Solusi Analitik Rambatan Panas dengan Syarat Batas Tak Homogen Analytical Solution of Heat ...

50 Pages·2017·3.53 MB·English

Solusi Analitik Rambatan Panas dengan Syarat Batas Tak
Homogen
Analytical Solution of Heat Flow with Nonhomogeneous Boundary
Conditions

Jefery Handoko1, Suharsono S.1
1Jurusan Matematika FMIPA Universitas Lampung
[email protected], [email protected]
Diterima 28 November 2016, direvisi 1 Januari 2017, diterbitkan 28 Mei 2017
Abstrak
Masalah rambatan panas dirumuskan dalam bentuk persamaan diferensial parsial yang tak bergantung pada
waktu t dengan syarat batas tak homogen. Persamaan ini diselesaikan dengan metode analitik di sekitar titik
temperatur kesetimbangan ditentukan dengan metode pemisah peubah sehingga diperoleh solusi analitik.
Kata-kata kunci : Persamaan Diferensial Parsial, Rambatan Panas, Syarat Batas Tak Homogen.
Abstract
Heat flow problem is defined in the form of partial differential equation which is not depend on time t completed
by nonhomogeneous boundary conditions. This equation solved by analytic method around temperature
equilibrium point determined by the method of separation of variables for finding analytic solutions.
Keywords : Partial Differential Equation, Heat Flow, Nonhomogeneous Boundary Conditions
Teori/Metode
Pendahuluan
Konsep rambatan panas merupakan 1. Rambatan panas dengan sumber dan
kemajuan dari perkembangan teknologi, salah syarat batas tak homogen
satu misalnya pertukaran panas dan 1.1. Syarat batas terhadap waktu
pembangkit listrik panas bumi [1]. Energi
Rambatan panas (tanpa
panas dapat digunakan dalam kimia sebagai
sumber) pada batang besi seragam
contoh pada elektron pengelasan balok [2]
dan proses hidrasi reaksi kimia dengan panjang L dengan
[3].Perambatan dilakukan secara konveksi temperatur tertentu dengan suhu
dengan tabung [4-5] dan konduktif-konveksi A0 dan B0 di sisi kiri dan kanan.
dengan rotasi dan gradien panas [6]. Jika syarat awal dipilih, masalah
Optimisasi topologi pada panas [7] dan matematika untuk suhu u(x,t)
material untuk efisiensi dan minimum berat
adalah
dan volume [8] menggunakan proses
u ku Q(x) (1.1a)
perambatan. Pemodelan matematika
t xx
dilakukan pada pemanasan sementara u(0,t) A (1.1b)
lempeng [9], efek hisap/tiup aliran stabil [10],
u(L,t) B (1.1c)
efek lepas penyusutan [11], serta efek radiasi
termal [12]. u(x,0) f(x) (1.1d)

Pandang sebuah model rambatan
1.2. Titik temperatur kesetimbangan
panas pada batang besi seragamsepanjang
L dengan temperatur konstan pada sisi kiri Titik temperatur
dan sisi kanan. Persamaan ini menggunakan kesetimbangan r(x,t) dengan
nilai awal dan syarat batas. Metode pemisah temperatur diketahui dikatakan stabil
peubah tidak dapat langsung digunakan pada persamaan panasmemenuhi
karena syarat batas tak homogen. Untuk
r 0 (1.2a)
menganalisis masalah ini, definisikan titik xx
temperatur kesetimbangan dengan peubah dengan
waktu bebas dengan mengabaikan nilai awal r(0,t) A(t) (1.2b)
[13]. r(L,t) B(t). (1.2c)
Seminar Nasional Riset dan Industri 2016 101
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Dengan mengabaikan nilai
awal pada titik temperatur Misalkan
kesetimbangan dapat dinyatakan u(x,t) v(x,t) r(x,t) (2.11)
unik dalam bentuk persamaan
dengan nilai awal
B(t) A(t)
r(x,t) A(t) x(1.2d) B A
v(x,0) f(x) A x(2.12)
L
L

