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 FOLIA OECONOMICA 182,2004
Grażyna Juszczak-Szumacher*
S E L E C T E D M E T H O D S O F M E A S U R IN G O F T E C H N O L O G IC A L
P R O G R E SS
Technological progress is a com m on phenom enon to be encountered on daily basis and in different aspects. Technological progress is perceived as a com bination o f quality changes in m anufacture and services along with accom panying organisational changes. They are result o f innovation that is brought about by various institutions on different econom ic levels. R esearch institutions and academ ic centres conduct basic research, R & D institutes concentrate on applied research and there is also developm ent and im plem entation w ork relating to the sphere o f econom ic practice. An alternative to conducting own research is to purchase patents and licences that can also be a driving force behind the developm ent and is often less expensive.
There are various classifications o f technological progress. T he m ost useful seems to be the division between three kinds o f innovations nam ely process, product and organisational innovations. The first type concerns the sphere o f m anufacture and relates to m odernisation of the production facilities substituting labour with equipm ent o f different m echanisation and autom ation degree. Product innovations concentrate on changing quality o f goods and services by means o f their m odernisation or by launching new products. O rganisational innovations involve the whole range o f activities aim ing at increasing efficiency of m anufacturing and distribution, efficiency being an inherent elem ent o f technological pro g ress1.
A broad concept of technological progress and its effects m akes this phenom enon very difficult to measure. The GUS (Polish C entral Statistical O ffice) carries out studies and publishes detailed inform ation on it. They concern for exam ple the efforts made by com panies to finance R& D, effects brought about by m echanisation and autom ation o f production processes or m odernisation o f goods and services. On the one hand such diversity is an advantage as it allow s for analysis o f different aspects o f technological progress,
* Prof., Chair o f Econom ic and Social Statistics, University o f Łódź.
1 Issues concerning technological progress are discussed in numerous monographs, and a concise summary is also given by G. Juszczak-Szumacher [1996].
but on the other it is a disadvantage if we want to m ake a thorough analysis of this phenom enon.
T his study show s how to reduce a num ber o f characteristics o f technological progress with the use o f taxonom ic m ethods and factor analysis. One approach allow s us to construct a synthetic m easure based on detailed characteristics or to m easure a distance betw een two com parable objects. T he other approach reduces the original set o f indicators to a group o f factors that provide the best explanation for the variability o f the phenom enon within the studied group of objects. Having the synthtetic m easure(s) of technological progress we can use it in regression analysis to explain the influence o f this phenom enon on the total econom ic activity or som e of its aspects (for exam ple foreign trade or labour productivity). T he both presented methods should be perceived as an exam ple of approaches that give a broader picture of technical progress when com pared with detailed characteristics published by GUS.
1. T a x o n o m ic m ethods
Taxonom ic m ethods enable us to com pare a set o f objects characterised with many features. The basis for calculations is the observation m atrix o f к value o f
d iagnostic features in n num ber o f objects: X = [x:j J (i = 1 , 2 ...n; j = 1, 2 ,..., k). Each m atrix row includes observations on all diagnostic features in a given object w hereas each colum n is a set o f values o f a given diagnostic variable (characteristic) in all studied o bjects2. In this analysis o f technological progress objects can be understood either as periods o f certain tim e intervals, as sectors o f econom y analysed in a given period o f time or as the sam e sectors studied in different periods o f time.
1.1. The construction o f the synthetic measure
C haracteristics o f com parable objects are expressed in various units o f m easure. In order to establish the synthetic m easure they need to be transform ed in a way that w ould enable com parability. Am ong m ethods o f such conversion are standardization and norm alization (see: Nowak E. 1990). Standardization is a conversion w here the arithm etic mean o f a feature value evaluated for all objects is subtracted from a feature value in i -th object and the difference is divided by the feature standard deviation. This gives us transform ed values which are expressed in standard deviation units. Norm alization is a transform ation
2 Selection o f diagnostic features for a comparative analysis o f objects is quite problematic. Various methods are used for this purpose e.g. H ellw ig’s parametric model [1981].
where the original feature value is divided by the norm alization factor which can be an average, m axim um or m inim um feature value or a feature value o f any object from the studied set.
W ith the use o f the transform ed feature values you can construct the synthetic m easure applying model or non-m odel m ethod, the other being easier. It requires all transform ed features to be o f the sam e character i.e. to be either stim ulants or destim ulants. T herefore our first step is transform ation of destim ulants into stim ulants as this is m ore natural synthetic m easure for technological progress w hose higher values will indicate better position o f an object. A synthetic m easure can then be an expression that is an arithm etic mean o f norm alised feature values:
x
*
- value o f y-th feature (as stim ulant) in /-th object,A" j - arithm etic m ean of j -th feature determ ined for all objects.
