A efficiecy approach to iovatio process Moica Mihaela Matei 1 1 Natioal Scietific Research Istitute for Labour ad Social Protectio, Bucharest, The Bucharest Academy of Ecoomic Studies e-mail: matei.moicamihaela@gmail.com Abstract The mai goal of this paper is to model iovatio pheomeo o atioal level usig Data evelopmet Aalysis (DEA) techique.we wat to evaluate the iovatio performace of 31 coutries from the poit of view of techical efficiecy. Give that the iovatio process is oe of the mai drivers for sustaied ecoomic growth, it is obvious that we eed iovatio policies based o rigorous catitattive aalysis. We thik that rakig coutries accordig to their iovatio performace may represet a useful tool for the policy makers ad we preset here a evaluatio based o the iformatio provided by Europea Iovatio Scoreboard (EIS) which is oe of the istrumets desiged to uderstad the sources ad patters of iovative activity. The efficiecy scores obtaied from a DEA model show that the coutries cosidered iovatio leaders, because their iovatio performace reflected by Summary Iovatio Idex is well above that of EU average, are ot also techically efficiet whe trasformig iovatio iputs ito iovatio outputs. Keywords: iovatio, techical efficiecy, DEA 1. Itroductio Iovatio is a complex pheomeo which has a systematic ature. Natioal Iovatio system is a cocept defied by Freema as the etwork of istitutios i the public ad private sectors whose activities ad iteractios iitiate, import, modify ad diffuse ew techologies (Freema 1995) ad by Ludvall as the elemets ad relatioships which iteract i the productio, diffusio ad use of ew, ad ecoomically useful, kowledge located withi or rooted iside the borders of a atio state (Ludvall, 1992). The mai goal of this paper is to model iovatio pheomeo o atioal level usig Data evelopmet Aalysis (DEA) techique.we wat to evaluate the iovatio performace of 31 coutries from the poit of view of techical efficiecy. Koopmas defiitio for techical efficiecy is: a iput-output vector is techically efficiet if ad oly if, icreasig ay output or decreasig ay iput is possible oly by decreasig some other output or icreasig some other iput. Give that the iovatio process is oe of the mai drivers for sustaied ecoomic growth, it is obvious that we eed iovatio policies based o rigorous catitattive aalysis. We thik that rakig coutries accordig to their iovatio
performace may represet a useful tool for the policy makers. As previous researchers have show, DEA provides meas for bechmarkig atioal policies i differet areas. I his study, Atero Kutvoe (Kutvoe, 2007) showed that a trasatioal compariso of regioal policies developed with a DEA model provides meaigful isights to regioal policy developmet that policymakers ca act o. Aother coclusio draw i his paper is that DEA model idetifies best practice cases of regioal iovatio policies. There is also a recet study (Ta-Wei Pa et all, 2010) which applies the data evelopmet aalysis approach for the evaluatio of the operatig performace of the Natioal Iovatio Systems (NIS) i 33 Asia ad Europea coutries. The aalysis was developed o data extracted from the World Competitiveess Yearbook (2004,2006) ad World Developmett Idicators (2004).The results obtaied from a DEA iput orieted model idicate that the Asia group is a better performer tha Europea group. We preset here a evaluatio based o the iformatio provided by Europea Iovatio Scoreboard (EIS) 2009 which is oe of the istrumets desiged to uderstad the sources ad patters of iovative activity. The idicators capturig the iputs of the iovatio process refer to: sciece, egieerig, social scieces ad humaities doctorate graduates, participatio i life log learig, public R&D expeditures, private credit, busiess R&D expeditures, public-private co-publicatios. The idicators of EIS capturig the outputs of the process refer to: employmet i medium-high ad high-tech maufacturig, medium ad high-tech maufacturig exports. We have icluded time lags betwee iputs ad outputs cosiderig that it takes time before iputs trasfer ito outputs. I our study we itroduce a bootstrap algorithm developed by Simar ad Wilso (1999) ad we compute ot oly poit estimates for the efficiecy scores but also 95% cofidece itervals ad bias corrected efficiecy scores. Also, by usig this algorithm we maaged to test the type of the returs to scale of the productio process. 