1
TOURISM AND ECONOMIC GROWTH: A me a-analysis o panel
da a s udies
Me cedes Cas o-Nuñoª, José A. Molina-Toucedo
b
and
Ma ía del P. Pablo-Rome o
c
a.
Depa men o Economic Analysis and Poli ical Economy, A da. Ramon y Cajal, 1
Uni e si y o Se ille, E-41018 Se ille, Spain
Tel.: (+34) 954 55 44 77
Fax: (+34) 954 55 76 29
[email p o ec ed]s
b. Depa men o Economic Analysis and Poli ical Economy, A da. Ramon y Cajal, 1
Uni e si y o Se ille, E-41018 Se ille, Spain
Tel.: (+34) 954 55 75 29
Fax: (+34) 954 55 76 29
[email protected]
c. Depa men o Economic Analysis and Poli ical Economy, A da. Ramon y Cajal, 1
Uni e si y o Se ille, E-41018 Se ille, Spain
Tel.: (+34) 954 55 76 11
Fax: (+34) 954 55 76 29
mpablo[email p o ec ed]
Abs ac
Al hough o decades i has been acknowledged ha ou ism likely con ibu es o
economic g ow h, heo e ical models ha conside a causal ela ionship be ween bo h
a e a ecen phenomenon. F om a sample o 11 s udies based on panel da a echniques
published h ough o 2011, and o a o al o 87 he e ogeneous es ima ions, a me a-
analysis is pe o med by applying models o bo h ixed and andom e ec s, wi h he
main objec i e being o calcula e a summa y measu e o he e ec s o ou ism on
economic g ow h. While he esul s ob ained poin o a posi i e elas ici y be ween
economic g ow h and ou ism, he magni ude o he e ec was ound o a y acco ding
o he me hodological p ocedu e employed in he o iginal s udies o empi ical
es ima ions.
KEYWORDS: Panel da a, Tou ism, Economic G ow h, Me a-analysis, Elas ici ies.
JEL Codes: C33, C83, L83, O40, O50.
2
1. INTRODUCTION
Al hough o decades i has been ecognized ha ou ism could con ibu e in
some way o economic g ow h, heo e ical models ha conside a causal ela ionship
be ween ou ism and economic g ow h a e a ecen phenomenon (Kim e al., 2006).
Lanza & Piglia u (2000) we e he i s o in es iga e his ela ion om an empi ical
poin o iew, while Balague & Can a ella-Jo da (2002) we e he i s o analyse he
ou ism-led g ow h hypo hesis (TLG) – i.e. he hypo hesis acco ding o which ou ism
gene a es economic g ow h – om an econome ic pe spec i e. F om he i s a emp ,
an inc easing numbe o a icles wi h he same objec i e – al hough o di e en
coun ies, using di e en me hodologies and ob aining di e en esul s –ha e been
published.
Mos o he s udies a e based on ime se ies and e e o a single economy.
Among hem, and wi hou p o iding an exhaus i e lis , se e al wa an men ion such as
ha o D i sakis (2004), Du ba y (2004), Ongan & Demi oz (2005), Gunduz &
Ha emi-J (2005), Oh (2005), Kim e al. (2006), Ka i cioglu (2007, 2009, 2010), Lee &
Chien (2008), B ida & Risso (2009). B ida e al. (2010), Chen & Chiou-Wei (2009) Jin
(2011), Lean & Tang (2010), and A slan u k e al. (2011). O hese, mos suppo he
TLG hypo hesis.
Among hese s udies he e is a g oup which uses panel da a analysis o
in es iga e he TLG hypo hesis. Al hough he numbe o hese s udies is smalle han
ha o ime-se ies s udies, a la ge numbe o coun ies a e included. This pe mi s an
unde s anding o be gained o he ela ionships ha occu ac oss a g oup o coun ies
(Lee & Chang, 2008) and an e alua ion o be made o he b oade o global impac o
ou ism (Sequei a & Nunes, 2008). Fu he o his, he ela ion be ween G oss Domes ic
P oduc (GDP) and ou ism in hese s udies is usually no isola ed because o he
a iables ha a e essen ial o g ow h a e also conside ed.
