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DYNAMIC ECONOMETRIC MODELS 
Vol. 9 – Nicolaus Copernicus University – Toruń – 2009 

Marek Szajt 
Technical University of Częstochowa 

Estimation of Disproportions in Patent Activity of OECD 
Countries Using Spatio-Temporal Methods 

A b s t r a c t. The article contains a presentation of possibility of using panel-based sample and 
modelling based on this sample as methods of determining indicators of patent activity. The 
research was conducted with the help of data from European countries. Results in association with 
used methodology, which takes into account modern approach to stationary and cointegration for 
panel-based samples, indicate the usefulness of applied methods. 

K e y w o r d s: patent activity, panel model, decomposition of intercept.  

1. Introduction  
Within the area of innovation, which enjoys an increasing interest of the 

economists, there are many ways of measurement. In the macro-economics 
conception – due to the requirements concerning the length of time series – 
space-time sample or panel sample are used frequently. 

Their advantages include, apart from the opportunity to conduct research it-
self, the possibility of obtaining results which are comparable for various ob-
jects, which are received on the basis of decomposition of a random term or 
intercept. These study are directly connected with the patents based on the in-
ventions understood as “original conception of technical innovation, which con-
tains theoretical possibility of action” (Budnikowski, 1995). The patent activity 
is one of the most accessible measures of innovation activity due to the possibil-
ity of obtaining fairly comparable data, which is a result of the legal framework 
behind the acceptance and granting patents. The available information comes 
mainly from the World Intellectual Property Organization (WIPO) and the 
European Patent Office (EPO). Putting aside the character of explanatory vari-
ables, the equation used to describe the patent activity with the use of panel data 
enables obtaining, as a result of decomposition, specific indices of patent activ-
ity. The differences between these values have a direct influence on the theo-



Marek Szajt 92

retical values of the dependent variable (depending on the model – additive or 
multiplicative) diversifying its value for various objects with the same basic 
assumptions.  

2. Assumptions 
In the present research the following assumptions were accepted:  
− the measure of patent activity is the number of patent applications submitted 

with the EPO per one thousand professionally active persons,  
− the determinants of patent activity are gross outlays for the research and de-

velopment activities as well as the researchers working within the research 
and development area,  

− the measurement (test) is of time cross-sectional character, and the data 
concern the periods from 1995–2005 and the European countries belonging 
to the OECD (together with Latvia and Estonia); on the one hand the use of 
longer sequences is impossible – lack of data, on the other hand there is a 
threat of disruption of the present relations by the introduced system 
changes, particularly in the Central and Eastern Europe area,  

− the possibility of interpolation is accepted in the case of occurring incidental 
lack of data or reproducibility of collected results less frequent than annual. 
Depending on the form of studied process, the segment method or a fitted 
trend function which has possibly most simplified analytical form (it con-
cerns mainly a degree of a polynomial) are used,  

− source data coming from the analyses of the EUROSTAT, OECD, WIPO 
and national statistical offices is not directly corrected in the cases of sus-
pected errors or inaccuracies. 

3. Introductory Calculations 
At the initial stage the space-time sequences which were supposed to form 

the basis of the model construction, were taken into consideration. Time series 
of 11 annual observations, despite they are short, seem to be sufficient to ob-
serve non-stationarity. What is more important, we want to treat the conclusions 
based on final calculations as independent of time factor. In this situation non-
stationarity of these series should be researched, assuming that integration order 
is not higher than 2 in the case of annual data (Gruszczyński, Podgórska, 2004). 
In order to realize it, the procedures contained in the Eviews package were used. 
These procedures enable a relatively fast evaluation of possible lack of station-
arity or the evaluation of the integration order. The tables below present the 
results of a few unit root tests, which indicate the existence of unit root. 