2. Methodology Like we said before, our fial purpose is to evaluate the performace of a certai umber of coutries from the poit of view of techical efficiecy. The coutries icluded i EIS are the producers or the decisio makig uits, ad they use iputs p R + q x to produce outputs y R +. I the process of efficiecy estimatio, the oly iformatio we have is the sample χ = {( xi, yi), i = 1,..., }, meaig we kow the iputs ad the outputs for producers. Havig the iputs ad the outputs for every uit, the productio set is defied as follows (Daraio, 2007): p q {, y) x R, y R, is feasible} ψ = (1) ( x + ' + I the efficiecy measuremet the upper boudary ofψ, also referred to as productio frotier is of iterest because uits that are techical efficiet operate o it. The productio frotier is defied by (Daraio, 2007): ψ = {(, y) ψ ( θx, y) ψ, 0 < θ < 1, ( x, λy) ψ, λ > 1} x (2)
Also, ψ ca be defied i terms of its sectios, usig the iput requiremet set or the output correspodece set. The iput requiremet set cosist of all iput vectors that ca q produce the output vector R.The output correspodece set cosists of all output y + p vectors that ca be produced by a give iput vector x R+. Choosig oe of these sectios meas we choose a iput orieted model or a output orieted model. The presetatio i this sectio refers to the output orieted models. I that case, the productio frotier is defied by (Daraio, 2007) : {(, y) ψ ( θx, y) ψ, 0 < θ < 1, ( x, λy) ψ, λ > 1} ψ = x (3) The most kow oparametric estimator of efficiecy frotiers is DEA (Data Evelopmet Aalysis) estimator. It is oparametric ad this meas it does ot eed the specificatio of a fuctioal form for the frotier. DEA employs liear programmig techiques to estimate the productio frotiers. Like we said before, efficiecy computatios are made relative to the frotier or evelopmet surface. There are two basic types of evelopmet surfaces i DEA, referred to as costat returs to scale ad variable returs to scale (Simar et al., 2008): p+ q ψˆ VRS = ( x, y) R y γ i yi; x γ ixifor ( γ1,..., γ ), γ i = 1; γ i 0, i = 1,.., (4) i= 1 i= 1 i= 1 This estimator is referred as ψˆ because it allows for variable returs to scale. I the VRS costat returs to scale situatio the equality costraied γ = 1 is dropped: p+ q ψ ˆCRS = ( x, y) R y γ i yi; x γ ixi for ( γ1,..., γ ), γ i 0, i = 1,.., (5) i= 1 i= 1 The estimator of the output efficiecy score for a give (x 0, y 0 ) is obtaied by solvig the followig liear program: ˆ λ VRS ( x0, y0) = max λ λy0 γ i yi; x0 γ ixi; λ > 0; γ i = 1; γ i 0; i = 1,..., (6) i= 1 i= 1 i= 1 We solve the liear program described above whe we choose a VRS model. Whe usig a DEA CRS model to estimate the score the liear program becomes: ˆ λ CRS ( x0, y0) = max λ λy0 γ i yi; x0 γ ixi ; λ > 0; γ i 0; i = 1,..., (7) i= 1 i= 1 Thus, before estimatig techical efficiecy, we eed to kow whether the techology is oe of costat retur to scale. The retur to scale is oe of the properties of the boudary of the productio set. The less restrictive model for RTS is the varyig retur to scale situatio (VRS) where the returs are allowed to be evetually locally icreasig, the costat ad fially o -icreasig. We use a procedure proposed by Simar ad Wilso (2002) i order to test the type of the retur to scale (Simar et al.,2008). The test hypotheses are: i= 1 i
H0 : ψ H1 : ψ is globally CRS is VRS (8) It is kow that VRS estimators are cosistet whatever beig the hypothesis o retur to scale ad that CRS are cosistet oly if the ull hypothesis is true. If the retur to scale is costat the CRS ad VRS estimators of the efficiecy scores are very similar. This represets the justificatio for the test statistic that will be used i the process of establishig if ull hypothesis is rejected or accepted is the followig: 1 Sˆ = CRS ( xi, yi ) T(χ ), (9) Sˆ ( x, y i= 1 VRS i i) ˆ 1 = ( CRS ) ˆ VRS where ˆ 1 S CRS λ ad ˆ S = ( λ VRS ). Also, give that Sˆ CRS Sˆ VRS, the ull hypothesis will be rejected if the test statistics is to small. The p-value of the ull hypothesis is the obtaied by computig: p value = Pr ob( T ( χ ) Tobs H 0 is true), where T obs is the value of T computed o the origial observed sample χ. I order to compute this probability, we use a bootstrap