Em pirical studies carried out with the use o f a m easure defined with formula (1) concerned three-year period 1999-2001 and a com parison o f 22 branches within the section o f industrial processing. T he set o f objects am ounted to 6 6 units. Each object was described with 10 features that determ ine different aspects o f technological progress. The choice o f these characteristics resulted from accessibility o f data base, published by GUS. The features were as follows:
- share o f new and m odernised goods in overall production value (in %),
- com puter controlled system s (in units),
- m achining centres (in units),
- industrial robots and m anipulators (in units), - autom atic production lines (in units),
- com puter-controlled production lines (in units), - capital expenditure on R&D (in mln zl),
- expenditure to purchase ready-m ade technology (in mln zl), - expenditure on m arketing new products (in mln zl),
- expenditure on m achines and technical equipm ent (in mln zl)3.
3 There are not all characteristics published by G US, but other data refer on ly to individual years. The set o f 10 features was a maximum option to ch oose for the studied period. The presented chractcrictics are absolute numbers because characteristics o f automation o f fixed assets
( 1)
where:
T he above calculation o f the synthetic m easure allow s fo r its clear interpretation. Its values are around I that is an average value o f the synthetic m easure for the w hole section in the studied period. A nd so 5, < I indicates progress in i-th branch below average and consequently if 5( > 1 it m eans that i-th branch is above average. T he breakdow n o f all values o f the synthetic m easure is given in the annex. S { values for the tw o poorest (m anufacture o f basic m etals and textile industry) and tw o best branches (m anufacture o f m achinery and equipm ent and m edical instrum ents) are d epicted in Fig. 1. 2.5 2 1.5 0.5 0
Metals Textile Machinery Med instruments
Fig. I . Comparison o f synthetic measures for chosen branches S o u r c e : Own elaboraton.
R elations betw een determ ined values o f the synthetic m easure o f “end” branches are significant. It is also interesting that in various branches changes go in different directions in time. In case o f textile industry the synthetic m easure has a rising tendency whreas in m anufacture o f m edical instrum ents a considerable fall o f the value can be observed.
1.2. Analysis o f similarities between objects
Taxonom ic m ethods also allow to determ ine a distance betw een objects described with various features. T. M ichalski [2002] points out to tw o types of distance, both o f which show differences in absolute values o f characteristics and em phasize structure differences. The appropriate m easures can be defined as follows:
are divided by gross value o f fixed assets in constant prices whereas the value o f outlay was referred to the production sold in a given branch.
- sim ilarity o f level o f objects s and q
cl(s,q ) = 1
-2,/ibil
(2)
X
— — is a standard feature value, where: ztJ =
- sim ilarity o f structure o f objects s and q
(3)
where: yU (s ,< r/) =
B oth m easures are set in interval < 0 ,1> which m akes their interpretation easier.
Sim ilarities betw een objects were determ ined for characteristics observed on m acroeconom ic level in 1990-2001, objects being consecutive years. Detailed indicators o f technological progress (features) are different for the whole econom y than those used for the analysis o f the production sector. On m acroeconom ic level R& D basic and applied research is analysed w hereas in case o f industry m ore em phasis is put on im plem entation. M acroeconom ic characteristics m ainly include a num ber o f issued patents and inventions claim ed in different classifications.
The set o f features for research carried out in 90s was assigned three m easures i.e. the synthetic m easure o f technological progress as given in a form ula (1), level sim ilarity m easure (2) and structure sim ilarity m easure (3). For the synthetic m easure a dynam ics index was defined as year 1990 = 1 whereas sim ilarity m easures were calculated for consecutive years in com parison with the year 1990. In the first sam ple year all m easures equal 1 as it is shown in Fig. 2.
The value o f the synthetic measure for all years is below the level o f 1990. The biggest drop noticed in 1993 is not suprising given a decline o f economic activity at the beginning of the 90s. In consecutive years S, dynam ics gradually increases only to fall dramatically in 2001. The level sim ilarity achieved the lowest value at the end o f the sample period and the structure sim ilarity in 1995. In Fig. 2 we can notice that two o f the three measure values converge in the last year.
However the picture we get is pessimistic as for chances for developm ent o f our economy and its com petitiveness on the EU market. Technological progress is the most important driving force behind this developm ent and if we neglect financing it the gap between Poland and the poorest EU countries will only widen.
1 . 2 1 0 . 8 0 .6 0.4 0 . 2
Fig. 2. Comparison o f changes in the synthetic measure for technological progress along with level and structure similarity measures
S o u r c e: A s same as Fig. 1.