3
The aim o he p esen wo k is o e i y whe he ou ism con ibu es o
economic g ow h and o de e mine he magni ude o his con ibu ion by calcula ing
global measu es based on published scien i ic e idence a ailable h ough un il 2011. To
his end, me a-analysis echniques ha e been used, which allow he quan i a i e
syn hesis o nume ous es ima ions ob ained in p e ious s udies, as well as o de e mine
how ce ain me hodological app oaches in luence alues ob ained in hese es ima es.
We will only conside hose s udies based on panel da a o co obo a e he TLG
hypo hesis as hey p o ide global es ima ions which, consis en wi h Lee & Chang
(2008), e e o la ge samples o coun ies. Despi e he ex ao dina y g ow h o he
s udies examining he ela ionship be ween ou ism and economic g ow h using panel
da a, in such a sho ime, no quan i a i e sys ema ic e iew ha in eg a es all o he
in o ma ion has ye been made.
The use o me a-analysis was in oduced by Glass, (1976). In con as o he
adi ional na a i e e iew, he basic pu pose o me a-analysis is o p o ide he same
me hodological igo o a li e a u e e iew ha is equi ed o expe imen al esea ch
(Rosen hal, 1995). In he case o economic g ow h and de elopmen s udies, his
echnique has been used o in eg a e indings on he e ec s o iscal policies (Nijkamp
& Poo , 2004; Phillips & Goss, 1995), he in luence o income inequali y condi ions o
poli ical s uc u es (De Dominicis, Flo ax, & De G oo , 2008; Doucouliagos &
Ulubasglu, 2008), he con ibu ion o social capi al o economic g ow h (Wes lund &
Adam, 2010) and popula ion g ow h (Headey & Hodge, 2009), o he e ec i eness o
de elopmen aid (Doucouliagos & Paldan, 2008). In he ield o ou ism, gene al
applica ions o his echnique can be ound in ou ism esea ch (Dann, Nash & Pea ce,
1988), ou ism o ecas ing (Calan one, Di Benede o & Bojanic, 1987), and mo e
speci ically on ou is and economic impac s udies (Wagne , 2002; Wagne & Wobe ,
2003).
4
Me a-analyses o pa icula impo ance in his ield conce n hose pe o med on
ou ism income mul iplie s (Baaijens, Nijkamp & Van Mon o , 1998), egional
ou ism mul iplie s (Baaijens & Nijkamp, 2000), and ou ism demand (C ouch, 1995;
Lim, 1999). Mo e ecen ly, epo s ha e been published conce ning speci ic b anches o
ou ism such as ha by Ca lsen & Boksbe ge (2011) on wine ou ism, Weed (2009) on
spo s ou ism and Sa iisik, Tu kay & Ako a (2011) on yach ing ou ism.
This wo k is di ided in o six sec ions which desc ibe he me a-analysis app oach
aken wi h espec o ou ism-economic g ow h.
2. METHODOLOGY.
Following Glass e al. (1981) and Lipsey & Wilson (2001), he me a-analysis
me hod consis s o deducing a summa y e ec based on he combina ion o di e en
es ima ions (e ec sizes) om a selec ed sample o s udies by means o di e en
s a is ical echniques: he ixed-e ec s model (FEM) and he andom-e ec s model
(REM).
Unde a FEM (Bo ens ein e al. 2009) he selec ed s udies a e combined on he
p emise ha he e is no he e ogenei y among hem and he only de e minan s o he
weigh o each s udy in he me a-analysis would be i s sample size and i s own a iance
o wi hin-s udy a iance (in e se a iance weigh ed me hod: Bi ge, 1932 and Coch an,
1937). Assuming a sample o "m" es ima es o e ec sizes, (i = 1, 2… m), ep esen ing
a measu e o an analyzed e ec called T
i
, a summa y e ec 
 may be o mula ed as
(Bo ens ein e al., 2009): 

