Panel data models for regional development

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P

ANEL DATA MODELS FOR REGIONAL DEVELOPMENT

Sorin Daniel MANOLE

Associate Professor, Ph.D., "Constantin Brâncoveanu" University of Piteşti e-mail: [email protected]

Antonio TACHE

Main researcher 3, National Institute for Research and Development in Constructions, Urbanism and Sustainable Spatial Development

URBAN-INCERC, e-mail: [email protected]

Abstract. O ne of t he goals of t he nat ional d evelopment policy is t o support the sustainable econom ic and social growt h of regions territorially ba lanced in Roma nia in ord er to reduce econom ic a nd social d isparities among regions. This paper aims at ident ifying inf luentia l factors to the num ber of tou rists and national road densit y, ind icators that charact erize tou rism, nam ely transp orts - two of the regional developm ent priorit ies. To t his end, pooled linea r regress ion models with spatia l specific eff ects have been us ed for cross-s ectiona l units. However, model equations qua ntify t he intensit y of highlight ed links a nd assess t he effects of influ ence factors upon t he t wo ind icators. The stud y shows t hat the nominal GDP is an important d irect inf luence factor upon nat ional road densit y and, the GDP per capita and the number of emp loyees per 1,000 inha bita nts are relevant factors which inf luence tourist activit y, the former d irectly and t he latter reversely.

Key words: regional development; sustainable development; panel data

models; Romania

1. I ntro ductio n

1.1. Re gional Deve lopment Policy Regional develo pme nt poli cy is one o f the mo st im por tant and mo st com ple x poli cies of the Euro pe an Union as by its aim of re ducing e co nomi c and soci al di spari ties am ong various re gions o f Euro pe , it acts upo n some signi fi cant ar eas to develo pme nt, such as: e conomi c gro wth and the SME se ctor , tr ansports, agri culture , urban developm ent, envi ronm ental

protection, em ployme nt and o ccupatio nal trai ning, education, ge nder eq uali ty etc.

Regional progr ess has paramo unt im por tance in term s o f the pri nci ple s and ob je cti ves of sustainable developm ent and due to the fact that o ur co untry shows a te ndency to increase re gional di spari ties r elate d to e co nomi c and soci al gro wth, r ational use o f re so ur ce s, and envi ronm ental infr astr ucture q uality (Mini stry o f

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Environm ent and Sustainable Gro wth, Natio nal C entre fo r Sustainable Growth, 2008).

At the same tim e, regional developm ent m ust have a key feature - sustai nabili ty . In or der to get a re al advantage in the futur e, Rom ani a m ust im pleme nt the sustainable developm ent co ncept at regional le vel, wher e str uctur es ar e mo re fl exi ble and the goo d practical solutions can be rapi dly assimilate d (Fistung et al , 2005).

The Regi onal De vel opme nt Natio nal Str ateg y (SNDR) fo r 2014-2020 whi ch shows the Rom ani an Go ver nm e nt’s vie w o n re gio nal develo pm ent sets r egi ons’ de vel o pme nt prio ritie s as wel l as the i nstitutio nal r el atio nshi ps that facili tate the co rr elati on with se ctor al strate gie s. Two of the develo pm e nt prio ri tie s e nvi sage tr anspor ts and to uri sm : De ve lo pme nt Pr ior ity 3 – The de ve lo pm ent o f re gio nal and lo cal i nfr astructure and Develo pm ent Pr iori ty 6 – Sustai nabl e To uri sm De ve lo pme nt.

The road network , a signi fi cant consti tuent o f tr ansport infr astructure i s the basi c suppo rt to an are a’s socio -e co nomi c d-ev-elo pm -ent. Th-e q uanti ty and q uality of ro ad infr astructure re fle ct bo th the civili zation le vel, and the availabili ty for de velo pment and gro wth (Mini str y o f Regional

Developm ent and Publi c

Admini str atio n, 2013).

To urism develo pme nt helps incr ease re gions’ attracti veness, q uali ty of life , e nviro nme nt protection and pre ser vati on, and al so achi eve a hig h degr ee of so ci al co hesi on (Mini stry o f

Regional Developm ent and Publi c Admini str atio n, 2013).