algorithm. Naïve *, b bootstrap ivolves, simulatig B pseudo samples χ of size uder the ull (usig the CRS estimate of the frotier for geeratig the pseudo samples), ad for each bootstrap *, b *, b sample computig the value T = T ( χ ). The p-value is the approximated by the proportio of bootstrap samples with values p value B b= 1 1( T *, b T B obs ) b T *, less tha the origial observed value T obs : I the boudary estimatio framework, the aïve bootstrap is ot cosistet (Keip et al, 2008). Keip, Simar ad Wilso proved the cosistecy of two approaches also based o bootstrap. The first, kow as subsamplig is based o drawig pseudo samples of size m smaller tha ad the secod oe is kow as smoothig techique because the geeratio is based o a smooth estimate fˆ (, ) of the joit pdf o (x,y). I order to approximate the probability p-value we used the secod oe by implemetig the homogeeous bootstrap algorithm developed by Simar ad Wilso (Simar et. Al, 2008) The basic idea i this algorithm is to create a bootstrap sample by projectig each observatio ( xi, yi ) oto the estimated frotier, ad the projectig this poit away from the frotier radomly. Because oe ca ot stop the aalysis after determiig the poit estimates, the bootstrap algorithm ca be used to give estimates of bias as well as of stadard error ad cofidece itervals. (10)
3. Data descriptio I order to ivestigate the iovatio process from a DEA poit of view we used 7 iputs ad 2 outputs. The idicators describig the iputs are (EIS 2009): I 1 : S&E ad SSH doctorate graduates per 1000 populatio aged 25-34. The umerator of this idicator is the umber of sciece, egieerig, social scieces ad humaities graduates at secod stage of tertiary educatio, ad the deomiator is the populatio betwee 24 ad 34 years. I 2 : Populatio with tertiary educatio per 100 populatio aged 25-64. This is a percet of the persos i age class with some form of postsecodary educatio i total populatio betwee 25 ad 64 years. I 3 : Participatio i life log learig per 100 populatio aged 25-64. It is calculated as a ratio betwee umber of persos ivolved i life-log learig (defied as participatio i ay type of educatio or traiig course durig the four weeks prior the survey) ad the populatio betwee 25 ad 64 years. I 4 : Public R&D expeditures (% of GDP), represets the ratio betwee all R&D expeditures i the govermet sector ad the higher educatio sector ad Gross Domestic Product I 5 : Private credit (relative to GDP). The omiator of this idicator is give by the claims o the private sector by commercial baks ad other fiacial istitutios that accept trasferable deposits such as demad deposits ad the deomiator is the Gross Domestic Product. I 6, Busiess R&D expeditures (% of GDP) shows all the R&D expeditures i the busiess sector as a percet of GDP. I 7 Public-private co-publicatios per millio populatio. The omiator of this idicator is the umber of public-private co-authored research publicatios i Web of Sciece Database ad the deomiator is Total populatio. The idicators we choose to describe the outputs of the iovatio process are: O 1 : Employmet i medium-high ad high-tech maufacturig (% of total workforce) O 2 : Medium ad high-tech maufacturig exports (% of total exports). Because it takes time before iputs trasfer ito outputs, we must iclude time lags betwee them. This is the reaso why the iputs data are draw from EIS 2005 ad the outputs from EIS 2009. We must reduce the dimesioality because i the DEA model, which is oparametric is preset the course of dimesioality. Give that we oly have a sample of 31 coutries, we reduced the dimesioality from 7+2 to 1+1 usig a aggregatio procedure described by Daraio (Daraio, 2007). The idicator reflectig the iovatio iputs is computed as a liear combiatio of I 1, I 2, I 3, I 4, I 5, I 6 ad I 7. First we correct the scale of the iputs by dividig each iput by its mea. So if the origial matrix has the colums I 1, I 2, I 3, I 4, I 5, I 6, I 7 we use the otatio X for the ew matrix of the scaled iputs. The purpose is to fid a factor, I calculated as a liear combiatio of all iputs: I= X v= v1i1 + v2i2 + v3i3 + ν 4I4 + ν 5I5 + ν 6I6 + ν 7I7 We will use the idea suggested by Daraio (2007). The vector v is determied by computig a eigevector of the matrix X X correspodig to its largest eigevalue.