∑ 
∑
[1], whe e w
i
is he s a is ical weigh o he
i- h es ima ion: 

 1

 [2]
,
and 

he a iance o he i- h es ima ion, so ha :
∑

 1 .
I is possible ha he a iabili y among s udies is highe han ha expec ed by
pu e andomness, which would be de ec able in he i s ins ance by es ing he
5
hypo hesis o homogenei y. The mos widely used es was o iginally de eloped by
Coch an (1954); i calcula es he pa ame e Q, acco ding o:   ∑



 


[3].
Because o he low powe o his es , highligh ed by Takkouche e al. (1999) i
is ecommended ha a subg oup analysis o s udies o ha addi ional p ocedu es o
quan i y he possible he e ogenei y, such as he pa ame e I
2
(Higgins e al., 2003),
which indica es he p opo ion o he a ia ion be ween s udies (be ween-s udies
a iance) in he o al a ia ion due o he e ogenei y: 



 
[4], whe e 

(Tau-
Squa ed) is he be ween-s udies a iance and 

he wi hin-s udy a iance (due o
andomness).
I he e ogenei y is de ec ed, a REM should be app op ia ed (Bo ens ein e al.,
2009), which conside s ha he es ima ed e ec s o he included s udies a e only a
andom sample o all hose possible, and he ue e ec sizes o hem would be
dis ibu ed abou a mean e ec (wi h wo possible sou ces o a ia ion: ha exis wi hin
he s udies o andom e o and he a ia ion be ween s udies o ue dispe sion).
Applying he a iance weigh ed me hod, unde he REM, exp ession [2] is ans o med
and we ha e, o each i- h es ima ion, adjus ed weigh s (


 acco ding o [5]:






 
[5], whe e 

(Tau-Squa ed) is he be ween-s udies a iance and w
i
he
s a is ical weigh o an i- h es ima ion unde a FEM.
Wi h ega ds o he summa y e ec 
 (i.e. a mean e ec ob ained om "a
dis ibu ion o e ec sizes") we can calcula e: 

∑

∑

[6].
The possibili y o ob aining a biased summa y e ec mus be assessed, which is
de i ed om he p esence o publica ion biases as a esul o he ac ha many
comple ed s udies a e no ac ually published because hey do no achie e signi ican
e ec s, because hey a e un a o able o because hey ha e nega i e ou comes (S e ne e
al., 2000; Tho n on & Lee, 2000).

