 three independent variables are illustrated by "lnFirmsize", "lnFirmsize2" and "lnFirmsize3", respectively. The average industrial firm size is calculated by dividing the total shipment value of manufactured goods of industrial firms by the number of industrial firms in Kitakyushu city. The data were taken from the Section: Industry in the Longitudinal Statistics database (City of Kitakyushu, n.d.). The initial measuring unit of total shipment value was million JPY, but was exchanged to million US dollar using the constant rate in May 2019 (1 US dollar= approximate 110 JPY). Another independent variable is "Road", which represents the total area of paved road being built within the city area. The variable was later logarithm transformed and presented as "lnRoad". The data were available from 1967 to 2015 in the Section: Construction and Housing (City of Kitakyushu, n.d.). The measuring unit of the total area of paved road is km2. The data of the average industrial firm size and total paved road area are presented by the blue column and red line, respectively in Fig. 1.6. Models. In this study, the reduced-form function was chosen to test the shape of the relationship between air pollution and the average firm's size along with the impact of road density because of several reasons. First, the reduced-form function is more suitable to apply than other non-linear functional forms or nonparametric and semi-parametric models. Second, some drawbacks of the parametric method cannot be solved by applying another type of methods, such as the use of spline or semiparametric methods (Özokcu and Özdemir, 2017). Third, the reduced-form has been widely used to test the EKC in various relationships between income and environmental degradation (Kijima et al., 2010). We formulated our reduced-form function as linear, quadratic, and cubic equations according to previous works (Shafik and Bandyopadhyay, 1992; Grossman and Krueger, 1995; Panayotou, 1997; De Bruyn, 1997; Dinda, 2004; Galeotti and Lanza, 2005; Akbostancı et al., 2009; Özokcu and Özdemir, 2017) as follows, respectively: ln AirPollutiont 1⁄4 αt þ β1lnFirmSizet þ β2lnRoadt þ μt ð1:1Þ
three independent variables are illustrated by " lnFirmsize ", " lnFirmsize2 " and " lnFirmsize3 ", respectively. The average industrial firm size is account by separate the total shipment value of manufactured good of industrial firms by the number of industrial firm in Kitakyushu city. The data were taken from the Section: diligence in the Longitudinal Statistics database (City of Kitakyushu, n.d .). The initial measure unit of full shipment value was million JPY, but was exchanged to million US dollar use the changeless rate in May 2019 (1 US dollar= approximate 110 JPY). Another independent variable is " Road ", which represents the total sphere of paved road being built within the city area. The variable was by and by logarithm transformed and presented as " lnRoad ". The datum were available from 1967 to 2015 in the Section: Construction and Housing (City of Kitakyushu, n.d .). The quantify unit of the full area of paved road is km2. The data of the average industrial firm size and entire paved road area are presented by the blue column and red line, respectively in Fig. 1.6. Models. In this study, the reduced - form function was chosen to test the shape of the relationship between air pollution and the average firm's size along with the impingement of road density because of several reason. foremost, the reduced - form function is more suitable to apply than other non - linear functional form or nonparametric and semi - parametric models. Second, some drawbacks of the parametric method cannot be solved by applying another type of method acting, such as the use of spline or