dan syarat batas
1.3. Metode pemisah peubah
v(0,t) 0 (2.13)
Misalkan
v(L,t) 0 (2.14)
u(x,t) v(x,t) r(x,t) (1.3a)
Dengan menyulihkan persamaan (1.3e -
dengan nilai awal
1.3g, 2.3) ke persamaan (1.3h) diperoleh
v(x,0) f(x) r(x,0)(1.3b)
v kv k . (2.15)
dan syarat batas t xx
Misalkan
v(0,t) u(0,t) r(0,t)(1.3c)
v(x,t) F(x) G(t) kt . (2.16)
v(L,t) u(L,t) r(L,t)(1.3d)
Dengan menggunakan metode pemisah
Dengan menggunakan metode
peubah didapat
pemisah peubah diperoleh
v F G k (2.17)
u v r (1.3e) t t
t t t
v F G (2.18)
u v r (1.3f) x x
x x x
dan differensiabel terhadap x vxx Fxx G . (2.19)
u v r . (1.3g) Substitusikan ke persamaan (2.16) denganc
xx xx xx
suatu konstanta diperoleh
Substitusikan persamaan (1.3d –
F
1.3f) ke persamaan (1.1a) sehingga
k xx c (2.20)
diperoleh
F
v kv Q(x,t) r kr .(1.3h)
t xx t xx G
Dengan metode pemisah peubah t c (2.21)
G
diperoleh hasil
sehingga
v(x,t) F(x) G(t) (1.3i)
c c
F G(t) k Fxx G (1.3j) F c cos x c sin x (2.22)
1 k 2 k

Hasil dan Diskusi
G Ce ct. (2.23)
Aplikasi Metode Pemisah Peubah Oleh karena itu
Diketahui persamaan panas dengan c c
v(x,t) e ct c cos x c sin x kt
sumber energi termal Q(x,t) sebagai berikut 1 k 2 k
u ku Q(x) (2.1)
t xx (2.24)
dengan
Akan dicari c dan c dengan syarat
u(x,0) f(x) (2.2) 1 2
batas dan nilai awal. Dengan persamaan (2.13
Q(x) k (2.3) - 2.15) diperoleh
u(0,t) A (2.4) 2
2n
u(L,t) B. (2.5) c k (2.25)
n L
Akan dicari solusi dari persamaan di atas.
Misal untuk studi kasus ini dipilih c ktecnt (2.26)
1,n
A(t) A (2.6) sehingga
B(t) B (2.7) v (x,t)
n
maka berdasarkan (1.2d) diperoleh
2n 2n
B A e cnt e cnt kt cos x c sin x kt. (2.27)
r(x,t) A x. (2.8) L 2,n L
L
Kemudian Dengan nilai awal v(x,0) diperoleh
r(0,t) A (2.9)
r L,t B . (2.10)
102 Seminar Nasional Riset dan Industri 2016
28 November 2016, Bandar Lampung, Indonesia
2n Persamaan panas dapat diselesaikan secara
c sin x g(x) (2.28) analitik dengan syarat batas tak homogen
2 L
n 1 menghasilkan solusi berbentuk
dengan 2n 2n
B A v(x,t) e cnt c cos x c sin x kt
g(x) f(x) A x (2.29) 1,n L 2,n L
n 1
L
Ucapan Terima Kasih
sehingga

2 L 2n Penulis mengucapkan terima kasih kepada
c g(x)sin xdx. (2.30)
2,n L 0 L seluruh dosen dan staff Jurusan Matematika
Universitas Lampung atas diskusi dan saran
Dengan prinsip superposisi
yang bermanfaat.
v(x,t) v (x,t). (2.31)
n
Referensi
n 1
sehingga diperoleh
[1] Salim N. Kazi, “An Overview of Heat
v(x,t)
Transfer Phenomena”, Penerbit