6
Analy ically, he publica ion biases can be de ec ed by he s a is ical me hods o
Begg (Begg & Mazumba, 1994), and Egge (Egge e al., 1997), and g aphically by he
namely unnel plo s diag ams. Howe e , he limi a ions o hese me hods (Tho n oln &
Lee, 2000; Macaskill e al., 2001), equi e applica ion o Du al and Tweedie's T im and
Fill echnique (Du al & Tweedie, 2000), which allows he numbe o missing s udies o
be de e mined and added o he analysis, ollowing which he combined e ec is
ecompu ed.
Finally, o assess he obus ness o s abili y o he calcula ed summa y e ec ,
sensi i i y analysis is pe o med.
3. PANEL DATA STUDIES AND ESTIMATIONS.
De ails o 13 s udies published h ough o 2011 which use panel da a o analyze
he ela ionship be ween ou ism and economic g ow h a e gi en in Table 1. These
s udies we e iden i ied by li e a u e sea ch echniques using Scopus, ScienceDi ec ,
Google Schoola and he main jou nals in ou ism esea ch
1
, using e ms as: ou ism,
economic g ow h, ou ism led g ow h hypo hesis and ela ed e ms. Pape s om o he
s udies iden i ied we e also used, which include no only a icles in scien i ic jou nals
lis ed in Jou nal Ci a ion Repo s (JCR) o o he da abases, bu also wo king pape s
(Wpape ) published on he In e ne ha ha e eached a ce ain scien i ic ecogni ion on
accoun o hei quali y o numbe o ci a ions.
All he s udies included in he analysis a e shown in Table 1 wi h an
iden i ica ion code, and he numbe o es ima ions in each s udy. Each o hese
es ima ions di e s depending on he es ima ion model, whe he o no addi ional
a iables we e used o explain economic g ow h, he ype o a iable used o measu e
1
Ryan (2005) shows he anking and a ing o academics and jou nals in ou ism esea ch.
7
ou ism, whe he he sample was classi ied in o subsamples, and he inclusion o no o
ins umen al a iables o dummy a iables o econome ic es ima ion.
Table 1: Panel da a s udies showing he ela ionship be ween ou ism and economic
g ow h.
Au ho
Yea
o
s udy
Code Classi ica ion
o s udy Sample Analysed
pe iod
No. o
es ima ions
Eugenio-
Ma in e
al.
2004 Eug Wpape La in Ame ican
coun ies
1985-1998 4
Sequei a
&
Campos
2005 Seca Wpape 72 coun ies 1980-1999 6
Sequei a
& Nunes
2008 Sequ JCR. Q3 Small, poo and
no mally
de eloped
coun ies
1980-2002 16
Fayissa e
al.
2008 Fayi JCR. Q3 Sub-Saha an
coun ies
1995-2004 4
Lee &
Chang
2008 Lee JCR. Q1 OCDE, Asia, La in
Ame ican and sub-
Saha an coun ies
1990-2002 20
Co és-
Jiménez
2008 Co JCR. Q3 Coas al egions o
I aly and Spain
1990-2000 12
P oenca &
Soukiazis
2008 Sou JCR. Q4 Po ugal egions
NUT II and NUT
III
1993-2001 6
Fayissa e
al.
2009 Fay Wpape La in Ame ican
coun ies
1995-2004 4
Adamau
&
Cle ides
2010 Adam open jou nal 162 coun ies 1980-2005 10
Na ayan
e al.
2010 Na a JCR. Q3 4 islands 1988-2004 2
Holzne 2011 Holz JCR. Q1 99 coun ies 1970-2007 4
See enah 2011 See JCR. Q1 Paci ic Islands and
de eloped
coun ies
1995-2007 6
D i sakis 2011 D i JCR. Q3 Medi e anean
coun ies
1980-2007 2
Sou ce: Own elabo a ion.
Two di e en empi ical models a e gene ally es ima ed: dynamic and non-
dynamic. The i s is de ined econome ically as ollows [7], in gene al e ms:
i ii i i i
uXTyy
ε
λ
β
φ
α
+
+
+
+
+
=
−1
[7], whe e y is he loga i hm o eal pe capi a
GDP, T is a measu e o ou ism de elopmen exp essed in loga i hmic e ms, X
8
ep esen s a ec o o o he explana o y a iables,
α
is a pe iod-speci ic in e cep e m
o cap u e changes common o all coun ies, u is an unobse ed coun y-speci ic and
ime-in a ian e ec ,
ε
is he e o e m and he subsc ip s i and ep esen coun y and
ime pe iod, espec i ely.
Non-dynamic models a e speci ied simila ly, bu wi hou he e m
1−i
y
φ
. They
can be de ined in gene al as ollows in [8]:
i ii i i
uXTy
ε
λ
β
α
+
+
+
+
=
[8].
The pa ame e β, which e lec s he es ima ed impac o ou ism on he GDP,
eaches a di e en in e p e a ion: in non-dynamic models, i e lec s he elas ici y o
p oduc i i y wi h espec o ou ism (because he a iables a e exp essed in na u al
loga i hms); while in dynamic models; i e lec s only pa o he e ec o ou ism on
