A C T A U N I V E R S I T A T I S L O D Z I E N S I S
F O L IA O E C O N O M IC A 194, 2005
M arek Szajt*
IDEN T IFIC A T IO N OF PATENT-ACTIVITY LEVEL W ITH T H E USAG E OF DISC R IM IN A N T ANA LY SIS
Abstract
T h e sub ject, w hich is m o re and m o re frequently discussed in eco n o m ic lite ratu re, is in n o v a tio n . A lot o f e la b o ratio n s refer to its description and im p o rta n ce in m o d em econom ies. In this p a p er an a tte m p t is m ad e to separate p articu la r co u n try g ro u p s in E u ro p e on th e basis o f p aten t activity. T h e division h as been m ade with the usage o f statistical m eth o d s - m ainly discrim in an t fu n ctio n . T h e analysis presented in th e p a p er allow s ch aracterizin g p a rtic u la r p a rtic ip a n ts and d raw in g o n e’s a tte n tio n to the differences in inno v ativ e policy c o n d u cted in d ifferen t countries.
Key words: in n o v atio n , p a te n t, d isc rim in an t fu nction.
L IN T R O D U C T IO N
N o w ad ay s, a significant influence o f inn o v atio n o n econom ic g ro w th is em phasized m ore and m ore often. Along with the form ing o f general economic theories, a lot o f different definitions connected w ith in no v atio n s have been created. T o d ay , an innovation is usually understood as a relatively new production application of scientific or technical information (K o t et al., 1993). T his definition, alth o u g h very sim ple, is clear an d equivalent to m any term s th a t have em erged in recent years.
In connection with new problem s th a t arise, we also enco u n ter difficulties connected w ith th eir precise quantification. F irst o f all, as the m ain source o f in n o v atio n , paten ts are ad opted. Persons o r institu tio n s from abro ad m ay su b m it the paten ts on the territory o f a given co u n try b o th by its residents and non-residents. T he num ber o f patents subm itted by the residents reflects the activity o f a given cou n try in th e sphere o f research and
* P h .D ., s tu d e n t, E co n o m etrics a n d S ta tistics D e p a rtm e n t, T e c h n ic a l U n iv ersity in C zęstochow a.
developm ent (R + D). In order to o b tain a better co m parab ility o f d a ta concerning the nu m b er o f patents, the d a ta is q uantified per area units or the n u m b er o f inhab itan ts.
In n o v ativ e activity m easured as a num b er o f p aten ts per one th ou sand o f in h ab itan ts is influenced by various factors. T o d ay , as the m ain d eter m in an ts o f innovative activity, the follow ing factors arc enum erated: first o f all, expenditures for the R + D sector, em ploym ent in this sector and the level o f econom ic grow th.
In this paper, an em pirical analysis o f the ab ovem entioned problem s was presented on the basis o f inform ation published by G łów ny U rząd S tatystyczny (G U S - the C entral Statistical Office) an d O rganisatio n of E conom ic C o o p era tio n and D evelopm ent (O E C D ).
II. C H A R A C T E R IS T IC S O F IN N O V A T IV E A C T IV IT Y D E T E R M IN A N T S
It would be difficult to overlook the ever-increasing expenditures for research an d developm ent activity, b o th in P oland and in o th e r countries. D espite the fact th a t Poland spends m ore m oney on R + D th an results from the tendency th a t can be observed in the O E C D cou ntries (Żółkiewski, 1999), these expenses, due to a low level o f n ation al w ealth do no t have m easu rab le effects.