The eigevalues of the matrix X X are: a1 = 296.805, a2 = 18.466, a 3 = 12.070, a 4 =4.813, a 5 =2.513, a 6 = 2.174, a 7 =1.283. Correlatio I2 I3 I4 I6 I7 I8 I9 I 0.657 0.667 0.938 0.836 0.628 0.922 0.958 Table 1 Correlatios betwee ew iput ad the origial variables These eigevalues do ot represet the factors variace because the data is ot cetered. A eigevector correspodig to a1 = 296.805 is v= (0.353 0.312 0.409 0.341 0.333 0.399 0.474) t ad we used it to obtai the factor I. Correlatios betwee the ew factor ad the origial iput variables show that this factor represets well the origial idicators. Also the ratio a 1 ( a1 + a2 + a3 + a4 + a5 + a6 + a7 ) is close to 1 (0.87) idicatig that the iertia explaied by I is high. I the output space, usig the same method, we aggregate O 1 ad O 2. Thus is calculated the output factor O = Yu = u1o 1 + u2o2, where Y is a matrix with the colums O1 ad O 2 (scaled), u= (0.728 0.685) t ad represets the eigevector correspodig to the first eigevalue of the matrix Y Y, a 1 =75.248. Correlatio O1 O3 O 0.959 0.888 Table 2 Correlatios betwee ew output ad the origial variables Correlatios betwee O, O1 ad O2 are 0.959 respectively 0,888 ad the ratio betwee first eigevalue ad the sum of the Y Y eigevalues is 0.977 idicatig that the factor O represets the origial variables very well, without loosig too much iformatio. The cloud of poits represetig the coutries i our sample is illustrated i Figure1. 2,50 SK HU CZ DE SI O 2,00 1,50 RO MT PL HR IT ES EE IE FR BE AT UK DK FI SE CH 1,00 TR BG LT PT NL LV EL NO 0,50 CY IS 0,00 1,00 2,00 3,00 4,00 5,00 6,00 7,00 I Fig. 1 Decisio makig uits
As we ca see i the figure above, Romaia, Bulgaria, Turkey are the coutries with the lowest level of iput. There are coutries with low levels of iputs but with a high level of output: Slovakia, Hugary, Czech Republic. 4. Techical efficiecy estimatio for NIS 4.1 Testig retur to scale Usig the ew variables to describe the efforts ad the results of the 31 DMU s we compute the efficiecy scores for every DMU usig a DEA output orieted model cosiderig both a variable retur to scale ad a costat retur to scale. Next we have compared the CRS ad the VRS scores for each coutry by computig the efficiecy score obtaied with a CRS DEA model ratio. The average of these 31 values efficiecy score obtaied with a VRS DEA model represets the observed value of the statistic defied i a previous sectio, T obs =0.591. I order to decide if we should use a CRS or a VRS model whe estimatig the efficiecy scores i the iovatio process, we must compute a p-value for the test which has a ull hypothesis that the frotier of the productio set is CRS. We obtaied this p-value by usig the homogeeous bootstrap algorithm of Simar ad Wilso (Simar et al., 1999)as follows: Step 1: B=1000 bootstrap samples of size 31 were geerated from a smooth estimate of the desity f(x,y). This estimate was costructed by a kerel method. We had to simulate the B samples uder the ull, thus we used CRS estimate of the frotier for geeratig them. Step 2: For every sample b, b=1, 2 B, were estimated the 31 efficiecy scores usig first a CRS DEA model ad the a VRS DEA model. Step 3: Performig the calculatios described for the origial sample we get 1000 average values of the ratios betwee CRS ad VRS scores, deoted by T * which will be compared with T obs. Step 4: p-value was approximated by: p value 1000 b= 1 1( T *, b 0.591) = 0.005 1000 Fially we obtai for this test with B=1000 a p-value of 0.005<0.05, hece we reject the ull hypothesis of costat returs to scale. Whe the productio process is the iovatio process, the frotier of the productio set is characterized by variable returs to scale. Hece a per cet icrease i the iovatio iput produce a bigger or a smaller tha per cet icrease i iovatio output. 4.2 Efficiecy scores estimatio The results preseted below are retured from a commad i the FEAR library (Frotier Efficiecy Aalysis with R) that implemets the homogeous bootstrap
