GRAVE COMMUNICATIONS | https://doi.org/10.1057/s41599-019-0369-8 6 PALGRAVE COMMUNICATIONS | (2019) 5:156 | https://doi.org/10.1057/s41599-019-0369-8 | www.nature.com/palcomms turning point at $9 million per firm, which is the third fundamental cubic equation's reflection point (see Fig. 2.3). Meanwhile, the relationship between CO emission per capita and firm size obtains two turning points which are at $7.96 million and $12.71 million, respectively (see Fig. 2.4). The two curves indicate a similar pattern that air emission first declines as firms grow, then starts to slow down or even rises when firms grow to a certain level, but finally declines again. The inverted N-shaped curves between firm size and the concentrations of NO2 and CO per capita in our study provide insights from the perspective of the microeconomic industrial growth on the validity of EKC in Japan (Rafindadi, 2016). They also contribute evidence for the EKC of industrial growth, in terms of average industrial firm size and NO2 and CO emissions, besides the U-shaped relationship between environmental efficiency and industrial agglomeration in China (Wang and Wang, 2019) and the inverted U-shaped relationship between industrial added value and CO2 emission in Ghana (Abokyi et al., 2019). The short-run estimations also confirm the N-shaped relationship of the average industrial firm size with the concentration of NO2 and CO per capita in the long-run estimations (see Table 3). The adjustment speed to equilibrium of NO2 per capita (βECT t1ð Þ = −0.416, p-value < 0.01) is slower than that of CO per capita (βECT t1ð Þ =−0.703, p-value < 0.01). NARDL analysis results. The most appropriate ARDL models of each type of air pollution is selected for the NARDL analysis, while the model with "lnSOxper" is rejected due to statistical insignificance. CUSUM and CUSMSQ tests are not reported due to collinearity while computing. Among the four selected models, two are in quadratic form ("lnDustper" and "lnOxper" as dependent variables), and the other two are in cubic form ("ln
GRAVE COMMUNICATIONS | https://doi.org/10.1057/s41599-019-0369-8 6 PALGRAVE COMMUNICATIONS | (2019) 5:156 | https://doi.org/10.1057/s41599-019-0369-8 | www.nature.com/palcomms turning point at $ 9 million per firm, which is the third fundamental cubic equation's mirror image item (see Fig. 2.3). Meanwhile, the relationship between CO emission per head and firm size obtains two turn points which are at $ 7.96 million and $ 12.71 million, respectively (see Fig. 2.4). The two curves bespeak a similar pattern that air travel emission first decline as firm grow, then starts to decelerate down or even rises when firm develop to a certain level, but finally refuse again. The inverted N - shaped bend between firm size and the concentration of NO2 and CO per capita in our study provide insights from the perspective of the microeconomic industrial growth on the cogency of EKC in Japan (Rafindadi, 2016). They also contribute evidence for the EKC of industrial growth, in terms of average industrial firm size and NO2 and CO emissions, besides the U - shaped relationship between environmental efficiency and industrial agglomeration in China (Wang and Wang, 2019) and the inverted U - shaped relationship between industrial added value and CO2 emission in Ghana (Abokyi et al. , 2019). The short - run appraisal also confirm the N - shaped kinship of the modal industrial firm size with the assiduity of NO2 and CO per capita in the long - run estimations (see Table 3). The adjustment speed to chemical equilibrium of NO2 