Spe ciali ze d li ter ature re fle cts regional developm ent issues i n many studies. Fi stung, in „Sustai nable Regional Growth, a New Co nce pt o r a Ne ed” com par ati vely analyzes the conce pts o f sustainable de velo pment and re gional develo pme nt and re views sustainable developm ent models at re gional level . Mocanu and Per dichi pro poses a model to assess sustainable develo pme nt at co unty and regio nal l evel com prisi ng 19 indi cator s gro upe d into fo ur dime nsio ns (e conomi c, so cial , insti tutio nal and envi ronm ental dime nsio ns) aggr egate d i nto a com posi te inde x. Chiri ţă and Dobre scu propo se several steps withi n national priori tie s as a Romanian develo pme nt mo del at re gional level . Anto ne scu sho ws that the pro fo und changes taking pl ace at worl d level m ake spe ciali sts develo p re gional theorie s and mo del s char acteri ze d by incr ease d re alism as com par e d to the ol d approaches, studies the issue of di spari tie s with m any face ts when i ntro ducing thi s conce pt (co nver gence , polarization, agglomer atio n, co ncentr ation, dispe rsio n) and analyzes the asse ssme nt o f publi c i nterve ntio ns at re gional le vel.

In or der to cl earl y r ender the pro ce sse s and phe nome na that o ccur in an e conomi c or admini strati ve system , with the aim o f i ncre asi ng e ffi cie ncy and i mproving its per form ance , a mo delli ng pro ce ss i s re qui re d. Multi ple mo del types for re gional de velo pme nt ar e highlig hted, willing to tr uly capture curre nt facts and to em phasize e co nomi c laws that appro ximate such facts.

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1.2. Panel Data Models in Econ omic and Econ ome tr ic S tudies

The pre se nce o f m ul ti pl e functio nal li nk s i n re gio nal e co no my amo ng pr o ce sse s, be ing vari ab le i n tim e and space l e ads to the use of pane l data m o del s. Such mo de ls include

r egre ss ion eq u ations wher e o ne use s se rie s that are a co mbi nati on o f ti me

s er ies and cr oss-section al data se rie s. Si nce the situatio n o ccur s fre q ue ntly whe n analy zi ng so cio -e cono mi c i ssue s and pro ce sse s, pane l data m o del s ar e the subje ct o f m any studie s in spe ci al ize d liter ature . F ischer , Manki w, Ro mer , Weil , Le vi ne and Renel t have under take n studie s rel ate d to lo ng-r un e cono mi c g ro wth b ase d on mo del s wi th panel data, b y using some larg e sample s o f co untri es. Br ue ck ner pr ovi de s an o ve rvi ew o f the strate gi c i nter actio n amo ng l o cal go ver nm e nts b ase d o n two cate gor ie s o f mo del s with panel data. Ar kadi evi ch Kholo dil in, Sil iver stovs and K ooths unde rtak e a for e cast of the annual gro wth r ate s o f the re al GDP i n e ach o f the 16 Ge rm an Lände r , using dy nami c panel data mo del s. Partri dge i nve sti gates the li nk be twee n the i ncom e di stri buti on and e cono mi c g ro wth i n the U.S.A. using 1960-2000 state data.

At the sam e time , the i ssue o f panel data mo del s pl ay s a ce ntr al rol e i n e conome tr i cs. C om ple x theo re ti cal de ve lo pm ents o f thi s to pi c ar e the sub je ct o f m any b ook s, o f whi ch: Analy si s o f Panel Data b y Hsi ao , Eco no me tri c Analy si s o f Panel Data b y Bal tagi and Wool dri dg e.