G D P per capita
C h a rt 1. E x p en d itu re fo r R & D activity and G N P (O E C D ) S ource: A u th o r’s calcu latio n s on the basis o f G U S d a ta
T he straig h t line in the diagram is a form regression line:
y = - 2 1 2 .9 1 6 - 0 .0 2 9 * (1)
estim ated fo r the d a ta from the year 1998 concerning expenditures for R + D per ca p ita (У) in relation to PK B per ca p ita (X ) in the O E C D countries. Even th o u g h fitting o f the eq uation calculated with the d eter m in atio n coefficient R 2 = 0,67 is n o t convincing, th e value o f the p aram eter present a t the independent variable significantly differs from zero. T he countries th a t lie above this line arc characterized by a tendency to invest th a t is higher th an the O E C D average. T he coun tries lying below the line bear expenses th a t are low er th an expected. D espite this, a certain flaw in o u r system is an unquestionable do m in atio n o f b ud get resources in the financing o f R + D activity. A higher share o f th e en terprise sector in the financing o f R + D activity is expected in the future.
P oland has insufficiently developed structures o f financing in no vatio n by the enterprise sector, because o f which the state budget is excessively burdened. In n o v atio n s are becom ing increasingly dependen t o n effective interactions betw een the scientific base and the business sector.
T h e vertical lines in the diagram den ote a division o f cou ntries from the p o in t o f view o f society w ealth calculated w ith the volum e o f G N P per 1000 in h ab itan ts, calculated in actual prices according to purchasing pow er p arity. In o u r case, we distinguished three g rou ps o f countries: countries characterized by the level o f PK B /1000 in h ab itan ts am o u n tin g to less th an 10 000, countries characterized by the value betw een 10 000 and 20 000 and those characterized by the value over 20 000. T hese groups som ehow determ ine the co u n try ’s capability to ab so rb advanced tech n o logies w hich are expensive because o f th eir character, especially at the m o m en t o f th eir im plem entation.
T h e horizontal line divides countries into tw o groups from the point of view o f the inn o v atio n financing volume. Below this line, th ere are co u n tries in w hich expenses for R + D activity per in h a b ita n t are low er th an the average fo r a given group. It is a certain d eterm in a n t o f the capabili ties o f a given co u n try and its scientists to create new technologies and inventions, which is usually connected w ith su b stan tial cost o f research and experim ents. T hese costs, besides m ark etin g costs, are the m o st im p o rtan t ones in the case o f creation and in tro d u ctio n o f a new p ro d u c t to the m ark et.
T h e th ird equally im p o rtan t facto r th a t has an influence on innovative activity is h u m an capital, which we will present as a n u m b er o f em ployees in the R + D sector. In o rd e r to o b tain better com p arab ility , this num ber was presented on full tim e basis. A bove all research and developm ent
em ployees are taken into consideration because o f th eir highest actual c o n trib u tio n to the creation o f new inventions. A d ditio nally , this num ber is converted into the capability o f a given co u n try from the p oin t o f view o f em ploym ent with reference to 1000 em ployed persons.
In o rd e r to investigate the innovative activity, wc can use the d a ta concerning the investigated country or a g ro u p o f countries. U n fo rtun ately , there exist a lot o f difficulties connectcd with the availability o f com plete d a ta concerning individual countries and with com p arab ility o f the data. In this case, the only optio n is to use the m eth o d s o f spatial and time analysis o r to use analyses based on discrete prog ram m in g. In this paper, we will p resen t possibilities o f use o f discrim inative analysis as a m ethod for o b tain in g a division o f countries according to the in no vatio n activity criterion.
In the p aper presented, a discrim inative function estim ated for the E urope an m em bers o f O E C D o n the basis o f the possessed in fo rm atio n from the years 1995-1999 will be used. T h e sam ple consists o f tw o p-dim ensional norm al distributions with expected values vectors x t and x 2 the same covarian ce m atrix S. T he discrim inative function will be a'x, where as th e vector a, we will a d o p t a vector th a t m axim izes the expression (M o rriso n , 1990):
w here a'S a = 1
V ector a is so lution o f the hom ogeneous system o f equations:
x 2) ( x 1 - x 2) ' - 2 S ] a = 0 (3) where:
Я = m a x 2(a) = J ^ 2 - ( x , - x ^ S ' 1^ - x 2) = Г 2 (4)
a N I + 1*2
the m atrix ran k o f this system equals p - 1, which determ ines the following form o f th e linear discrim inative function:
у = ( x t - x 2) 'S _1x. (5)
Because o f the com p arab le variance o f the observed variables, we can m ove on to the estim ation o f the discrim inative function.