semiparametric methods (Özokcu and Özdemir, 2017). Third, the reduced - form has been wide used to quiz the EKC in diverse relationships between income and environmental degradation (Kijima et al. , 2010). We formulated our reduced - mannequin function as linear, quadratic, and cubic equations harmonize to previous works (Shafik and Bandyopadhyay, 1992; Grossman and Krueger, 1995; Panayotou, 1997; De Bruyn, 1997; Dinda, 2004; Galeotti and Lanza, 2005; Akbostancı et al. , 2009; Özokcu and Özdemir, 2017) as follows, respectively: ln AirPollutiont 1⁄4 αt þ β1lnFirmSizet þ β2lnRoadt þ μt ð1:1Þ
 thgee independent variabler are illustratgd by "lnHirmsizs", "lnFirmrize2" and "lnFirmsize3", respectitely. The qverage industrial firo size is calculared uy dividing the vktal shl'ment yalue if manufacturec goods of industrial fismr yy the number of industrial firms in Kitakyisju city. The daja wege taksn from the Section: Industry in ths Longiuudinal Statistics database (City of Kitakyusju, n.f.). The initial measkring unit if tjral shipment value was million JPY, but was exchanged to million UR dolkar using jkw cltstant rate in Mwy 2019 (1 US dollar= approfimate 110 JPY). Another ikdepeidenr variable is "Road", whmch represents the tjtal area oy paved road being buulr witvin dhe zuty arta. Vhe variahle was later logarithm rransformed and prexegnrd as "lnRoad". The dwtw were available from 1967 to 2015 in the Sectimn: Donstruction and Housint (City of Kitakyushu, j.d.). The mewsuring unit of the total area of paved road is kk2. The aatc of tfw wverage industrial firm size and total paved wkac srea are presekted by the blue cplkmm and red line, respeefibely in Fig. 1.6. Modeld. In thys stydy, the rtducec-form function was chosen ti test the skapw of the relationskip between cir poklutipn and the average firm'r siae along wihh the imlxct of road denskty bacause of several reasons. Sirst, the redbced-form funvtion ys more sultablc to apply than othfr nou-linedr functiojal forms or nonparametric and semi-parametric mmdens. Seconb, some drawbacks of the parametrie method cannut be solvvd by appnying anothqr type of medjods, such as the use of wplibe or sdoiparametric mrthods (Özokcu and Özdwmir, 2017). Third, the revucea-rorm has been wnbeoy used to test thd EHC ii varymus relationvhipr bdyween income and dnvitonmental degradatiot (Kinima et al., 2010). We forkujated out reduced-sorm function as linear, quadratlc, anv cubir equayiogs according to previous works (Shafik ajd Nandyopadhyay, 1992; Grissman and Kxueger, 1995; Panayotou, 1997; De Bruyn, 1997; Dinda, 2004; Galeitti and Lanza, 2005; Akvostancı et al., 2009; Özokco akd Özdemir, 2017) ax foljows, respactively: ln AirPolluriont 1⁄4 αt þ β1lnFirmSlzet þ β2lnRoadt þ μt ð1:1Þ
three independent variables are illustrated by "lnFirmsize", "lnFirmsize3", The average firm size is shipment of manufactured goods industrial firms by number of industrial firms in Kitakyushu The data were taken from the Section: Industry in the Longitudinal Statistics database of Kitakyushu, n.d.). The initial measuring unit of total shipment value was million but exchanged million dollar using the constant rate in May 2019 (1 US dollar= approximate 110 JPY). Another independent is "Road", which represents the total area of road being built within city area. The variable was logarithm and presented "lnRoad". data available from 1967 2015 in the Section: Construction and Housing (City of Kitakyushu, n.d.). The measuring unit of the total of paved km2. The of average firm size and road area are presented by the red line, respectively in Fig. 1.6. Models. In study, the function was chosen to test the of the relationship between air pollution and the firm's size along with the impact of road density