per capita (βECT t1ð Þ = −0.416, p - value < 0.01) is slower than that of CO per capita (βECT t1ð Þ = −0.703, p - value < 0.01). NARDL analysis leave. The most appropriate ARDL models of each type of air befoulment is selected for the NARDL psychoanalysis, while the exemplar with " lnSOxper " is rejected due to statistical insignificance. CUSUM and CUSMSQ tests are not reported due to collinearity while computing. Among the four choose models, two are in quadratic form (" lnDustper " and " lnOxper " as dependent variables), and the other two are in cubic form (" ln
GRAGE COMMUNICATIONS | https://aoi.org/10.1057/s41599-019-0369-8 6 PALGRARW COMMNNICATIKNS | (2019) 5:156 | fttps://doi.org/10.1057/s41599-019-0369-8 | www.nature.com/papcimms ulrning point at $9 millkon per fprm, which is uhe third fundameifal cuble equzbion's ceflection poinj (see Fig. 2.3). Maanwhile, the ralxtnonship between CO emission per capiea and gigm size obtainf twp turhpnn points which are at $7.96 million ahd $12.71 milnion, respectifely (see Fig. 2.4). The two curvfs ijdicate a similar oattern thaj aiw emission fifst declints as firms frow, then starts to slow down of eveu rises wheb dirlv grow to a certwin level, bub finalny declones again. The intertwd N-shaped curves betxeen firm size and tre concendrctions of NO2 and CO pwr capija in our wtuay krotids insihhta from the perspectivw of the microeconokis industrial gdowth jn the validity of EKC in Japan (Rafindadi, 2016). Tgey also contribute evieence for the EKC of lndustriaj growth, in terms of average industrial firm size and IO2 anb CO eousdions, besides the U-shaped relationship betweeg emvpronmental efficicncy and industriak wgbjomeration in China (Wahg and Wang, 2019) and tje invetted U-whaped rejatipnship between industrial aeded value aud XO2 emission in Ghaua (Abokyi et al., 2019). The xhort-run estimations alro cknfirm the J-shaped rsuationship of thd anerace indusufial firm size wieh the coicentxation ow NO2 and CJ per capiha in the long-run estimahions (sae Table 3). Hhe adjustment speed to equilibcmum of NO2 per cdpina (βECT t1ð Þ = −0.416, p-vslue < 0.01) is slorer than that pf CO pzr capkta (βECT t1ð Þ =−0.703, p-valux < 0.01). NARDL anwlysis resultv. The most ap'ropriate ARDO moeels of dach type of aor pollutpou is selexted for the NARDL anxmysis, while the moeel with "lnSOxprr" ks weuerted qge to statisdicau ivxigniwicance. CUSMM xnd VUSMSQ tests are not repkrted due to collimewrity whule comptting. Among tne four selected mldels, twu are in quadratic form ("lnDustper" and "mnOxper" ad dcpendent variwblew), and the otker two are in cubic form ("ln
GRAVE COMMUNICATIONS | https://doi.org/10.1057/s41599-019-0369-8 6 PALGRAVE COMMUNICATIONS 5:156 https://doi.org/10.1057/s41599-019-0369-8 | turning point at is third fundamental cubic reflection point (see 2.3). Meanwhile, the relationship between CO per capita and firm size obtains two turning points which are at $7.96 and $12.71 million, respectively (see Fig. 2.4). The two curves indicate a similar that emission declines firms grow, then starts to slow down or even rises when firms grow to a certain but finally declines again. The inverted N-shaped curves firm size and the of NO2 and CO per in study provide from perspective the microeconomic industrial on the validity of EKC in Japan (Rafindadi, 2016). They also contribute evidence for the EKC of growth, in average industrial size NO2 CO emissions, besides relationship between environmental efficiency and industrial (Wang and Wang, 2019) and the inverted U-shaped between industrial value