Intech,Open Access,2012, p. 125
2n 2n [2] R. Rai, P. Burgardt, J. O. Milewski, T. J.
e cnt c cos x c sin x kt. (2.32)
1,n L 2,n L Lienert, and T. DebRoy,”Heat Transfer
n1 and fluid flow during electron beam
Sebagai contoh misalnya
welding of 21Cr-6Ni-9Mn steel and Ti-
k 1 (2.33)
6Al-4V alloy”,Journal of Physics D:
A 5 (2.34) Applied Phyics 42,1-12 (2009)
B 10 (2.35) [3] K. Meinhard and R. Lackner,”Multi-
phase hydration model for prediction of
f(x) x (2.36)
hydration-heat release of blended
L 3 (2.37)
cements”, Cement and Concrete
n 10 (2.38) Research 38, 794-802 (2008)
maka [4] P. Canhoto and A. H. Reis,”Optimization
g(x) 2 x 5. (2.39) of fluid flow and internal geometric of
3 volumes cooled by forced convection in
Gunakan persamaan (2.25 – 2.27) sehingga
an array of parallel tubes”, International
diperoleh persamaan (2.32) yang dapat
Journal of Heat and Mass Transfer
digambarkan sebagai berikut.
54,4288-4299 (2011)

[5] T. Yokomine, J. Takeuchi, H.
Nakaharai,S. Satake, T. Kunugi, N. B.
Morley, and M. A. Abdou,”Experimental
investigation of turbulent heat transfer of
high prandtl number fluid flow under
strong magnetic field”, Fusion Science
and Technology 52, 625-629 (2007)
[6] J. M. Lopez, F. Marques, and M.
Avila,”Conductive and convective heat
transfer in fluid flows between
differentially heated and rotating
cylinders”, International Journal of Heat
and Mass Transfer 90, 959-967 (2015)
[7] E. M. Dede, “Multiphysics topology
optimization of heat transfer and fluid
flow systems”,Proceedings of the
COMSOL conference 2009 Boston,
October 8-10, 2009,MA,USA
Gambar 1. Model rambatan panas. [8] A. Kopanidis, A. Theodorakakos, E.
Gavaises, and D. Bouris,”3D numerical
simulation of flow and conjugate heat
Kesimpulan transfer through a pore scale of high
porosity open cell metal foam”,
International Journal of Heat and Mass
Transfer 53, 2539-2550 (2010)
Seminar Nasional Riset dan Industri 2016 103
28 November 2016, Bandar Lampung, Indonesia
[9] M. Y. Kim, “A heat transfer model for the
analysis of transient heating of the slab
in a direct-fired walking beam type
reheating furnace”, International Journal
of Heat and Mass Transfer 50,3740-
3748 (2007)
[10] K. Bhattacharyya and G. C. Layek,
“Effects of suction/blowing on steady
boundary layer stagnation-point flow
and heat transfer towards a shrinking
sheet with thermal radiation”,
International Journal of Heat and Mass
Transfer 54, 302-307 (2011)
[11] K. Bhattacharyya, S. Mukhopadhyay,
and G. C. Layek, “Slip effects on
boundary layer stagnation-point flow
and heat transfer towards a shrinking
sheet”, International Journal of Heat and
Mass Transfer 54, 308-313 (2011)
[12] K. Bhattacharyya, S. Mukhopadhyay, G.
C. Layek, and I. Pop, “Effects of thermal
radiation on micropolar fluid flow and
heat transfer over a porous shrinking
sheet”, International Journal of Heat and
Mass Transfer 55, 2945-2952 (2012)
[13] R. Haberman, “Applied Partial
Differential Equations with Fourier
Series and Boundary Value Problems,
Pearson Prentice Hall, 5th Edition,
2013.