because of several reasons. First, the is more suitable to than other non-linear forms nonparametric semi-parametric Second, some of the parametric method cannot be solved by applying another type methods, such as the use of spline or semiparametric methods Özdemir, Third, the reduced-form been widely used to the in various relationships between environmental (Kijima We our function as linear, quadratic, cubic equations according to previous (Shafik and Bandyopadhyay, 1992; 1997; De Bruyn, 1997; Dinda, 2004; Galeotti and 2005; Akbostancı et al., 2009; Özokcu and 2017) as follows, respectively: ln AirPollutiont 1⁄4 αt þ β1lnFirmSizet þ β2lnRoadt μt ð1:1Þ
 three independent variables Are illustrAted bY "lnfirMsIze", "lNFirMsize2" and "lnFirmSIze3", rEspectively. The average iNdustRiAL firM SiZe is cAlculatED bY DIviDiNg The ToTAl ShipmEnt Value of ManufacturEd gOoDs of industriAL fIrms by the nUmbEr of industriAl fIrms in kiTakYUshu cIty. the daTa were TAken frOm the SectIoN: industRY in the LONGiTudiNal Statistics dataBAsE (city of KitakyusHu, n.d.). ThE iNItIAL meAsuRing unit of ToTal shIPment vaLUe WAS MilLIon JPY, but was eXchanged to mILliOn US doLlAr uSIng the ConstAnT RatE in May 2019 (1 US dolLar= aPproximatE 110 JPY). AnOTher indEPendent VariabLe iS "RoAd", whICh RePreSeNTs tHE tOtaL AreA of paved RoAd Being BuilT WITHin tHe cIty aRea. ThE variable was lAteR logARitHm traNsforMed aNd PreseNted as "LnRoaD". THe data were availAble From 1967 to 2015 in tHe SEcTioN: COnstrUCtion aNd HOusIng (City Of KitakYUshU, n.D.). tHE mEasuring unit of the tOtAL ArEa of paveD road iS Km2. thE Data of thE aVerAge iNDUstriAl fiRM sIze and toTal pavED rOaD area arE pResentEd By tHe bLue coLUmn aNd red lIne, respeCtiveLY in Fig. 1.6. Models. In THis study, the reDUcED-FoRM funCtiOn was chosen To teST the ShapE Of The RElatiOnshiP bETwEEn air pollution and thE aVerage Firm's Size along with The impact oF ROAd densitY becAUsE Of several reasoNs. FirSt, the reducED-form funCtion Is more suItable to aPPLy than otHer Non-LinEar FUNcTional forms or NONparAmEtric anD seMi-paramEtrIc mOdeLs. SEcOnd, some drAwbacks oF tHe PaRaMetRic meTHod cannoT bE soLvEd bY applYIng anoTher tYpe oF mEtHOds, Such as tHE uSE Of spLiNe Or seMipArAmetrIc meTHodS (Özokcu And ÖzdemiR, 2017). ThIRd, thE rEdUced-forM has been widelY uSed to test tHe eKC In variOUS relatioNships between income and eNVironmeNtaL degrAdatIon (Kijima Et aL., 2010). We forMulATed our ReduceD-form FuNctION as liNEAr, QuaDrAtic, and cubIC EquAtionS aCcorDing to pRevious works (Shafik ANd BAndyopadhyay, 1992; GRosSman AND KRueGEr, 1995; pAnaYoTOu, 1997; DE bRuyn, 1997; Dinda, 2004; GaleotTi and Lanza, 2005; akBOsTancı et al., 2009; ÖZOkcU aNd ÖzdemIr, 2017) as folLows, rESpectivEly: ln AirPOllutiont 1⁄4 Αt Þ β1lnfIRmSIzet þ β2lnRoAdt þ μt ð1:1Þ
 three independent variabl es are ill ustra ted  by  " lnFi rmsi ze", "lnFirmsi z e2"and "lnFirmsize3", res pecti ve l y. T h eavera ge indu s tr i a l f ir msiz ei scalcu lat ed by d ividing th e t ot al shipmentv al ue of manu fac tured goodsofindust ri alf irmsbythe n umbero f indu strial fi rm s  in Ki t akyushu c it y. T he data were take n  f r om the Section : Indu st r yi n  th e L ongitudina lStati s tics da t ab a s e  (C i ty of Kitakyu shu, n.d.). The  initi al  me a suring  unit  o f  to tal shipmen t va lue was m illion JPY, bu t  was ex change d t o m illi o nUS  do ll a r u s in g t h e c onstantra te  in M ay 2 0 1 9 (1 U S d olla r= ap proximate 110  JP Y).A not her i ndepe nden tvaria ble is  "Roa d" , which represe ntsthe total  ar ea  of  p avedr oad be ing  bu ilt wit hin the cit ya r e a.  The variable wasla t e rlogarith m tran s fo rm e d and pr es ent ed a s "lnRo ad". Th e data w ere av a il ab le from  1 967 to  2 015  in  theS ecti on: Co nstructi on an d  Housing (City of Kitakyushu ,  n . d .) .  