2. F actor a n alysis
In this analysis a set o f features describing objects is substituted by a sm aller num ber o f unobservable factors. It is assum ed that each original feature is a linear function o f m com m on factors and one specific factor that can be represented in a follow ing system o f equations (see: W. Pluta 1977):
X, = a n Fi + a n F2 +... + a imFm + a iU l
X j ~ a j\F x + a j2F2 +... + a JmFm + a jU j (4)
X к ~ a k \ F \ + a k 2 ^ 2 + • • • + а кт ^'т + a k ^ k
where:
X - original variable (observation vector for all objects), Fj - /-th com m on factor (value vector for all objects), U j - ;-th specific factor (value vector for all objects), a j;,a j so called factor loadings.
It is dem onstrated that a factor loading a,, is a coefficient o f linear correlation betw een j'-th observed standardised variable and i-th com m on factor. A variance o f ;-th variable can be formulated as a sum o f squares o f factor loadings from 7-th row o f the above system. Com mon factors should explain the biggest part o f this variance so as to m axim ise so called com m unality given in a formula:
In the analysis we use reduced correlation m atrix that m eets a condition:
w here the main diagonal com m unality estim ates are placed. O ther m atrix elem ents are coefficiants o f linear correlation betw een standardised observable characteristcs. T he equation (6) is a basic relationship used to determ ine factor loadings.
I he most popular m ethod o f factor extraction is the
principal component
method.
T he lirst factor is the one that has m axim um share in com m on variance which m eans selecting appropriate factor loading values so as to m axim ise the follow ing expression:W e proceed with other factors in a sim ilar way. T he difference is that a starting point is a m odified correlation matrix after elim inaing the im pact of the first factor (and others). W e repeat this procedure until a specific condition is fulfiled. It can be K aiser criterion (see: G.A. Ferguson, Y. Takane 1997), which provides for the analysis o f characteristic root. Only those factors are worth considering that explain more variablilities than a single variable w hich means that their values should exceed 1. The last stage that facilitates factor interpretation is a rotation made for instance with the use o f varim ax m ethod that m axim ises variances in colum ns o f m atrices o f norm alised factor loadings.
F actor values can be determ ined as a product o f factor loading m atrices and standardised values o f observed variables:
R =A A T
(6)
(7)
F=A TZ
(
8)
Em pirical analysis that uses factor analysis and main com ponent method was conducted for 1 0 characteristics observed in 2 2 branches o f industrial processing sector for the year 2001. Table 1 gives prelim inary results o f the
analysis i.e. characteristic roots determ ined for m axim um num ber o f factors (equal the num ber o f characteristics).
Table 1. Characteristic roots and share in total com ponent variability (results o f main com ponent method)
Component Characteristic roots % variance Accum ulated % variance
1 2 .7 8 8 27.88 27.88 2 1.914 19.14 47.01 3 1.766 17.66 64.67 4 1.108 11.08 75.75 5 0 .7 9 4 7.94 83.7 0 6 0 .6 1 6 6.61 89.8 6 7 0 .4 1 0 4.10 9 3 .9 6 8 0.337 3.37 97.33 9 0.1 7 2 1.72 9 9.05 10 0.095 0.95 100.00 S o u r c e : Own calculations.
Table 2. Unrotated factor loadings and communality matrix
Variable Factor Communality
FI F2 F3 F4 UPN 0.6 9 4 0 .4 2 6 0.149 0.335 0.794 ALA 0.279 -0.644 0.578 -0.257 0.894 AK 0 .8 1 0 -0.003 -0.288 -0.055 0.739 ALA К 0 .3 3 0 -0.756 0.444 -0.044 0.879 ACO 0.771 -0.017 -0.253 -0.184 0.693 ARM 0 .777 -0.238 -0.173 0.213 0.736 DBR 0 .443 0 .332 -0.195 -0.313 0.441 ZT 0.2 3 4 0 .6 4 6 0.599 -0 .0 7 6 0.835 NIM 0 .0 7 4 -0.025 0.365 0 .807 0.791 MAR 0 .0 9 6 0.401 0.713 -0.304 0.770 S o u r с e: A s same as Tab. 1.
Only first four com ponents fulfill K aiser criterion. T herefore four com m on factors are defined here. Tab. 2 shows values o f factor loadings and and their square sum i.e. com m unality. ALA has the gratest value o f com m unality as it is nearly 90% . The low est value, lower by 50%, is given for DB R variable.
Interpretation o f the factors was carried out with the use o f varim ax rotation. The trasform ed factor loadings are given in Tab. 3. The bold values indicate the follow ing connections betw een factors and individual variables:
FI
UPN AK ACO ARM DBRF2
ALA ALAKF3
ZT M ARF4
E xpenditure on m achines and technical equipm ent
Table 3. Rotated factor loadings matrix
Variable Factor FI F2 F3 F4 UPN 0.632 -0.149 0 .419 0 .447 ALA 0.035 0.935 0 .127 -0.037 AK 0.856 0.055 -0.041 -0.037 ALAK 0 .1 1 2 0.918 -0.083 0.131 ACO 0.812 0.101 -0.002 -0.154 ARM 0.766 0.236 -0.181 0 .2 4 6 DBR 0.514 -0.193 0.228 -0.297 ZT 0 .0 8 0 -0.103 0.895 0.1 3 4 NIM -0.068 0.072 0.059 0.882 MAR -0.099 0.162 0.854 -0.064 S o u r с e: A s same as Tab. 1.