T h e d iscrim inative p o in t in o u r investigation is:
population A < ( i j — x"2) 'S _ 1(3T1 — x 2) < population B.
As a criterio n , we will use the A nderson classification statistic:
W = ( x ! - x 2)'S " l x - 0.5(x x - x 2)'S ~ x( x ! + x 2) (6) where: x belongs to p o p u latio n 1 (having low innovative activity) when
W < 0 , and to p o p u latio n 2 (having high innovative activity) when W > 0 .
A s the criterion , we will a d o p t innovative activity m easured as a num ber o f p aten ts subm itted by the residents per 1000 in h ab itan ts. Wc treat the activity as to o low (0), when it am o u n ts to less th an 0.1 p a te n t per 1000 em ployed persons, and sufficient (1) when it exceeds the value o f 0.1 p aten t em ployed person. T he feature investigated will depend on th ree features:
X u - gross expenditures for the R + D activity per 1000 in h ab itan ts
according to the purchasing pow er p arity in S in actual prices from 1999 for a given co u n try i,
X 2i - n u m b er o f research and developm ent em ployees per 1000 em ployed
persons fo r a given co u n try i,
X it - G N P according to the purchasing pow er parity in S per one
in h ab itan t in actual prices from 1999 for a given co u n try i.
Even th o u g h in the contents we have tak en the year 1999 as the base year, the analyses were carried o u t on the basis o f d a ta from different years, while the d a ta from the year 1999 was presented as the m ost up-to-date and thus giving th e clearest results.
III. R E S U L T S O F E S T IM A T IO N
In the first phase o f the calculation, it tu rned ou t th a t the value o f the p aram eter present at the variable responsible for w ealth o f the society - Х ъ - is insignificant in com parison with the rest o f the variables. N o n e o f the sam ple eq u atio n s fo r the years from the period 1995-1999 did no t confirm its significance. T herefore, in fu rth e r sam ples, variables X l and X 2 were classified for the equation.
As a result o f the estim ation, the following discrim inative function equation was obtained:
w ith th e discrim ination point o f the value o f 3.389. T h is eq u a tio n was assessed th ro u g h the replacem ent o f individual values o f explanatory variables w ith value 0 fo r А ^ < 0 .1 ; 1 fo r 1 < A rJ i< 0 .4 ; 2 for X ^ > 0 .4 . In the case o f real d a ta , the value o f discrim inative function p aram eters am o u n ts to:
y, = 1.388x1( + 8.526x2( (8)
at the discrim inative p o in t = 4.20
T h e m atch in g m easured with accuracy coefficient (Aczel, 2000) is higher in th e case o f function (8) and am o u n ts to 0.9524, w hereas the p ro p o rtio n al chances criterion = 0.528.
T abic I. Values o f discrim inative fu n ctio n s fo r selected co u n tries
C o u n try F u n c tio n v alu e fo r e q u atio n 7 F u n c tio n value fo r eq u atio n 8
C zech R epublic 2.166 2.141 Belgium 4.877 4.011 Italy 2.166 2.879 Iceland 4.877 4.620 A ccuracy coefficient 0.901 0.9524 Source: A u th o r’s ow n calculations.
T ab le 1 presents the values for the best (from the p oint o f view o f the discrim inative function value) countries. As we ca n see, only in the case o f Italy the discrim inative function value does not agree with th e assum ptions o f th e eq u a tio n (Italy belonged to countries o f sufficient in novative activity).