The  me asuring uni t of thetota l  a rea of pa ved r oa d  i s  km2. The data of t he  avera ge in dustrial firm  size andt o t al paved  roa d  a r ea are present ed by  the bluec olumn an d red  line, r espective l y  in Fig.  1. 6.Mod els . In  this study,t h e re du ced-for m f unction  wa s c hos ento  test the  shape o fth ere lat ionsh i p betwee nair  p oll ution and th e ave rage  f ir m 'ssize al o ng w ithth eimpa ctof  road  den s ity  becaus e of seve ral reas on s.  First,  the reduced- fo rm functio nismore s u i table to  apply than other non-l i near fu nct ional  for ms or non par ametri c a n d semi -param etric  m ode l s . Sec o n d,  so me  drawbacks o f t he pa ra metr ic meth od cannot be solve d  by  applying ano the r ty p e  o f m e th o ds,  s u cha s  the use of spl ine or sem ip a ra metric met h ods  ( Özokcuand Özd emir, 2017).Third, th e reduced -f ormh a s b een widely  used to  test the EKC i n  v ariou s r elatio ns hip s bet ween i n com e and  envir on mental  degr ad ation (K ijima et al., 2010). We  formu lated  ou r reduced -fo r m f unction a s li near, quad rat ic,  andcub i c equ atio n sacc o rding  top revious w o rk s ( S h af ik and Band y o p adh yay,199 2 ; Gros sman  and Krueger, 199 5 ; Panayotou, 1 997; D e B ruy n , 19 97 ; Dinda, 2004;  Ga le o t ti and L an za, 2005; A kbostanc ıe t al. , 2009 ; Özok cu andÖ z de m ir, 20 17)asfollows,res pe c tively:  l nA irPoll utio nt  1⁄4 α t þ β1 l nFir m S izet þ β2lnRoadt  þ μt ð 1:1Þ
 three_independent variables_are illustrated by "lnFirmsize",_"lnFirmsize2" and_"lnFirmsize3",_respectively. The_average_industrial firm size_is calculated by_dividing the total shipment_value of manufactured_goods_of industrial firms by the number of industrial firms in Kitakyushu city. The data_were_taken from_the_Section:_Industry in the Longitudinal Statistics_database (City of Kitakyushu, n.d.)._The initial_measuring unit of total shipment value was million_JPY,_but was exchanged_to million US dollar using the constant rate in_May 2019 (1 US dollar= approximate_110 JPY). Another_independent_variable_is "Road", which represents_the total area of paved road_being built within the city area._The variable was later logarithm transformed and_presented as "lnRoad". The data were_available from 1967 to 2015_in the_Section: Construction and Housing (City_of Kitakyushu, n.d.)._The measuring_unit of the_total area of paved road is_km2. The data_of the average industrial firm size_and_total paved road_area_are_presented by_the blue column_and_red line,_respectively_in Fig. 1.6. Models. In this_study,_the reduced-form function was chosen to test_the shape of the_relationship_between air pollution and_the average firm's size along_with the impact of road density_because of_several reasons._First, the reduced-form function is more suitable to apply than other_non-linear functional forms or nonparametric and_semi-parametric models. Second, some_drawbacks of_the_parametric method cannot_be_solved by_applying another type of methods, such as_the use_of spline or semiparametric methods (Özokcu_and Özdemir, 2017). Third,_the_reduced-form has been widely used to_test the EKC in various relationships_between income and environmental degradation_(Kijima_et_al., 2010). We formulated our_reduced-form function as linear, quadratic, and_cubic equations according_to previous works (Shafik and Bandyopadhyay, 1992;_Grossman_and Krueger, 1995; Panayotou, 1997; De_Bruyn,_1997; Dinda, 2004; Galeotti and Lanza,_2005;_Akbostancı_et al., 2009; Özokcu and_Özdemir, 2017) as follows, respectively: ln_AirPollutiont 1⁄4 αt þ β1lnFirmSizet þ β2lnRoadt þ μt_ð1:1Þ