Nume ro us ar ti cl es appr oach the study o f spe ci fi c issues r el ate d to

panel data mo del s. Thus, Bai tackle s the i ssue o f panel data mo del s with unob se rvab le i nte racti ve effe cts whi ch are cor rel ate d with the r eg re ssor s, i f bo th the cro ss-se ctio nal di me nsio n and the tem por al di me nsio n are l ar ge . El hor st e ffe cts a sur vey o f the spe cifi catio n and e stim atio n o f spatial pane l data m o del s, in the ci r cum stance o f i ncl udi ng spati al e rr or auto cor rel atio n or usi ng a spati al ly l ag ge d de pendent var iable . Hsi ao , Pe sar an and Tahmi sci ogl u fo cus o n the e stim atio n o f fi xe d effe cts dy nami c panel data mo dels by m axim izi ng the li kel ihoo d functi on, afte r the appli cati on of a l ine ar tr ansfo rm ati on that el imi nates the i ndi vi dual effe cts. Do nal d and Lang i nve sti gate the i nfer ence in panel data whe n the num ber of gro ups i s sm all as i s ty pi call y the case for the DID (di ffe re nce s – i n - diffe re nce s) e stim atio n m etho d and whe n so me vari able s ar e fi xe d withi n gr o ups. Wool dri dg e pr opose s a si m ple , fle xi ble , wi del y appli cabl e appr oach to handli ng the ini ti al condi tio ns pr obl em in dy nami c, no n-li ne ar , unob se rve d effe cts panel data m o del s.

2. Meto do logy

2.1. Panel Data Models The following are panel data models in a parti cular fo rm, wi th one and two expl anatory variables, as nee de d in the long run.

One can notice two and thr ee variable s (featur es) re spe ctively x and y , and x, y and z for N units (marke d

N , , 2 ,

1 K _{), called cross-se ctional units}

for Tconsecutive periods

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(

xi,t,yi,t

)

, i=1,2,K,N, 1 , , 2 , 1 , ₀ ₀ ₀ 0 + + + − =t t t t T t K

(

)

t i t i t i y z x_, , _,, _, , , , , 2 , 1 N i ₌ K _, ₁_, ₂_, _, ₁ 0 0 0 0 + + + − =t t t t T t K

The cr oss-se ctio nal dime nsio n i s N , and the tem por al dime nsio n i s T_, he nce the size o f the panel data i s

,

β

1,

β

2 are model

par ameter s to be de termine d;

i

δ

repre sents spe cifi c (r andom or fixe d) effects for cro ss-se ctio nal units;

t

γ

repre sents spe cifi c (r andom or fixe d) effects for time perio ds;

t i,

ε

is the error terms.

+

ε

_, ,i ₌1,2,K,N, 1 , , 2 , 1 , ₀ ₀ ₀ 0 + + + − =t t t t T t K _(2’)

In or der to e stimate mo de ls (2), and (2’) re spe cti vely , fi rst the spati al fixe d effe cts

δ

i are e limi nate d from

the reg re ssi on e q uatio n by dem eani ng the de pende nt and i nde pe nde nt vari able s. Then, the transfo rme d r egre ssio n eq uatio n i s e stimate d by the or di nary le ast sq uare s metho d (El hor st, 2010).

2.2. Mode l S tructur e The mo del i ncl ude s five vari able s and i s made up o f two i nde pe ndent b ehavio ral eq uatio ns. The m o del pur sue s the q uanti fi cation of factor s’ i nfl uence rel ate d to e co nomi c e ffi cie ncy (the numb er o f em plo yee s pe r 1,000 i nhabi tants) and to gro wth le vel (GDP pe r capita and no minal GDP) upo n indi cator s that char acteri ze transpor t i nfr astr ucture (nati onal ro ad densi ty) and to uri sm pe rfo rmance (the num ber o f to uri sts) using data abo ut regio ns i n Ro mania. The following inform ation is used in the two e quations:

Dens_dr_nat = national road density (km./100 sq. km.) (e ndoge nous variable);

Nr_tur = numb er of to urists (endogeno us vari able);

PIB_pr_c = nominal gross dom esti c product (million Lei) (exoge nous variable);

PIB_per _cap = gross dome stic product per capita (Lei/i nhabi tant) (exoge nous variable);

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R_sal = number of employ ees pe r 1,000 inhabitants (exog eno us variable);

23 22 21 12

11,a ,a ,a ,a

a = equation par ameter s to be determine d.

To estimate model e quations, the authors have used the value s of the five indi cators during 2007 – 2011, in eight Rom anian regio ns. That is why we ne ed two indices:

t = generi c i ndex of time 2011 , , 2008 , 2007 K = t ;

i = generi c i ndex of r egion _i₌1,2,K,8 accor ding to corre spo ndence:

North-We st r egion →1; Central region →2; North-East region →3; South–East region →4; South-Muntenia region →5; Bucure şti-Ilfov region →6; South-West Olte nia region →7; West region →8.