 
  



Estimation of Disproportions in Patent Activity of OECD Countries … 93

Table 1. The results of unit root tests for levels (H0: δ = 0)  

Variable Estimator: 
Method: 

Newey-West Andrews 
statistic p-value statistic p-value 

PET 

Levin, Lin & Chu t* -7.1708 0.0000 -7.0058 0.0000 
Im, Pesaran and Shin W- statistic -1.9999 0.0228 -1.9999 0.0228 
ADF - Fisher χ2 69.8771 0.0331 69.8771 0.0331 
PP - Fisher χ2 118.7770 0.0000 83.3070 0.0022 

GERD 

Levin, Lin & Chu t* -1.1929 0.1165 -8.4510 0.0000 
Im, Pesaran and Shin W- statistic 0.8544 0.8036 -5.4559 0.0000 
ADF - Fisher χ2 51.6001 0.4110 123.3190 0.0000 
PP - Fisher χ2 54.5887 0.3044 121.3650 0.0000 

RECH 

Levin, Lin & Chu t* -3.0271 0.0012 -9.5927 0.0000 
Im, Pesaran and Shin W- statistic 1.6752 0.9531 -5.5232 0.0000 
ADF - Fisher χ2 39.2213 0.8641 120.3260 0.0000 
PP - Fisher χ2 42.0529 0.7804 117.9310 0.0000 

Note: * assumes common unit root process. 

The probabilities for Fisher test are computed using an asymptotic Chi-
square distribution. All other tests assume asymptotic normal distribution. 

Table 2. The unit root tests results for first difference (H0: δ = 0) 

Variable Estimator: 
Method: 

Newey-West Andrews 
statistic p-value statistic p-value 

PET 
 
 

Levin, Lin & Chu t* -10.2833 0.0000 -10.4350 0.0000 
Im, Pesaran and Shin W- statistic -6.2851 0.0000 -6.2851 0.0000 
ADF - Fisher χ2 133.2590 0.0000 133.2590 0.0000 
PP - Fisher χ2 150.2810 0.0000 142.5140 0.0000 

GERD 
 
 

Levin, Lin & Chu t* -9.7824 0.0000 -8.4510 0.0000 
Im, Pesaran and Shin W- statistic -5.4559 0.0000 -5.4559 0.0000 
ADF - Fisher χ2 123.3190 0.0000 123.3190 0.0000 
PP - Fisher χ2 144.5690 0.0000 121.3650 0.0000 

RECH 
 
 

Levin, Lin & Chu t* -11.0622 0.0000 -9.5927 0.0000 
Im, Pesaran and Shin W- statistic -5.5232 0.0000 -5.5232 0.0000 
ADF - Fisher χ2 120.3260 0.0000 120.3260 0.0000 
PP - Fisher χ2 131.2820 0.0000 117.9310 0.0000 

Note: * assumes common unit root process. 

Regarding the endogenous variable (PET), all the tests results indicate sta-
tionarity. The remaining variables are characterized by different results, particu-
larly the ones obtained with the use of Newey-West estimator. The Andrews 
estimator, produce more stable bandwidth estimates than the Newey-West pro-
cedure (indicating the stationarity in this situation), which could be expected 
taking into account the PP test and the previous research conducted by Yin-



Marek Szajt 94

Wong Cheung and Kon S. Lai (1997). Therefore, taking into account possible 
existence of unit roots, we can assume that our variables are integrated on order 
1, ~ I (1) (what is suggested by the consistent results of all tests). Hence assum-
ing the integration order is common for all the variables, we try to test the exis-
tence of cointegration in the assumed system, i.e. equation with PET as depend-
ent variable and GERD and RECH as independent variables.  

The estimation with the use of Eviews programme gives the possibility of 
obtaining (in the case of using summarised results) the evaluation of statistics 
for seven tests. However, the use of these tests is difficult, as they can give (and 
such is our case) different results. It is connected with the size of applied panel. 
Pedroni (2004), who researched situations of this kind with the use of Monte 
Carlo simulation, indicated that the use of panel test-v and group test-rho gives 
bad results even in the case when the length of time series  in the panel is 
smaller than 20 observations. In such cases, the group test – ADF and panel test 
– ADF are more appropriate.  

The test results are tabulated in Table 3. 