104 Seminar Nasional Riset dan Industri 2016
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The Analysis of Causal Relationship between Innovation, Research
& Development Expenditures and Economic Growth in Indonesia
Devi Oktiani
Baristand Industri Bandar Lampung
divya_de_vi @yahoo.com
Diterima 28 November 2016, direvisi 1 Januari 2017, diterbitkan 28 Mei 2017
Abstract
This paper starts with the overview of Research and Development (R&D) expenditures as an indicator
of innovation. The objective of this research is to investigate the relationship between innovation
which represented as government‟s R&D expenditure and economic growth in country level in
Indonesia. Economic growth is represented by gross domestic product (GDP). The research focuses
on agriculture, forestry, and fishery sectors. The analysis uses Granger‟s causality test,u nit root test,
and Vector Auto Regression (VAR) model estimation. The causal relationship were analyzed on the
level which is stationary and has no co-integration relationship between variables. According to
Granger‟s causality test applied, there are short term and long term causal relationship between R&D
expenditure and economic growth.
Key word : R&D expenditures, GDP, Granger‟s causality, VAR mode l.
impacts of R&D expenditures on economic
Introduction
growth will be mentions, and then the results
The goal of innovation is create a positive will be presented and evaluated in the
change which make someone or something empirical findings section. The methodology
better, it also means renewal of science and part will offer information about the data set
technology that provide economic and social and methodology used in the empirical part
benefit [1]. This study focus on Research and of this study.
Development (R&D) expenditures and
economic growth related to innovation. R&D Literature Review and Methodology
activities are generally accepted as the