The fo rmer model eq uation expre sse s the linear de pende nce betwe en national road densi ty and nomi nal gross dome sti c pro duct, hence i ts ne xt form obtaine d by customi zing equation (2): t i, t Dens_dr_na =a11+a12 PIB_pr_ci,t+

δ

i+

ε

i,t , _i₌1,2,K,8_, 2011 , , 2008 , 2007 K = t (3) where

ε

i,t is a resi dual variable , and

δ

i

repre sents cro ss-se ction spe cifi c fixe d

effe cts. The l atter mo del eq uation em phasize s

the linear de pendence between the number of touri sts per gross dom esti c product per capita and the numb er of employees per 1,000 i nhabitants, wi th expl anatory variable s acting with a two-ye ar lag. Equation (2’) shows that the functional relation has the following form: t i, Nr_tur =a21+a22 PIB_per_capi,t−2 +a23 R_sali,t−2+

δ

i′+

ε

i′,t, i=1,2,K,8, 2011 , 2010 , 2009 = t ; (4) where

ε

i′,t is a resi dual variable and

δ

i′

repre sents cro ss-se ction spe cifi c fixe d effe cts.

3. Results

3.1. Statis tical Par ame ters and Tests The req uir ed e conome tri c val ues have be en per forme d by me ans of the EVie ws 9.0 progr amme package . Estimating the coe ffi cie nts in the former e quatio n has bee n base d o n the data i n Tabl e 1 and Table 2 (pr ogre ss o f national road density and nominal GDP duri ng 2007-2011 for eig ht Romanian r egions). For the latter eq uation, estimating the par ame ter s has b een done accor di ng to the data i n Table 3, Table 4 and Tabl e 5 (change s in the number o f to uri sts, i n the GDP per capita and i n the numbe r o f em ployee s per 1,000 inhabitants duri ng 2007-2011, in eig ht Romanian r egions).

First, one performs the Hausman Te st to determine whe ther to choose random effe cts or fixe d effe cts for the models. The random effe cts nee d to be uncorrel ated with the e xplanatory variables. At the same time, the Hausman Test compares the fixe d and random effe cts estimates of coeffi cients.

The null hy pothesi s of the Hausm an Test is that the random effects estimates of coeffi cients are consistent, namely the random effects are uncorrel ated with the e xplanatory variables. One reje cts null hypothe sis if the diffe rence between the two estimators i s large.

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Table 1. Dynamics of National Road Density during 2007-2011 in Romanian Regions

National road density (km./100 sq. km.) Region 2007 2008 2009 2010 2011 North-West region 5.922051 6.434340 6.560216 6.630473 6.738785 Central region 6.568969 6.633486 6.639351 6.624688 6.727328 North-East region 7.256479 7.248337 7.278188 7.283616 7.294471 South-East region 5.950500 6.610424 6.176999 6.182592 6.193777 South-Muntenia region 8.100893 8.086381 8.092186 8.109601 8.100893 Bucureşti -Ilfov region 16.967301 16.967301 16.967301 16.967301 16.967301 South-West Oltenia region 7.055395 7.247099 7.250522 7.250522 7.452496 West region 5.906378 5.906378 5.906378 5.968813 5.975056 Source: The table data have been generated by the

authors according to the information in the 2008-2012 Romanian Statistical Yearly Book

Table 2. Nominal GDP during 2007-2011 in Romanian Regions

Nominal gross domestic product (million Lei) Region 2007 2008 2009 2010 2011 North-West region 50724 58639 57900 59293 61370 Central region 49417 57303 57101 59120 63669 North-East region 45990 55022 54408 55669 60298 South-East region 44273 53851 52706 56340 60841 South-Muntenia region 52014 64535 65142 66115 70923 Bucureşti-Ilfov region 95798 134163 124289 131579 137579 South-West Oltenia region 34420 40340 39954 41941 44841 West region 42996 50393 49200 52983 56507

Source: The table data have been generated by the authors according to the information in the