Table 3. The results of cointegration test for Pedroni residuals in the model of PET on 
GERD and RECH variables 

Alternative hypothesis: common AR coefficients (within-dimension) 
Model type No deterministic trend No deterministic intercept or trend 
Test type statistic p-value statistic p-value 

Panel v-Statistic -0.8536 0.8033 0.9798 0.1636 
Panel rho-Statistic 2.3876 0.9915 0.3700 0.6443 
Panel PP-Statistic -0.0985 0.4608 -1.7103 0.0436 

Panel ADF-Statistic -0.4230 0.3361 -1.8798 0.0301 
Alternative hypothesis: individual AR coefficients (between-dimension) 

Test type statistic p-value statistic p-value 
Group rho-Statistic 3.0116 0.9987 1.9235 0.9728 
Group PP-Statistic -5.0759 0.0000 -3.5982 0.0002 

Group ADF-Statistic -2.5234 0.0058 -3.4899 0.0002 

Only the results based on “group” tests- (recognized as being more  power-
ful than “panel” tests when conducting a research on smaller samples (cf. 
Pedroni, 1995)) – indicate the existence of cointegration. Excluding the exis-
tence of intercept, tests based on v and rho do not reject the H0 of the lack of 
cointegration what is undesired from the point of view of this research.  

However, taking into account the remarks of Pedroni, we find the results of 
ADF tests as the more appropriate ones, which reject the H0. 

However, taking into account the remarks of Pedroni, we find the results of 
ADF test which indicate the rejection of H0 as more appropriate. Hence, the 
existence of cointegrating vector can be stated.  



Estimation of Disproportions in Patent Activity of OECD Countries … 95

It is worth emphasizing that the PP test also gives expected result. It should 
be remembered that the “group” tests, in contrast to the “panel” ones, assume 
that the autoregression coefficients do not have to be homogenous for all ob-
jects (Hsu-Ling and others, 2008). Therefore, assuming the low power of the 
group test-rho, the results of remaining group tests indicating the existence of 
cointegration are accepted  

The achieved results do not offer the possibility of making an unambiguous 
decision by the researcher. On the one hand we can assume that the cointegra-
tion vector exists, if we exclude the intercept in our model. However, it should 
be remembered that this model, due to the panel construction, will have the 
decomposed intercept. This intercept, depending on the significance of its par-
ticular parts will be “complete” intercept (consisted of so many parts as many 
countries contains the model) or will be equivalent of a few dummies variables 
included in the model.  

On the other hand, having in mind the fact of PET stationarity, the recogni-
tion of PET variable as integrated of first order seems to be misused. 

In connection with the indicated doubts concerning the existence of cointe-
grating relations, the error correction model was proposed which in such cases 
is one of the most popular tools (Strzała, 2005).  

Ids additional advantage is taking into account both short- and long-term re-
lationships. As a result, the interpretation of the decomposed intercepts (funda-
mental in this research) is more precise. The possible dynamic dependencies are 
more visible in the estimates of structural parameters (for independent vari-
ables). 

The following form of model was proposed: 

,log                      
log)log                      

log)(log1('log

2

112

1111

itit

itit

ititiit

RECHA
GERDPRECHA

GERDPPATAaPATA

ξβ
βδ

δρ

++
Δ+−
−−+=Δ

−

−−

 (1) 

where: a’i denotes the intercept decomposed into i = 25 objects – countries, 
PATAit – number of patents application, submitted by the residents of a given 

country i per number of professionally active persons in the period t, 
GERDPit – gross expenditures on research and development (R+D) activities 

per the R+D staff working on full-time basis in the country i in the pe-
riod t, 

RECHAit – persons employed as researchers on full time basis in comparison 
to the number of professionally active persons in the country i in the 
period t, 



Marek Szajt 96

4. Results 
In accordance with the accepted assumptions the estimated model (with the 

full decomposition of intercept) has showed dependence for logarithms of va-
riables (Szajt, 2006). Due to the differences in the directions of dependencies 
between the particular variables for different countries, 16 countries were quali-
fied to the final test. The Gretl programme was used to estimate the model. At 
the beginning a test for variability of intercept was used. The test statistics  
F(15, 140) = 3.814 with the value p = 1.15252e-005 confirms the validity of 
estimation of panel model with fixed effects. During the estimation process the 
insignificant variable GERDt-1 was removed from the model. The final results 
are presented in the Table 4.  