driving force of economic growth [2]. The
1. Theoretical Background
increase of R&D in a certain level required in
every country as the basis of innovation to Economic growth is influenced by
move [1]. innovation and imitation. Innovation means
firms invest significant resources in research
Indonesia, as the biggest country in south
and development (R&D) activities to discover
east Asia in term of nominal GDP and a
qualitatively improved products and capture
country with the big number population, its
associated profits. Imitation means when the
economic growth has impact in regional and
firms are successful, other firms were
international trade. Government of Indonesia
attracted by these profits and then they
spend 0.08 % of GDP as R&D expenditure, imitate and improve the development and
this number is far below the average of production of new products [4].
countries in the world which is 2.1 % of GDP
[3]. This study focuses on government The theoretical literature on R&D races
expenditure in agriculture, fishery, and between firms focuses almost exclusively on
forestry, as this three sectors has big impact the development of new products or
on national GDP. processes [4]. Economic growth depends on
several factors, includes the country‟s rate of
The objective of this study is to empirically
saving, the stock of productive inputs, and
observe the causal relationship between technical change. Technical change related
R&D expenditures and economic growth in to innovation, and this is a major determinant
Indonesia. In the study, Granger‟s acusality of economic growth [5]. The expenditures on
test will be applied by considering the data new product development, the R&D is the
about government expenditure and GDP. main factor for the economic growth of both
The positive or negative impact is analyzed developed and developing countries [6].
using Varian Autoregressive (VAR) model. In
the literature review section of this study the
Seminar Nasional Riset dan Industri 2016 105
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Innovation is not only related to or driven According to the theory of economic
by a relatively small group of high technology growth, since technical progress is closely
industries. Industries that are regarded as associated with the knowledge emerging
traditional industry or mature or „low-tech‟ from R&D activities, the technical change is
often generate substantial amounts of sales considered to be generated by formal R&D
from technologically new products and activities. Therefore, the new growth
processes. The service sector is also strongly economic theory included R&D as a factor of
innovative, across almost all of its component influence in the macroeconomic models [17].
activities, and this is particularly important
The impact of a technological innovation
since the service sector is the largest sector
will generally depend not only on its inventors,
in all advanced economies [7].
but also on the creativity of the eventual
On measuring the innovation, researchers users of the new technology [18].
may use either input measures such as R&D
Agricultural R&D is characterized by very
expenditures or innovation outcomes such as
long lags between research investments and
patents [8]. R&D intensity, the ratio of R&D
their impacts. The benefits of today‟s
expenditure to GDP is an important indicator
research investments may accrue primarily to
to measure the extent of a country's efforts in
some future generation of producers and
technological innovation. R&D expenditure,
consumers. As a result agricultural R&D has
by source of funds are grouped into:
been a highly profitable investment from
government funds, corporate funds, foreign
society‟s point of view [19]. Measuring
funds, and other funds [9], [10].
innovation in agricultural firms is complicated
Innovation process also requires a due to the complexities and uncertainties
number of non-R&D activities such as the linked to the sector [20]. A common
acquisition of patent, design, trial production, perception is that agricultural research is
training of personnel, market research and, primarily the domain of the public sector,
investment in new production capacity. [11]. while research in other sectors is the domain
R&D outputs includes copyrights, trademarks, of private sector. Recent years, R&D in
patents, and other forms of intellectual agricultural sectors is prominent in rich
property protection. Similar to tangible capital countries. The trend has trended up
assets such as machinery and equipment, significantly since 1981 and now almost half
the R&D outputs can be used repeatedly, the OECD‟s agricultural R&D is performed by
and generate income in a long period. the business sector [19].
Therefore, R&D expenditures is in common
For governments in developing countries,
with investment expenditures than with the
structuring agriculture to contribute to
intermediate expenditures that firms make to
economic growth has become a challenge
support their production processes [12].The
[21], it includes technological innovation to
non-R&D expenditure may be of
raise adequate food supply and
considerable quantitative importance. In
intensification of innovative agrarian
many of these countries, information about
programs [22]. While in OECD countries, the
non-R&D expen- diture on innovation is
composition of R&D has shifted from low to
virtually not available [11]. As a result,
high technology areas [23].
innovation measurement is consider only
R&D however, this is frequently considered Theoretically, there is a positive linkage
unsatisfactory. R&D is naturally and strongly between innovation and economic growth.
depend on the human capital factor, According to this hypothesis, R&D plays a
especially the highly qualified human major role in innovation, raising productivity
resources in science and technology. So to and accelerating economic growth [Cetin
support the R&D means not only to support 2013].The high level of R&D investment
the R&D projects and businesses but also leads to higher level of total factor
the human capital involved [13]. Research productivity (TFP), which will accelerates
and development is a key long-run economic growth. It is also possible that
determinant of productivity and consumer economic growth positively affect total R&D
welfare and Innovation is widely rcognized as investment. As a result, it can be argued that
the key to long-term economic prosperity [14], total R&D investment can Granger – cause