2008-2012 Romanian Statistical Yearly Book

Table 3. Dynamics of the Number of Tourists during 2007-2011 in Romanian Regions

Number of tourists Region 2007 2008 2009 2010 2011 North-West region 889707 908076 732474 702838 799774 Central region 1329992 1291514 1072785 1126887 1435771 North-East region 717592 725646 656501 620961 696188 South-East region 1231058 1308569 1157087 1044043 1134824 South-Muntenia region 729221 750157 591251 572912 615931 Bucureşti -Ilfov region 996740 1038161 989805 1125213 1282616 South-West Oltenia region 403071 429370 366114 337102 426845 West region 674544 673814 575118 542801 639657

2008-2012 Romanian Statistical Yearly Book

Table 4. GDP per capita during 2007-2011 in Romanian Regions

Gross domestic product per capita (Lei/inhabitant) Region 2007 2008 2009 2010 2011 N-W region 18611 21542 21297 21827 22583 Central region 19580 22708 22619 23428 25239 N-E region 12341 14795 14649 15015 16282 S-E region 15642 19099 18738 20077 21709 South-Muntenia region 15758 19648 19914 20288 21798 Bucureşti-Ilfov region 43037 59680 55079 58137 60677 S-W Oltenia region 15097 17832 17753 18735 20083 West region 22342 26173 25602 27640 29526

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Table 5. Number of Employees per 1,000 Inhabitants during 2007-2011 in Romanian Regions

Gross domestic product per capita (Lei/inhabitant) Region 2007 2008 2009 2010 2011 N-W region 231,751 237.163 225.840 210.951 209.453 Central region 242,658 250.669 232.153 215.571 216.612 N-E region 155,351 159.138 149.720 134.499 132.905 S-E region 202,975 209.076 197.740 178.995 174.473 South-Muntenia region 180,656 182.494 175.365 158.841 157.997 Bucureşti-Ilfov region 423,708 457.531 440.546 405.920 402.014 S-W Oltenia region 184,177 186.674 177.668 161.978 162.013 West region 270,960 277.023 254.838 236.926 242.755

2008-2012 Romanian Statistical Yearly Book The relevant portion of the test output is: a) for the former equation

Correlated Random Effects - Hausman Test Pool: POOL02

Test cross-section random effects Test

Summary

Chi-Sq.

Statistic Chi-Sq. d.f. Prob. Cross-section

random 62.444692 1 0.0000

Cross-section random effects test comparisons: Variable Fixed Random Var(Diff.) Prob. PIB_PR_

C? 0.000006 0.000011 0.000000 0.0000

b) for the latter equation

Correlated Random Effects - Hausman Test Pool: POOL02

Test cross-section random effects Test Summary Chi-Sq. Statistic Chi-Sq. d.f. Prob. Cross-section random 7.975731 2 0.0185

Cross-section random effects test comparisons: Variable Fixed Random Var(Diff.) Prob. PIB_ PER_ CAP? (-2) 20.750058 16.777168 2.034478 0.0053 R_SAL? (-2) -7569.65223 -2230.77863 3889023.823 0.0068

According to the above-shown information, the fixed effects are selected for both equations. For the estimation of panel data models, the Pooled Least Squares Method has been used for this type of data. Additionally, it is necessary one should choose a method for computing the variance-covariance matrix of estimators. The author has chosen the White cross-section standard errors, considering the cross-section heteroskedasticity. The above-mentioned software has provided the following information regarding the estimation of coefficients and the econometrics tests: a) for the former equation

Dependent Variable: DENS_DR_NAT? Method: Pooled Least Squares

Date: 04/24/14 Time: 13:33 Sample: 2007 2011

Included observations: 5 Cross-sections included: 8

Total pool (balanced) observations: 40

White cross-section standard errors & covariance (d.f. corrected) Variable Coefficient Std. Error t-Statistic Prob. C 7.732894 0.039438 196.0748 0.0000 PIB_PR_C? 5.93E-06 4.04E-07 14.69244 0.0000

Fixed Effects (Cross) _01--C -1.617261 _02--C -1.434109 _03--C -0.782597 _04--C -1.827952 _05--C -0.012982 _06--C 8.494916 07--C -0.720703 _08--C -2.099312 Effects Specification

Cross-section fixed (dummy variables) R-squared 0.998569 Mean dependent var 8.105014 Adjusted R-squared 0.998200 S.D. dependent var 3.457374 S.E. of regression 0.146686 Akaike info criterion -0.805935 Sum squared resid 0.667022 Schwarz criterion -0.425937 Log likelihood 25.11870 Hannan-Quinn criter. -0.668540 F-statistic 2704.377 Durbin-Watson stat 1.699482 Prob(F-statistic) 0.000000