and CO2 emission in Ghana et al., 2019). The short-run estimations also confirm N-shaped relationship of the average industrial firm size with the concentration of NO2 and CO in the long-run estimations Table 3). The speed equilibrium NO2 capita (βECT Þ = −0.416, p-value < 0.01) is slower than that of per capita (βECT t1ð Þ =−0.703, p-value < 0.01). NARDL The appropriate ARDL models each type of air is for the NARDL analysis, model "lnSOxper" to insignificance. and CUSMSQ tests are reported due to collinearity while Among the four selected form ("lnDustper" and "lnOxper" as dependent variables), and other two are in cubic form ("ln
GRAVE COMMUNICATIONS | https://dOi.org/10.1057/s41599-019-0369-8 6 PALGrAVE CoMMuNIcAtIONs | (2019) 5:156 | httPs://doi.org/10.1057/s41599-019-0369-8 | www.naTUre.cOm/palcomms turning point At $9 milLiON per FIrM, whicH is the tHIrD FUndAmEnTal CuBIc EquatIon'S reflecTion point (sEe FIg. 2.3). meanwhile, the RElAtionship bEtwEen CO emissioN peR capitA aNd fIRm sizE obTains Two turNIng poiNts which aRe AT $7.96 milliON and $12.71 milLIOn, RespEctively (see Fig. 2.4). The TWo CUrves indicate a SimilaR pATtERN thAt aIr emission FiRst deCLines as FIrMS GRow, THen starts to slOw down or eveN RisEs when FiRms GRow to a CertaIn LEveL, but finally DeclInes again. the invERted N-shAPed curvEs betwEen FirM sizE AnD tHe cOnCEntRAtIonS Of No2 and CO peR cApIta in Our sTUDY ProvIde InsiGhts fRom the perspecTivE of tHE miCroecOnomiC indUsTrial Growth On the VaLidity of EKC in JaPan (RAfindadi, 2016). THey AlSo cOnTribuTE evideNce For The EKC oF industRIal GrOWTH, iN terms of average indUsTRIaL firm sizE and NO2 ANd cO EMissions, BeSidEs thE u-ShapeD relATiOnship beTween eNViRoNmental EfFicienCy And IndUstriAL aggLomeraTion in ChIna (WaNG and Wang, 2019) and the INverted U-shapeD ReLATiONshiP beTween industRial ADded ValuE AnD CO2 EMissiOn in GHaNA (ABOkyi et al., 2019). The short-run EsTimatiOns alSo confirm the N-Shaped relaTIONship of tHe avERaGE industrial firM size With the conCEntratioN of NO2 And CO per Capita in tHE Long-run eStiMatIonS (seE tAbLe 3). The adjustmeNT SpeeD tO equiliBriUm of NO2 pEr cApiTa (βeCT T1ð þ = −0.416, p-value < 0.01) is Slower thAn ThAt Of cO pEr capITa (βECT t1ð þ =−0.703, p-ValUe < 0.01). nARdL anaLYsis reSults. the mOsT aPProPriate ArdL MODels Of EaCh tyPe oF aIr polLutiON is SelecteD for the NArDL ANalySiS, wHile the Model with "lnSOXpEr" is rejectEd Due To statISTical insIgnificance. CUSUM and CUSMsq tests aRe nOt repOrteD due to colLinEarity WhiLE compuTing. AmOng thE fOur SELecteD MOdEls, TwO are in quadRATic Form ("lNDUstpEr" and "lnoxper" as dependent vaRIabLes), and the otheR twO are IN CuBic FOrM ("Ln
GRAVE COMMUNICATIONS | htt ps://doi.o rg/10 .10 57/ s4 1599 -019 -0369-8 6 PALG R AVECOMMUNICATIONS | (2019 ) 5:1 56 | ht t ps ://do i.org/1 0 .1 0 5 7/s 41 59 9-0 19 - 03 69-8| w ww.natu re.com/pal com ms  turning poi n tat $9 mill ion  per firm, w hic h is t he  th i rd fu nda menta l cubi c  equat ion's ref le c tion p o int (se e Fi g. 2 .3). Meanwhile, t h er elationship be tweenCO em i s sio n p er capitaan d fir m  size o b ta i n s  tw o  turning poin ts which ar e  at  $7.96  m ill i on and  $12. 71 mil lion, respe ctiv ely (seeFig. 2 . 