p oduc i i y (which is p oduced in he same pe iod). The e ec s o ou ism expand in
ime, which is o say ha ou ism has an e ec on p oduc i i y a ious pe iods
he ea e depending on he alue o φ in [7].
I espec i e o whe he he models a e dynamic o no , he s udies also di e in
e ms o hose ha use addi ional a iables such as educa ion, physical capi al, e c., o
explain he g ow h o eal pe capi a GDP, compa ed wi h hose ha ela e only o he
ou ism g ow h a iable (A o B espec i ely) . O he impo an di e ences can be
summa ized as ollows: 1. Whe he he empo al e ec is included by i ue o he
coe icien α in he es ima ion ( ime dummies used); 2. The p oxy o ou ism expansion,
which is used o de ine T
2
(indica o s o ou ism a i als s. indica o s o ou ism
eceip s); 3. Those es ima ions ha using ins umen al a iables in es ima ing he
unc ion o no ; 4. Depending on he wide sample o coun ies o a speci ic se o
coun ies ha make up he panel da a.
2
Soukiazis & P oenca (2008) use as a p oxy o he ou ism a iable he accommoda ion capaci y o he
ou ism sec o . This p oxy is no based on ou ism a i als and ou ism eceip s, and is he e o e no
classi ied in ou me a-analysis ollowing his c i e ion.
9
Gi en hese di e ences, he me a-analysis conside s di e en g oups o simila
es ima ions, as shown in Table 2. The e a e wo se s o es ima ions ( ype 1 scena ios) –
dynamic and non-dynamic – because as s a ed abo e, he es ima ed β coe icien s a e
no di ec ly compa able be ween he wo model ypes. Wi hin each ype 1 scena io, 3
clus e s can in u n be made: hose ha con empla e he whole sample o each scena io
(o e all), and es ima ions ha include only ype A o ype B es ima ions ( ype 2
scena ios). Fu he mo e, wi hin each ype 2 scena io, 9 clus e s can be o med: hose
ha con empla e he whole sample o es ima ions o he scena io (o e all) and ype 3
scena ios. These combina ions gi e ise o a o al o 42 scena ios.
4. META-ANALYSIS RESULTS.
Thi een s udies we e iden i ied in ou sea ch, bu he es ima ions o Sequei a &
Campos (2005) and Fayissa e al. (2009), we e excluded om he me a-analysis because
he da a p o ided we e insu icien . The s udy hus encompassed he empi ical esul s
om 11 p e ious s udies (Table 1) ha ga e ise o a o al o 87 es ima ions ( he sample
o ou me a-analysis amewo k) epo ed in he o m o elas ici ies , which exp ess he
impac o he ou ism sec o on economic g ow h.
Table 2 summa izes he main esul s o he me a-analysis pe o med on ha
sample.
16
o e all sample o dynamic and non-dynamic scena ios, as well o hei espec i e A
and B subg oups.
I was ound ha he inclusion o empo a y a iables and he use o
ins umen al a iables ended o dec ease he andom poin es ima ions alue in all o
he ype 2 scena ios, and ha he andom poin es ima ions alue ob ained o hese
scena ios we e highe when a el income was used o measu e ou ism han when he
numbe o a i als was used.
Fu he o his, he andom poin es ima ion ended o be g ea e when he
es ima ions ha conside only la ge samples o coun ies (gene al coun ies) we e used.
In such cases, he es ima ed alue is unbiased. I es ima ions e e only o speci ic
coun ies, i.e. samples e e only o coun ies wi h a ce ain p o ile, he elas ici y ends
o be lowe . Howe e , i mus be aken in o accoun ha g oups o coun ies in his
scena io we e e y di e se, anging om Asian, La in Ame ican, Medi e anean and
sub-Saha an coun ies, o island g oups, economically poo coun ies, small coun ies.
This sugges s ha a mo e de ailed s udy o elas ici ies is equi ed based on he
cha ac e is ics o he coun ies in hose samples.
6. CONCLUSIONS
Theo e ical models ha conside a causal ela ionship be ween economic g ow h
and ou ism a e a mo e ecen phenomenon. Since 2002, an inc easing numbe o
a icles ha ha e in es iga ed his ela ion om an econome ic pe spec i e ha e been
published. A conside able p opo ion o hese s udies a e based on panel da a o analyze
e ec s o ou ism on economic g ow h ac oss a la ge numbe o coun ies. Acco ding o
he me a-analysis p esen ed in his pape , om 87 es ima ions ob ained using panel da a
echniques we can conclude ha ou ism posi i ely a ec s economic g ow h. Howe e ,