[15]. The innovation, R&D expenditures and economic growth, just as economic growth
the investments in technology are ensuring can Granger cause total R&D investment
competitiveness, progress, and a sustainable [24].
economic growth [16].
There are previous research which
studies the causal relationship between R&D
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expenditure and economic growth. Haskel sub-components (business and government
(2013) find a statistically significant R&D spending) on economic growth in 18
correlation between market sector TFP OECD countries over the period 1981-2012
growth and Research Council spending [25]. indicate that total and business R&D
Akcay (2011) use VAR model, Johansen co spending do not have a statistically
integration, Granger causalty to analyze the significant effect on economic growth.
causal relationship [24]. Pece (2015) provide However, government R&D spending
evidence of a positive relationship between influences economic growth in both the short
economic growth and innovation [16]. and long run. While R&D spending by
Sylwester (2001) investigates relationship government has a negative effect on
between R&D and economic growth in 20 economic growth in the short run this effect
OECD and G7 countries, employing multi becomes positive in the long run. [30].
varian regression analysis. The rsults
Sylvester (2001 studies the association
indicates that there is no strong causal
between R&D and economic growth in 20
relationship found between R&De
OECD countries using a multivariate
xpenditures and economic growth in OECD
regression. There is not found to be a strong
countries, while a positive relationship
association between the two. But when
between industry R&D expenditures and
considering only G-7 countries, there is re-
economic growth is establish in the case of
ported to be a positive association between
the G7 countries [24],[26]. The results of
industry R&D expenditures and economic
Granger causality test of R&D expenditures
growth [26].
cause GDP for Finland, France and Spain
indicate that GDP causes R&D expenditures The economic growth as an effect of R&D
in Denmark and there is no causality in the EU15 countries is less significant than
between variables in other countries [27]. that for other industrialized countries.
Comparation between EU 15 and the US
Bayarcelik (2012) develops a model to
indicates that the US has been able to
examine the relation between researchers
generate a stronger growth response from its
employed in R&D departments, R&D
R&D spending [31].
expenditures, patents as innovation
indicators, and Gross Domestic Product The impact of R&D activity has significant
(GDP) as economic growth. The results impact on economic growth only among the
indicates that there is a positive and more developed countries. Among middle
significant relationship between R&D income and less developed ones, the effects
investment and number of the employees in are insignificant [32]. As an example, Tuna
the R&D department with GDP. However, (2015) applies the Granger‟s causality
there is a significant but negative relation analysis, it is mentioned that there is no
between GDP and number of patents. Patent causality relationship between the R&D
involves costs in terms of various fees goverment expenditure and GDP in Turkey
including, such as, filing fees, agent fees and [2]. The empirical analysis finds that R&D
translation fees which makes patenting costly investment has played an important role in
in the short-run [28]. fostering productivity growth and productivity
impact of R&D is stronger in more advanced
Gumus (2015) provides an empirical
industries [33].
analysis of the relationship between R&D
expenditures and economic growth, and There are also instances where studies
determines whether this relationship differs show that innovative activities have a
with respect to the degree of development. negative impact on firm growth, most
The study includes data from 52 countries commonly caused by the inability of the high
from 1996 to 2010 and employs a dynamic cost of research to be recovered through
panel data model. The results indicate that increased sales or profits [34].
R&D expenditure has a positive and
According to the findings of Sylwestern‟s
significant effect on economic growth for all
study, which analyses the relationship
countries in the long run, which is consistent
between economic growth and R&D in OECD
with the relevant literature. While for
countries, it is not likely to reach a conclusion
developing countries, the effect is weak in the
proving that there is a relationship between
short run but strong in the long run, as
R&D expenditures and economic growth.
expected. The study adds new empirical
However, there is a positive relation between
evidence to the literature [29].
economic growth and the investments in
The study of the effect of total research industrial sectors in case of G-7 countries
and development (R&D) spending and its [26], [2].
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Innovation has a positive effect on per a. GDP Granger cause RND
capita outputs of both developed and H0: There is no significant impact of GDP o n
developing countries. However, only the RND.
large market OECD countries are able to H1: There is a significant impact of GDP on
increase their innovation by investing in R&D RND.
and the remaining OECD countries seem to b. RD Granger cause GDP
promote their innovation by using the know- H0: There is no significant impact of RND on
how of other OECD countries [35]. R&D GDP.
subsidies and R&D tax incentive are used by H1: There is a significant impact of RND on
most OECD countries and an increasing GDP.
number of emerging economies [36].
The positive impact of innovative activities
Result and Discussion
on firm is limited to the fastest growing firms,
while for the others it often plays a negative
The GDP of Indonesia is tend to increase
role, that for those firms that R&D does not
(Figure 1), the government expenditure f or
lead to a successful new product or process,
R&D is also increase (Figure 2), even the
it is simply a very large cost [29] .
percentage is still below the average
The analysis o f the efficiency of R&D countries. The government espenditure on
investment concludes that in the longer run, R&D is increase almost four times during
investment in capital goods is more efficient 2006, compare to 2005.
in achieving higher economic growth [37]. An