algorithm described by Simar ad Wilso. The bootstrap estimates were produced usig B=2000 bootstrap replicatios. Table 3 displays results of the homogeous bootstrap algorithm, givig the origial efficiecy estimates as well as the bias corrected estimates ad the 95% cofidece itervals for DEA estimators. The efficiecy scores are estimated usig a variable returs to scale, output orieted DEA with oe iput ad oe output. These are greater tha or equal to 1 give that the FEAR commad retured Farrell output efficiecy estimates. The decisios makig uits with efficiecy score equal to 1 are efficiet. The DMU s with scores greater tha 1 are iefficiet. The higher the efficiecy score the more iefficiet the DMU is. Coutry Scores Bias corrected scores Lower boud Upper Boud Variace BE 1,590 1,692 1,595 1,852 0,005 BG 1,754 2,067 1,801 2,411 0,024 CZ 1,000 1,104 1,024 1,232 0,003 DK 1,764 1,853 1,767 2,023 0,005 DE 1,033 1,093 1,036 1,195 0,002 EE 2,059 2,262 2,086 2,518 0,012 IE 1,691 1,814 1,699 1,996 0,006 EL 3,167 3,528 3,207 4,021 0,047 ES 1,748 1,884 1,758 2,076 0,007 FR 1,483 1,580 1,488 1,732 0,004 IT 1,423 1,559 1,438 1,731 0,006 CY 3,545 3,907 3,596 4,408 0,047 LV 3,097 3,500 3,158 3,992 0,049 LT 2,582 2,854 2,618 3,232 0,028 HU 1,067 1,178 1,081 1,333 0,005 MT 1,178 1,363 1,199 1,558 0,009 NL 2,376 2,506 2,381 2,735 0,009 AT 1,581 1,668 1,584 1,820 0,004 PL 1,511 1,751 1,536 1,995 0,014 PT 2,462 2,664 2,480 2,942 0,014 RO 1,000 1,398 1,039 1,779 0,044 SI 1,201 1,284 1,206 1,411 0,003 SK 1,000 1,161 1,022 1,317 0,006 FI 1,429 1,500 1,431 1,638 0,003 SE 1,541 1,618 1,544 1,766 0,003 UK 1,761 1,857 1,765 2,027 0,005 HR 1,811 2,029 1,839 2,315 0,016 TR 1,295 1,648 1,318 2,119 0,045 IS 4,769 5,010 4,778 5,470 0,033 NO 3,209 3,391 3,218 3,705 0,016 CH 1,300 1,364 1,302 1,488 0,002 Table 3 Efficiecy scores (FEAR results)
Give that the variace ad also the stadard error estimates are small relative to the bias estimates we will trust the bias corrected efficiecy estimates. This is the reaso why our rakig will be made accordig to the corrected scores. The most efficiet NIS is the oe i Germay, eve if its iitial efficiecy score was ot 1. Czech Republic ad Slovakia come i at secod positio. The case of Romaia is more iterestig because eve if the origial score was equal to 1 it comes i at the 8 th positio. Thece it is evidet that if a coutry receives a poit estimate equal to 1 this is ot a strog reaso to cosider that the coutry is 100% efficiet. It is iterestig to compare the hierarchy determied usig the results from the bootstrap algorithm (Table 3) with the comparative aalysis from the report Europea Iovatio Scoreboard 2009. Actually we wat to see if coutries with iovatio performace well above that of EU average ad all other coutries (where the iovatio performace is reflected by the composite idex kow as Summary Iovatio Idex- SII), kow as iovatio leaders are also techically efficiet. Accordig to the report Europea Iovatio Scoreboard 2009, Germay is oe of the iovatio leaders ad as metioed before its NIS is also techically efficiet. But we ca ot say the same thig about the other iovatio leaders like Demark, UK, Filad ad Switzerlad which are ot efficiet, give their efficiecy scores are over 1.3. Of these 4 coutries, Switzerlad is the most efficiet (raked the 7 th ) i our rakig based o DEA results Accordig to EIS 2009, Slovakia ad Czech Republic are amog the coutries with iovatio performace below the EU27. But their efficiecy scores are close to 1, showig they are techically efficiet whe trasformig iovatio iputs ito iovatio outputs. The results i Table 3 show that the most iefficiet atioal iovatio systems are those of Latvia, Greece, Cyprus, ad Icelad. Cyprus ad Icelad have techically iefficiet iovatio systems although they are cosidered iovatio followers i EIS report. This meas their iovatio performace reflected by Summary Iovatio Idex is below that of the iovatio leaders but close to or above that of the EU27. However, we fid a cocordace betwee iovatio performaces measured by SII ad techical efficiecy estimated usig DEA models i the Latvia case which belogs to the cachig up coutries group. Coclusios We thik that it is importat for policy makers to see how their coutries positio themselves, i terms of achieved efficiecy i relatio to other coutries. Thus we propose a rakig based o bias corrected estimates of the efficiecy scores which will show which are the most efficiet coutries. The the iefficiet coutries could study the strategies ad the policies of the most efficiet coutries i order to improve their ability to trasform iovatio iputs ito iovatio outputs. The efficiecy scores obtaied from a DEA model show that the coutries cosidered iovatio leaders, because their iovatio performace reflected by Summary Iovatio Idex is well above that of EU average, are ot also techically efficiet whe trasformig iovatio iputs ito iovatio outputs. We thik that
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