data Third Edition. England : John
Wiley and Sons, LTD.
Dray S et al. 2006. Spatial modeling: a
comprehensive framework for principal
coordinate analysis of neighbor matrices
(PCNM). Ecological Modelling 196 483493.Department of Biology, University of
Regina.
Dubin
R.
2009.
Spatial
Weights.
Fotheringham AS, PA Rogerson, editor,
Handbook of Spatial Analysis. London :
Sage Publications.
Elhorst JP. 2010. Spatial Panel Data Models.
Fischer MM, A Getis, editor, Handbook of
Applied Spatial Analysis. New York :
Springer.
Food Security Council. 2006. Kebijakan
Umum Ketahanan Pangan 2006-2009.
Jakarta.
Gujarati DN. 2009. Basic Econometrics. Fifth
Edition. Singapore: The McGraw-Hill
Companies, Inc.

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Maria R, Da LS, Utma A, Simon S. 2009.
Faktor-Faktor
yang
Mempengaruhi
Ketersediaan Pangan Pokok Rumah
Tangga Petani di Desa Oenenu Utara
Kecamatan Bikomi Tengah Kabupaten
TTU. Department of Nutritient and Society
Health. Nusa Cendana University. NTT.
Nurfitriani L. 2012. Analisis Kinerja Fiskal
dan Faktor-Faktor yang Mempengaruhi
Ketahanan Pangan di Provinsi NTT
[Minithesi]. Bogor: Faculty of Economics,
Bogor Agricultural University.

Saliem H et al . 2001. Analisis Ketahanan
Pangan Tingkat Rumah Tangga dan
Regional. Research and Development
Agricultural Socio-Economics Center.
Bogor.
Sutawi. 2008. Tinjauan Distribusi Pangan.
Department of Agribusiness. University
of Muhammadiyah Malang.

9

APPENDIX

10

Appendix 1 Description of response and explanatory variables
Name of
Variables
Y

Description

Source

Unit

Percentage of citizen with food insecure that
consume calorie under basic requirement 2100
kkal/capita/day

National SosioEconomic Survey

%

X1

Total number of harvest area of paddy in each
regency or municipality

Central Java in
Figure

ha

X2

Total number of paddy production in each regency
or municipality

Central Java in
Figure

ton

X3

Total number of local government original receipt
in each regency or municipality

Central Java in
Figure

thousand
rupiahs

X4

Total number of actual receipt in each regency or
municipality

Central Java in
Figure

million
rupiahs

X5

Percentage of expenditure per capita for food in
each regency or municipality

Data and Proverty
Information

%

Appendix 2 Average value for over time of response variable for whole regency or municipality
Region/Municipality
Cilacap
Banyumas
Purbalingga
Banjarnegara
Kebumen
Purworejo
Wonosobo
Magelang
Boyolali
Klaten
Sukoharjo
Wonogiri
Karanganyar
Sragen
Grobogan
Blora
Rembang
Pati

Note:

i. =

�
�=1

�

��

i.

0.203
0.216
0.266
0.263
0.265
0.179
0.271
0.157
0.161
0.201
0.121
0.198
0.154
0.196
0.203
0.184
0.266
0.169

, T=1,2,3,4

Region/Municipality
Kudus
Jepara
Demak
Semarang
Temanggung
Kendal
Batang
Pekalongan
Pemalang
Tegal
Brebes
Magelang (Municipality)
Surakarta (Municipality)
Salatiga (Municipality)
Semarang (Municipality)
Pekalongan (Municipality)
Tegal (Municipality)

i.

0.108
0.103
0.207
0.112
0.153
0.205
0.174
0.184
0.221
0.152
0.252
0.105
0.146
0.084
0.053
0.087
0.102

11

Appendix 3 The result of panel data analysis for pooled model
Variable

Coefficient

C
X1
X2
X3
X4
X5

1.097055
0.127684
-0.014024
-0.241124
0.043435
1.374909
0.413388
0.391499
0.310027
18.88604
0.000000

R-squared
Adjusted R-squared
S.E. of regression
F-statistic
Prob(F-statistic)

Std. Error

t-Statistic

Prob.

1.589936
0.689999
0.4914
0.376613
0.339033
0.7351
0.369484
-0.037956
0.9698
0.081182
-2.970168
0.0035
0.077981
0.557001
0.5785
0.629900
2.182744
0.0308
Mean dependent var
-1.815267
S.D. dependent var
0.397438
Sum squared resid
12.87965
Durbin-Watson stat
0.245417

Appendix 4 The result of panel data analysis for fixed effect model
Variable
C
X1
X2
X3
X4
X5

Coefficient
Std. Error
t-Statistic
Prob.
10.25102
1.465146
6.996585
0.0000
0.136703
0.291376
0.469162
0.6400
-0.622441
0.247167
-2.518297
0.0134
-0.358664
0.075156
-4.772287
0.0000
0.020536
0.030485
0.673649
0.5021
0.044663
0.274924
0.162454
0.8713
Effects Specification
Cross-section fixed (dummy variables)
R-squared
0.951259 Mean dependent var
-1.815267
Adjusted R-squared
0.932250 S.D. dependent var
0.397438
S.E. of regression
0.103448 Sum squared resid
1.070155
F-statistic
50.04266 Durbin-Watson stat
1.767417
Prob(F-statistic)
0.000000

Appendix 5 The result of panel data analysis for random effect model
Variable
C
X1
X2
X3
X4
X5

Cross-section random
Idiosyncratic random
R-squared
Adjusted R-squared
S.E. of regression
F-statistic
Prob(F-statistic)

Coefficient
Std. Error
5.543601
1.065395
0.768167
0.238880
-0.647324
0.233087
-0.415564
0.064163
-0.000793
0.029905
0.047823
0.271125
Effects Specification

0.329833
0.304827
0.111886
13.19002
0.000000

t-Statistic
5.203328
3.215705
-2.777175
-6.476648
-0.026520
0.176385

Prob.
0.0000
0.0016
0.0063
0.0000
0.9789
0.8603

S.D.
Rho
0.291097
0.8879
0.103448
0.1121
Mean dependent var
-0.317575
S.D. dependent var
0.134193
Sum squared resid
1.677486
Durbin-Watson stat
1.281900

12

Appendix 6 Cross-section effect value (�� )
Region/Municipality
Cilacap
Banyumas
Purbalingga
Banjarnegara
Kebumen
Purworejo
Wonosobo
Magelang
Boyolali
Klaten
Sukoharjo
Wonogiri
Karanganyar
Sragen
Grobogan
Blora
Rembang
Pati
Kudus
Jepara
Demak
Semarang
Temanggung
Kendal
Batang
Pekalongan
Pemalang
Tegal
Brebes
Magelang (Municipality)
Surakarta (Municipality)
Salatiga (Municipality)
Semarang (Municipality)
Pekalongan (Municipality)
Tegal (Municipality)

��
0.287
0.274
0.492
0.384
0.364
-0.014
0.324
-0.013
-0.004
0.093
-0.408
0.003
-0.062
0.113
0.063
-0.150
0.331
0.006
-0.406
-0.472
-0.010
-0.309
-0.175
0.203
-0.218
-0.074
0.161
-0.127
0.391
-0.091
0.551
-0.420
-0.408
-0.706
0.031

13

Appendix 7 Map of Central Java Province

= Municipality
= Regency