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b) for the latter equation

Dependent Variable: NR_TUR? Method: Pooled Least Squares Date: 05/05/14 Time: 00:49 Sample (adjusted): 2009 2011

Included observations: 3 after adjustments Cross-sections included: 8

Total pool (balanced) observations: 24

White cross-section standard errors & covariance (d.f. corrected)

Variable Coefficient Std. Error t-Statistic Prob. C 2117774. 526098.4 4.025434 0.0013 PIB_PER_CA

P?(-2) 20.75006 2.330065 8.905356 0.0000 R_SAL?(-2) -7569.652 2341.876 -3.232303 0.0060 Fixed Effects (Cross)

_01--C -44759.61 _02--C 475644.1 _03--C -577606.1 _04--C 162950.3 _05--C -548250.1 _06--C 1258495. _07--C -707605.6 _08--C -18868.30 Effects Specification

Cross-section fixed (dummy variables)

R-squared 0.965875 Mean dependent var 801895.8 Adjusted

R-squared 0.943937 S.D. dependent var 305737.0 S.E. of

regression 72391.22 Akaike info criterion 25.51189 Sum squared

resid 7.34E+10 Schwarz criterion 26.00275 Log likelihood -296.1427 Hannan-Quinn criter. 25.64212 F-statistic 44.02816 Durbin-Watson stat 1.828083

Prob

(F-statistic) 0.000000

The coefficient estimates in the two equations (respectively aˆ11,aˆ12 and aˆ21,

22

ˆ

a , aˆ23) are to be found in the Coefficient

column of the above tables, whereas the region-specific fixed effects (respectively

8 2 1,

δ

, ,

δ

K _and 8 2 1,

δ

, ,

δ

The last colum n (Prob.) of the tables

includes the sig nificance levels to which the equation coefficie nts are different from zero, re spe ctively

The coefficie nt of de termination ( R-squared) that indicates how much of the

variability of a variable can be explaine d by its relationship to the other variables has high val ues (0.998569 – for the former equation and 0.965875 – for the latter eq uation), which shows that the factors consi dered in the mo del are esse ntial. Moreover, the adjusted value of this coeffi cient that has a similar interpretation as R-squared, but is much more accur ate and helps prote ct us against overfitting by penalizing us for including too many usele ss variables, i s high (0.998200 - for the former equation and 0.943937 - for the latter eq uation).

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The F-stati sti c r e por te d i n the table s abo ve i s ne ce ssar y to te st the null hy po the si s that all o f the co effi ci e nts i n a reg re ssio n ar e eq ual to zero . Si nce the sig ni fi cance l evel o f the F - stati sti c (Prob (F -stati sti c)) i s le ss than 0.05, o ne re je cts the null hy po the si s, he nce at le ast o ne of the r eg re ssio n parame te rs i s non-ze ro . The r e sul ts pro vi de d by these e co no me tr i c te sts vali date the mo del and le ad to i ts acce ptance and po ssi bl e use i n an e co no mi c fo re cast.

3.2. Econ omic An alysis of the Mode l The mo del, by the two univo cal dependencie s among eco nomic-so cial variable s relate d to develo pment le vel, economi c efficie ncy, transport effi ciency and to uri sm per formance, highlights a few e sse ntial issue s concerni ng re gional de velopme nt. The form er e q uation sho ws the li ne ar functional rel ationship b etwee n natio nal ro ad de nsity and no minal g ross dome sti c pro duct, whi ch i s a dir e ct rel atio nshi p. Ther efo re , an i ncre ase i n the nominal GDP re sults i n an incre ase i n natio nal ro ad de nsity . Stil l, the hig h val ue o f the coe ffi cie nt of determi natio n (0.998569) me ans that 99.86% o f the natio nal r oad de nsi ty var iation i s due to a vari ati on of the nomi nal GDP, i n the co nte xt o f incl udi ng spe cifi c fi xe d e ffe cts. That sho ws the factor co nsi dere d wi thi n the eq uatio n i s e sse nti al .