Table 2. V alues o f d iscrim inative fun ctio n a t sim ulative values o f e x p la n a to ry variables
N o. * 2 F u n ctio n value No. * 2 F u n c tio n value 1 0 0.1 0.853 11 0.2 0.3 4.836 2 0 0.2 1.705 12 0.2 0.4 5.68« 3 0 0.3 2.558 13 0.3 0.1 4.269 4 0 0.4 3.411 14 0.3 0.2 5.122 5 0.1 0.1 1.991 15 0.3 0.3 5.974 6 0.1 0.2 2.844 16 0.3 0.4 6.827 7 0.1 0.3 3.697 17 0.4 0.1 5.408 8 0.1 0.4 4.549 18 0.4 0.2 6.260 9 0.2 0.1 3.130 19 0.4 0.3 7.113 10 0.2 0.2 3.983 20 0.4 0.4 7.966
It is necessary to stress th a t the d a ta for Italy - especially the d a ta concerning dom estic p aten ts - is incom plete, which m ay result in a lack o f consistency in their presentation. T h e next table presents sim ulative values correspo nd ing to individual changes in the value o f explanatory changes. In the sim ulations, values sim ilar to those real were taken into consideration.
T h e above calculations (T ab. 2) prove th a t only an ap p ro p ria te num ber of research and developm ent employees w orking on the basis o f firm financial basis g u arantees a high level o f patent activity. It is w o rth em phasizing th a t from ob servation 8 it follows th a t, despite the co rrect value o f the discrim inative function a t relatively low expenditures we m ay talk ab o u t a very low efficiency o f the R + D personnel in this case. W ith correct financing, one fo u rth o f this personnel can generate a sim ilar num b er o f patents. It is w orth em phasizing the increasing efficiency o f researchers in the case o f an increase in expenditures, which is n o t connected w ith an increase in salary, bu t ra th e r with an increase in the ability for purchasing research eq uip m ent and financing o f experim ents th a t are often expensive.
IV. C O N C L U S IO N S
T h e presented way o f identification o f p aten t activity is characterized by a few advantages:
it has a b etter m atch in co m parison with regression functions and a rb itra ry classification,
- om its outcom e o f tim e effects, which results in simplicity o f calculations, - allow s a d o p tin g o f d a ta o f lower accuracy,
- quickly reacts to distinct changes o f explan atory variables,
- facilitates p lan n in g and provides info rm atio n a b o u t the existing flaws in innovative policy.
T h e presented m eth o d o f p aten t activity identification based on linear discrim inative fu n ctio n m ay serve as one o f the elem ents o f innovation analysis. O nce again, a sim ple statistical instru m en t allow s the d raw ing o f concrete an d , I hope accurate econom ic conclusions.
R E F E R E N C E S
A czel. A .D . (2000), S ta ty s ty k a w zarządzaniu, PW N , W arszaw a.
Ja ju g a K . (1993), S ta ty sty cz n a analiza wielowymiarowa, P W N , W arszaw a.
K o t S .M ., K a rs k a A., Z ając K . (1993), M a tem a tyczn e m odele procesów d yfu zji innowacji, P W N , W arszaw a.
M o rriso n D .F . (1990), W ielowym iarowa analiza sta tystyczn a , P W N , W arszaw a. Ż ółkiew ski Z. (ed.), (1999), R achunek satelitarny nauki 1996-1997, G U S , W arszaw a.
M a re k Szajt
ID E N T Y F IK A C JA P O Z IO M U A K T Y W N O Ś C I P A T E N T O W E J Z W Y K O R Z Y S T A N IE M A N A L IZY D Y S K R Y M IN A C Y JN E J
Streszczenie
T em atem co raz częściej p o ru szan y m w literatu rze ekonom icznej są innow acje. Wiele o p ra co w a ń d o ty czy ich opisu czy zw rócenia uw agi n a ich rolę we w spółczesnych g o sp o d ark ach . W p racy p o d jęto p ró b ę w yodrębnienia poszczególnych g ru p p a ń stw w E u ro p ie z p u n k tu w idzenia aktyw ności patentow ej. P odział d o k o n a n y został z w ykorzystaniem m etod statystycznych - w tym głów nie funkcji dyskrym inacyjnej. P rzedstaw iona a n aliza po zw ala ch arak tery zo w ać poszczególnych uczestników o raz zwrócić uwagę n a różnice w p ro w ad zo n ej polityce innowacyjnej w ró żn y ch p ań stw a ch .