17
he du a ion o his posi i e e ec depends on me hodological ea u es o es ima ions
made in he o iginal s udies. Thus, he me a-analysis applied o es ima ions based on
dynamic unc ions shows ha elas ici y ( he p oduc i i y wi h espec o ou ism) in he
sho e m is small, yielding a andom poin e-adjus ed es ima ion o 0.002. Howe e ,
he ini ial e ec is p olonged in ime, so ha in he long e m he a e age alue o he
elas ici y is aised o 0.179, o signi ican and s able es ima ions.
The me a-analysis applied o es ima ions based on non-dynamic unc ions
showed ha he elas ici ies had an a e age alue o 0.266 o he o e all sample. The
alue o hese elas ici ies is none heless a ec ed by a ange o ea u es used in he
es ima ions ca ied ou . We ound ha as he model becomes mo e speci ic, he alue o
elas ici y, i espec i e o he case, ends o dec ease. Thus, he inclusion o explana o y
a iables o economic g ow h, in addi ion o ha o ou ism, ends o educe he alue
o he elas ici y, especially wi h espec o non-dynamic models. Also, when empo a y
a iables and ins umen al a iables a e conside ed, he alue o he elas ici y ends o
diminish.
Fu he mo e, he a iable used o measu e ou ism also a ec s he elas ici y. I
ou ism is measu ed in e ms o a el income, hen elas ici y ends o be highe han i
he ou ism is measu ed in e ms o ou is a i als.
Finally, i should be no ed ha he a e age elas ici y calcula ed in ou me a-
analysis was highe only when he s udies included we e based on a la ge sample o
ype-speci ic coun ies. Based on he me a-analysis p esen ed, we we e unable o
deduce a clea pa e n o how elas ici y a ies ac oss de ined g oups o coun ies,
because he es ima ions ob ained using panel da a o hese de ined g oups we e e y
he e ogeneous and di icul o compa e in his ega d. Thus, i may be in e es ing o
pe o m a me a-analysis on which he a e age elas ici y is de ined o g oups o
18
coun ies and ob ained using es ima ions om ime se ies and ela ed o indi idual
coun ies.
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ANNEX I
Table 3. Long-Te m dynamic mul iplie o ou ism on economic g ow h
CODE Model ype β
φ
Dynamic
mul iplie
(DM)
Adam 1 A 0.002**
(0.00056)
-0.1**
(0.0077) 0.02ª
Adam 3 A 0.00018**
(4.50E-05)
-0.01**
(0.0073) 0.018ª
Adam 4 A 0.00012*
(0.00006)
-0.09**
(0.017) 0.001ª
Adam 6 A 0.0041**
(0.00096)
-0.101**
(0.0076) 0.041ª
Adam 7 A 0.0039**
(0.0012)
-0.101**
(0.018) 0.038ª
Adam 8 A 0.00048**
(0.00012)
-0.1**
(0.0074) 0.004ª
Holz 1 A 0.011**
(2.00)
0.941***
(35.98) 0.186
Holz 2 A 0.018***
(2.84)
0.95***
(35.49) 0.360
Holz 3 A 0.008**
(2.08)
0.97***
(52.93) 0.267
Co 1 A 0.001**
(n.a)
0.895***
(n.a) 0.010
Co 2 A 0.006*
(n.a)
0.884 ***
(n.a) 0.052
Co 3 A 0.001**
(n.a)
0.919***
(n.a) 0.012
Co 4 A 0.006***
(n.a)
0.907***
(n.a) 0.065
Co 6 A -0.015
(n.a)
0.891***
(n.a) -0.138
Co 8 A -0.017**
(n.a)
0.942***
(n.a) -0.293
Co 9 A 0.001*
(n.a)
0.831***
(n.a) 0.006
Co 10 A 0.007***
(n.a)
0.830***
(n.a) 0.041
Co 11 A 0.001**
(n.a)
0.869***
(n.a) 0.008
Co 12 A 0.006***
(n.a)
0.857***
(n.a) 0.042
Eug 1 A 0.00036*
(1.68)
0.777*
(19.30) 0.007
Eug 2 A -0.0002*
(2.54)
0.765*
(12.64) -0.001
Eug 3 A 0.00063*
(1.92)
0.738*
(10.16) 0.002
Eug 4 A 0.00062*
(2.63)
0.597*
(4.14) 0.002
Fayi 3 A 0.0249***
(0.0081)
0.568***
(0.073) 0.058
See 1 A 0.12*
(1,95)
0.24**
(215) 0.158
See 2 A 0.06*
(1.95)
0.23***
(2.52) 0.078
See 3 A 0.064*
(1.96)
0.34***
(2.43) 0.097
See 4 A 0.14*
(2.04)
0.17*
(2.17) 0.169
See 5 A 0.033*
(1.87)
0.25**
(2.15) 0.044
See 6 A 0.08*
(1.89)
0.37**
(2.19) 0.127
Sequ 2 A 0.041** 0.927*** 0.562
25
(2.42) (17.47)
Sequ 3 A 0.026*
(1.92)
0.931***
(18.37) 0.379
Sequ 4 A 0.025*
(1.85)
0.891***
(20.77) 0.229
Sequ 5 A 0.048**
(3.77)
0.943***
(24.73) 0.842
Sequ 6 A 0.041**
(2.69)
0.924***
(23.14) 0.539
Sequ 7 A 0.095***
(4.44)
0.87***
(7.96) 0.731
A e age alue
o DM - - - 0.179
No e: Signi icance a ***1%, **5%, *10%, espec i ely.
The es ima ed unc ion is
yy
β
θ
+
=
∆
−1
. So
yy
β
θ
+
+
=
−1
)1(
, and
θ
β
=MD
n.a. No a ailable.
Sou ce: Own elabo a ion.