Table 4. The values of structural parameter assessments in power model  

Variable Parameter Parameter estimate t - statistics p-value 
PETA i,t-1 α1 0.5683 -6.9836 0.0000 

RECHA i,t-1 δ2 0.7809 1.9086 0.0584 
ΔGERDPi,t β1 1.0802 3.5093 0.0006 
ΔRECHA i,t β2 0.7617 2.6235 0.0097 

BEt αBE 0.3060 -2.9727 0.0035 
CZt  αCZ 0.1137 -5.1812 0.0000 
DKt  αDK 0.2999 -2.9377 0.0039 
DEt  αDE 0.4010 -2.5089 0.0133 
EEt  αEE 0.0767 -5.0538 0.0000 
IEt  αIE 0.2281 -3.8027 0.0002 
FRt  αFR 0.3007 -3.0255 0.0030 
LVt  αLV 0.0709 -5.4952 0.0000 
HUt  αHU 0.1259 -5.1246 0.0000 
NLt  αNL 0.3877 -2.8611 0.0049 
ATt  αAT 0.3329 -3.0377 0.0028 
PLt  αPL 0.0597 -5.3160 0.0000 
PTt  αPT 0.0853 -5.2087 0.0000 
FIt  αFI 0.2972 -2.4965 0.0137 
SEt  αSE 0.3160 -2.6370 0.0093 
NOt  αNO 0.1891 -3.3407 0.0011 

It should be noted that all the estimates concerning the decomposed inter-
cept are highly statistically significant, which is to a large degree the objective 
of this estimation. What is even more important, in connection with the form of 
function, the intercept has multiplicative character.  



Estimation of Disproportions in Patent Activity of OECD Countries … 97

 
Figure 1. The values of assessments of decomposed intercept (for simple countries) 

Presented on the Figure 1 constant level 0.1873 reflects the estimated in 
a test common intercept (an equivalent of the average level of patent activity) 
for the whole group. In comparison to it, such countries as Germany or the 
Netherlands turned out to be absolute leaders, whereas Poland, Latvia and Esto-
nia were outsiders. The consequents of such conclusions are important. In prac-
tice, with equal factors determining the patent activity, difference of final reac-
tion – in the long -run - will be close to differences presented on Figure 1 
Therefore, a very high or low patent activity of particular countries can be 
found.  

As it is seen, this simple method (using panel sample construction) enables 
obtaining very valuable, comparable indicators. It is also important that, their 
estimates usually are not strongly sensitive on the changes of main determinants 
of studied process. In extreme cases, together with characteristic values (for 
chosen countries) we can obtain “typical” values represented by a common (for 
all countries) intercept. 

References  
Budnikowski, F. (1995), Ekonomia. Innowacje ekonomiczne w gospodarce narodowej (Economy. 

Economic Innovation in National Economy), OWPR, Rzeszów. 
Gruszczyński, M., Podgórska, M. (2004), Ekonometria (Econometrics), Oficyna Wydawnicza 

SGH, Warszawa.  
Hsu-Ling, Ch., Yahn-Shir, Ch., Chi-Wei, S., Ya-Wen, Ch. (2008), The Relationship between 

Stock Price and EPS: Evidence Based on Taiwan Panel Data, Economics Bulletin, Vol. 3, 
No. 30. 

Pedroni, P. (2004), Panel Cointegration: Asymptotic and Finite Sample Properties of Pooled Time 
Series Tests with an Application to the PPP Hypothesis, Econometric Theory, 20,  
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Pedroni, P. (1995), Panel Cointegration, Asymptotic and Finite Sample Properties of Pooled Time 
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Yin-Wong, Ch., Kon, S. L. (1997), Bandwidth Selection, Prewhitening, and the Power of the 
Phillips-Perron Test, Econometric Theory, 13, Cambridge University Press, 679–691. 

Szacowanie dysproporcji w aktywności patentowej państw OECD  
z wykorzystaniem metod przestrzenno-czasowych 

Z a r y s t r e ś c i. W artykule przedstawiono możliwość zastosowania próby panelowej i mode-
lowania w oparciu o nią jako metody wyznaczenia wskaźników aktywności patentowej. Badanie 
przeprowadzono z wykorzystaniem danych dla państw europejskich. Otrzymane wyniki w zesta-
wieniu z zastosowaną metodologią uwzględniającą nowoczesne podejście do badania stacjonar-
ności i kointegracji dla prób panelowych, wskazują na użyteczność stosowanych metod.  

S ł o w a k l u c z o w e: aktywność patentowa, model panelowy, dekompozycja wyrazu wolnego.  