economy with a larger stock of human capital
will experience faster growth [38] .
Because of the different results related to
causal relatioship between R&D expenditure
and economic growth, several governments
increases their policy commitment to
innovation with significant impacts on levels
of R&D expenditures of their countries [39]. It
is important t o reform the management and
funding of public investment in science and
research, as well as public support to
innovative activity in the private sector.
2 . Methodology

Economic growth is measured as GDP.
Innovation is measured as Government Figure 1. Annual GDP of Indonesia (Million
expenditure for R&D in agriculture, fishery, Rupiah)
and forestry. The annual secondary data of Source : Food and Agriculture Organization
GDP and R&D government expenditure are ot The United nations[ 40]
collected from FAO [40], [41]. The stationary
of each variable, GDP and R&D are tested by
unit root test. The Granger‟s causality test is
applied on analyses the causal relationship
Woo l. Analysis uses Eviews software.
The variables is set in natural logarithmic
in order to satisfy the linear parameter
condition. The following model is used :
lnGDP = c +α1 ln RND + U …………..
it it i t
(1 )
where GDP is GDP and RND is government

expenditure for R&D. This model is used in
previous research [29], [42] ,[6] .
Figure 2. Annual Government R&D
The following hypothesis for analyze the
Expenditure of Indonesia( Million Rupiah)
causal relationship :
108 Seminar Nasional Riset dan Industri 2016
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Source : Food and Agriculture Organization ADF test statistic for LNRND (-48.62) is
ot The United nations [41]. below the ADF critical value on 5 %
significant level (-4.24), the null hypothesis
Variable RD is exponential, in order to satisfy ran be rejected, it means LNRND has no unit
the linear parameter condition as one root or stationary.
prerequisite condition in linear regression
A causal relationship test is applied in
method, the variables is converted in natural
order to determine the direction of cause and
logarithmic (Figure 3)
effect relationship between series examined
in the research. Granger causality test based
on Vector Autoregression (VAR) model is
applied using stationary LNGDP and LNRND
series. In VAR model, the causal relationship
considering the variables in the previous year.
This analysis considering the second lag (t-2).
Software Eviews estimates the causal
relationship based on the following equation:
LNGDP = α + α1LNGDP + αLNGDP +
t 0 t-1 t-2
β1LNRND + β2LNRND +ε ……. (2)
t-1 t-2 t
LNRNDt = α0 + α1LNRND + αLNRND +
t-1 t-2
Figure 3. Ln GDP and Ln RND β1LNGDP + β2LNGDP +μ ……. (3)
t-1 t-2 t
The Granger causality indicates that
The stationary of series included in the
LNRND Granger‟s cause LNGDP, while
analysis is tested. In the process, ADF root
LNGDP does not Granger‟s cause LNRND
test is applied on the level, using the Akaike
(Table 3). The null hypothesis that LNRND
Information Criteria (AIC). The basic
does not Granger cause LNGDP can be
hypothesis for the unit root test is that each
rejected on 10 % significant level because
variable has a unit root.
the probability is 0,0684 , less than 10%. The
null hypothesis that LNGDP does not
Table 1. LNGDP Unit Root Test
Granger Cause LNRND cannot be rejected
t-Statistic Probability as the probability is 0.1092.
ADF test statistic - 0.0421
Table 3. Granger Causality Test
3.451329
Test 1% - F-
critical level 4.582648 Null Hypothesis Statistic Prob.
values 5% - LNRND does not Granger
level 3.320969 Cause LNGDP 13.6265 0.0684
10% - LNGDP does not Granger
level 2.801384 Cause LNRND 8.15447 0.1092