The interpretation o f factors F2, F3 and F4 seems quite clear. F2 is a characteristic o f the most autom ated production process since it covers whole production lines. F3 concerns financing innovative activities w hereas interpretation o f F4 is neutral as it relates only to one original variable. F I due to the nature o f the m ethod used provides expalation for the largest part o f com m unality indicating the im pact o f five variables o f different character. This factor can be called a broad m easure for technological progress.
3. Summary
The exam ples presented here show how to use m ethods for broad statistical anaylysis. H ow ever they do not exploit all possibilities o f analysis of technological progress. At that stage it was a suggestion o f approach where a large scope o f inform ation on m anifestations o f technological progress and on a range o f financing it will be substituted with one (synthetic m easure) or several (factors in factor analysis) characteristics that provide a com prehensive picture of the whole phenom enon. It also gives an opportunity to use non-observable characteristics in further analysis that concerns the im pact technological progress exerts upon m echanism s in national economy.
R eferences
F e r g u s o n G. A. , T a k a n e Y. (1997), Analiza statystyczn a w p sy c h o lo g ii i p ed a g o g ice. Warszawa.
H e l l w i g Z. (1 9 8 1 ), W ielow ym iarow a analiza po ró w n a w cza i j e j za sto so w a n ie w badaniach w ielocecliow ych ob iek tó w gospodarczych. Warszawa.
J u s z c z a k - S z u m a c h e r G. (1996), M akroekonom etryczna a n aliza pro cesu produ kcyjnego, Lódź.
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G r a ż y n a J u s z c z a k -S z u m a c h e r
M E T O D Y PO M IA R U PO STĘPU T E C H N IC Z N E G O
Autorka podejmuje próbę oceny sposobów pomiaru postępu technicznego za pom ocą metod taksonom icznych i analizy czynnikowej. Przeprowadzone badania em piryczne pozw oliły na budowę syntetycznych m ierników rozwoju postępu technicznego. Z kolei metoda czynnikow a wskazuje, że spośród 10 charakterystyk postępu technicznego obserw ow anych w 22 branżach sektora produkcji przem ysłowej tylko 4 mają istotne znaczenie dla ocen y postępu technicznego.
An n e x .
Values o f synthetic measure for branches o f industrial processing section
Branches 1999 20 0 0 2001
Manufacture o f food products and beverages 1.2332 0 .6 6 2 4 0.7 3 4 2 Manufacture o f tabacco products 1. 2111 0 .8 4 8 0 0.6432
Textile industry 0.3868 0.4 8 8 8 0 .5 9 1 2
Manufacture o f wearing apparel and furs 0.9752 0.3 2 3 9 0 .4 1 1 6 Manufacture dressed leather products 0.4222 0 .4 3 0 9 0.5 2 9 4 Manufacture o f w ood and o f products o f wood 0 .5 9 4 4 0.7007 0.5 3 3 7 Manufacture o f pulp and paper 0.4739 0.4543 0 .4 8 7 5 Publishing and printing 0.6 1 1 7 0.7121 0 .5 0 3 6 Manufacture o f coke and refined petroleum products 1.6643 1.0175 0 .8 4 3 4 Manufacture o f chem ical products 1.2661 1.4853 1.2527 Manufacture o f rubber and plastic products 0 .7 9 8 0 0 .9 6 7 8 1. 1163 Manufacture o f non-m etallic mineral products 0.7451 1.2071 0 .8 1 7 2 Manufacture o f basic metals 0.4 7 4 4 0.3 6 4 0
0 .3 5 1 4 Manufacture o f metal products 0.9317 0.7 9 4 9 0.8729 Manufacture o f machinery and equipment 1.8168 1.5382 1.5925 Manufacture o f office machinery and computers 1.8932 1.3192 1.1456 Manufacture o f electrical machinery and apparatus 1.4961 1.2548 1.4846 Manufacture o f radio equipment and apparatus 1.3308 1.3937 1.5270 Manufacture o f medical instruments 2 .1 3 4 4 1.9789 1.7588 Manufacture o f motor vehicles 1.1687 1.0806 1. 1812 Manufacture o f other transport equipment 1.2374 1.1560 1.2496 Manufacture o f furniture and other manufacturing 1.0363 1.1669 1. 1371