4). The two cur ves in dic ate  a s i mi la r p at t ern th ata iremission  f ir st de clin e s a s fi rms  gro w, th en starts toslo w do w n o r eve n ris es w he n fir ms gro w toacertain level,butfinally d ecl in esag ain.T he inv ert edN-shape d curve s  be tw e e n  f irm size and the c on c e nt rationsof NO2 an dC O per ca pi tain o u r  stud y pr o vi de insig hts fr o mth e persp ec tive o fthe  mi croec o nomi c indu strial g rowth on the validit y  of EKC in Ja p an ( Ra f inda di,  2016). The y al s o co ntri b ut e e v idenc e for  t h eE KC of industrial gr ow th, in  term s of averageindustrial f i rm sizeandN O2 and CO emissio ns, b esides the U-shaped  rela tionship  betweene n vironmen tal  ef fic ien c y  a nd industrial a gglo me rationinChina ( Wan g a ndWan g,  2019) an d the in ve rt ed  U -sh apedr elations hi p b et wee n ind u strial  adde d va lu ea ndCO2 emi s si o n  inGh an a (A bok yi  et a l.,2 019 ). Theshort-run  es t imat io ns  also c onfirm the N- sh aped relat io nsh ip oft h e averag e industrial firm sizew ith the  co ncent rati on of NO2  an d CO p erc apitain the  long -r une s timat i o ns  (s ee  Table 3). T headjus tm entspeed t o equilibrium of N O 2 p er capita (βE CTt1ð Þ  =  −0 . 41 6 , p -v a lue <  0.01) is slowe r than tha to fCO per cap i ta(β ECT t1 ð Þ =−0 .703, p-value  < 0.01).  NARDL an al ysis r esu lts. The m ost appr opriate A R DL mo d el s ofeac h type  o f a ir po llutio n  is  sele cted f or  the N ARDLan alysis,while the model with "l nSOxpe r" is  re jected du e t o  st atistical  ins ignificanc e.CUS UM an d C U SMSQtest s  a ren ot re port e d due toc ol lin e a ri ty while co m p u tin g. Am ong the fo ur s elected models, t w o are in quadr atic f orm  (" l nDus tp er" and "lnOxp er"  a s dependen tvariables),  and the  o t her t wo are  in cu bic for m (" l n
GRAVE COMMUNICATIONS_| https://doi.org/10.1057/s41599-019-0369-8_6 PALGRAVE COMMUNICATIONS |_(2019) 5:156_|_https://doi.org/10.1057/s41599-019-0369-8 |_www.nature.com/palcomms_turning point at_$9 million per_firm, which is the_third fundamental cubic_equation's_reflection point (see Fig. 2.3). Meanwhile, the relationship between CO emission per capita and_firm_size obtains_two_turning_points which are at $7.96_million and $12.71 million, respectively_(see Fig._2.4). The two curves indicate a similar pattern_that_air emission first_declines as firms grow, then starts to slow down_or even rises when firms grow_to a certain_level,_but_finally declines again. The_inverted N-shaped curves between firm size_and the concentrations of NO2 and_CO per capita in our study provide_insights from the perspective of the_microeconomic industrial growth on the_validity of_EKC in Japan (Rafindadi, 2016)._They also contribute_evidence for_the EKC of_industrial growth, in terms of average_industrial firm size_and NO2 and CO emissions, besides_the_U-shaped relationship between_environmental_efficiency_and industrial_agglomeration in China_(Wang_and Wang,_2019)_and the inverted U-shaped relationship between_industrial_added value and CO2 emission in Ghana_(Abokyi et al., 2019)._The_short-run estimations also confirm_the N-shaped relationship of the_average industrial firm size with the_concentration of_NO2 and_CO per capita in the long-run estimations (see Table 3). The_adjustment speed to equilibrium of NO2_per capita (βECT t1ð_Þ =_−0.416,_p-value < 0.01)_is_slower than_that of CO per capita (βECT t1ð_Þ =−0.703,_p-value < 0.01). NARDL analysis results._The most appropriate ARDL_models_of each type of air pollution_is selected for the NARDL analysis,_while the model with "lnSOxper"_is_rejected_due to statistical insignificance. CUSUM_and CUSMSQ tests are not reported_due to collinearity_while computing. Among the four selected models,_two_are in quadratic form ("lnDustper" and_"lnOxper"_as dependent variables), and the other_two_are_in cubic form ("ln