The e sti matio n of the no minal gr oss dom esti c pro duct co effi cie nt i n e q uation (5) sho ws that an incre ase i n the nominal gro ss dom esti c pro duct b y 1 millio n Lei pro duces an i ncre ase

i n national road densi ty b y 5.93⋅10-6 km ./100 km.2.

The latter eq uation quantifies the linear de pendence among the number of touri sts, the GDP per capita and the number of em ployee s per 1,000 inhabitants. For the eq uation, there is a dire ct relatio nshi p as compare d to the former factor and an inver se relationship as to the latter factor. The dire ct relationship between the number of to urists and the GDP per capita is a normal issue since an incre ase in the GDP per capita le ads to an incre ase in the numbe r of touri sts. At the sam e time, the inver se relationship with the latter factor is sur prisi ng as it shows that an increase in the number o f employe es per 1,000 inhabitants ge nerates a decr ease in the number of touri sts. Several expl anations of this can be give n, generated b y the current so cio-economi c co nte xt of o ur co untry. A possible expl anation co ul d be that an incre ase in the numbe r of employee s per 1,000 inhabitants, whi ch woul d mean an increase in the numb er of employees, wo uld cause a decrease in average per sonal income, al tho ugh the economi c crisi s has not ye t com e to an end and it woul d le ad to a de cline in tourism perform ance, since it woul d reduce ho use hold budge ts allocate d for recre ational trips. It is also esse ntial that lately, the Romanians have been biased to visit de sti nations outsi de the co untr y, with high quality servi ces at reasonable pri ce s. However , migration is continui ng and migrants e spe cially spend their vacations ab road, for the re asons shown abo ve.

The val ue of the coe ffi cient of determi natio n shows that, withi n the

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context o f including speci fic fixe d effe cts, 96.59% of the variatio n in the number of to urists is due to the variatio n of the GDP per capita and to the number of em ployee s per 1,000 inhabitants which means the two indi cator s are strong infl uence factor s to an endoge nous variable .

Equation (6) re sults in the fact that an incre ase in the GDP per capi ta by 1 Le u leads to an incre asing number of tourists by 21 over the ne xt two y ear s. Still the same equation sho ws that an incre ase in the numbe r of employee s per 1,000 inhabitants by 1 has the effe ct of a re ductio n in the numb er of tourists by 7570 over the ne xt two years.

4. Co nclusio ns

The results show that the study demonstr ates the nee d for the use of panel data mo del s for well-fo unde d scie ntifi c analyse s in the fi eld of regional develo pment. Moreove r, the study shows that nomi nal gross domestic product is an impo rtant dire ct influe nce factor upo n road infrastr ucture. Furthe rmore, GDP per capita and the number of employee s per 1,000 inhabitants are signifi cant factors that infl uence touri st perform ance, the fo rmer dire ctly and the latter reversely . He nce , there is the need to im plement cer tain steps to enco urag e the Romanian to urism . It is also req uire d that an accurate assessm ent of touri sm infrastr ucture shoul d be do ne and i ts im proveme nt shoul d take pl ace.

The mo del sho wn is a regio nal develo pment model that can al so be use d to fo recast the e conomi c and social pro cesses at the level of admini str ative units.

In order to get a more consi ste nt analy sis at regio nal level , it wo ul d be firstly necessary to have a larger number of signifi cant indicator s. Among the pro cesses at r egional le vel, there is a lot of inter-de pende ncie s and inter-conditioni ng, variable i n time and space. Highlighting these inte r-dependencie s and inter-conditio ning coul d be achieve d thro ugh a more comple x mo del that, in additio n to the already hig hlighte d equations, mig ht also incl ude sim ultaneous eq uations and a whole series of defi ning equations, balance shee t equations and equilibrium eq uatio ns. Meanwhile, for better relevance of information that can be obtai ne d, it woul d be ne ce ssary to have a more e xte nsive stati sti cal data b ase including the values of indi cator s over a longe r perio d of time, possibly 15 to 20 ye ars.

The data from thi s analysis coul d be of great use to central and lo cal authoritie s in or der to im prove integrate d ter ritorial de velopme nt strategies for various terri tories and to correlate national de velopme nt strategies with the regional one s so that to concentrate and speci alize urban and r ural are as.

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