ADF test statistic for LNGDP (-3.45) is The following VAR models based on
below the ADF critical value on 5 % equation 2 and 3 is applied :
significant level (-3.32), the null hypothesis
LNGDP = 2.543712 + 0.147829 LNGDP +
ran be rejected, it means LNGDP has no unit t t-1
0.398960 LNGDP + 0.527563 LNRND +
root or stationary. t-2 t-1
0.037125 LNRND …. (5)
t-2
Table 2. LNRD Unit Root Test LNRNDt = 4.144854 + 0.203361 LNRND +
t-1
0.263321 LNRND + 0.082252 LNGDP +
t-Statistic Probability t-2 t-1
0.263321 LNGDP …… (6)
ADF test statistic - 0.0001 t-2
48.62525 Table 4. Vector Autoregression (VAR)
Test 1% - Estimates
critical level 5.835186
LNGDP LNRND
values 5% -
level 4.246503
10% - LNGDP(-1) 0.147829 0.082252
level 3.590496 standar error (0.16927) (0.17032)
t-statistic [ 0.87331] [ 0.48294]
Seminar Nasional Riset dan Industri 2016 109
28 November 2016, Bandar Lampung, Indonesia
has significant and positive impact on
LNGDP(-2) 0.39896 0.263321 economic growth.
standar error (0.17292) (0.17399)
Referensi
t-statistic [ 2.30712] [ 1.51343]
[1] Burcay Yasar Akcali and Elcin
LNRND(-1) 0.527563 0.203361 Sismanoglu, “Innovation and the effect
standar error (0.22388) (0.22526) of research and development (R&D)
expenditure on growth in some
t-statistic [ 2.35647] [ 0.90280]
developing and developed countries”,
Social and Behavioral Science 195,
LNRND(-2) 0.037125 -0.052704
768-775 (2015)
standar error (0.02135) (0.02148)
[2] Kadir Tuna, Emir Kayacan, and Hakan
t-statistic [ 1.73906] [-2.45372]
Bektas, “The relationship between
research & development expenditure
C 2.543712 4.144854 and economic growth : the case of
standar error (1.26843) -1.27624 Turkey”, Social and Behavioral Science
t-statistic [ 2.00540] [ 3.24771] 195, 501-507 (2015)
[3] The worlbank, http://data.worldbank.org/
R-squared 0.999567 0.997851 indicator/GB.XPD.RSDV.GD.ZS,
accessed 20 November 2016
F-statistic 1153.755 232.2076
[4] Paul S. Segerstrom, “Innovation,
Akaike AIC -6.118065 -6.105797
imitation and economic growth”
Akaike AIC -12.4013
Econometrics and Economic Theory
Paper 8818, 1-38, 1990
[5] Phillip LeBel , “The role of creative
In order to observe the stability of VAR innovation in economic growth: Some
model it is necessary to check the roots of international comparisons”, Journal of
characteristic polynomial. If all of the roots in Asian Economics 631, 1-14 (2008)
polynomial fungtion is within the circle or its [6] Erdil Sahin B, “The relationship between
absolute value is less then 1, it means that R&D expenditures and economic
VAR model is stable. VAR model in this growth: panel data analysis 1990-2013”,
analysis is stable (Table 4) the absolute EY International Congress on
value of each variable is less than 1 (Table 5). Economics II "Growth, Inequality and
Poverty” November 5-6, 2015, Ankara
Table 5. Unit Root Test of VAR Model
Turkey, pp. 1-18
Root Modulus [7] Lynn K. Mytelka and Keith Smith,
“ Innovation theory and innovation
0.88753 0.88753
policy: bridging the gap”, Paper
-0.44915 0.449151
presented to DRUID Conference,
-0.043595 - 0.274536i 0.277976 Aalborg, June 12-15
-0.043595 + 0.274536i 0.277976 2001,UNU/INTECH1 Keizer Karelplein
19 6211 Maastricht, The Netherlands,
It can be concluded that government
pp. 1-22
expenditure on research and development
[8] Poh Kam Wong, Yuen Ping Ho, and
has significant and positive impact on
Erkko Autio, “Entrepreneurship,
economic growth. It is necessary to make
innovation and economic growth:
policy and regulation more conducive to
evidence from GEM data”, Small
innovation. Government investment in
Business Economics 24, 335–350
science and research development can play
(2005)
an important role in development and other
[9] Hi Nongfu and Zhang Shiyun, “ Impacts
general-purpose technologies and in
of R&D expenditure on economic
enabling further innovation.
growth and structure based on Beijing
dynamic CGE model”, unpublished
Conclusion
[10] Ioan Radu Petrariu, Robert Bumbac,
The Granger causality indicates that in and Radu Ciobanu, “Innovation: a path
Indonesia, government expenditure on R&D to competitiveness and economic
Granger cause economic growth on GDP, growth. The case of CEE countries”,
while GDP does not Granger cause R&D Theoretical and Applied Economics
Government expenditure. Government Vol.XX no.5(582), 15-26, 2013
expenditure on research and development