The Externalities of Enterprises’ Innovative Activity – An Input-Output Approach

Abstract The article assesses the impact of final demand for domestic products on the innovative activity of Polish enterprises. The activity is analysed in terms of their involvement in research and development (R&D) processes, which are considered crucial for an economy to be able to create a stock of knowledge. The main purpose of the analysis is to identify products that contribute to the largest increases in enterprises’ R&D expenditures. To study the effect of final demand on enterprises’ R&D activity, the input-output analysis method has been adopted. The presented analysis is part of author’s research on the intersectoral diffusion of knowledge in the Polish economy.


Introduction
In today's world, knowledge and innovations are considered to be the key factors driving the development of contemporary economies. This view is founded on the findings of many economists who have analysed economic growth processes from both theoretical perspective 1 and empirical perspective 2 . It is worth noting that dynamic development of the modern-day economies depends as much on their knowledge stock as their capacity for absorbing knowledge and technologies from abroad.
This situation makes knowledge a special resource, a prerequisite for the creation and development of innovations. Innovation is defined as "breaking up with the existing practice, striving to attain competitive advantage by increasing the efficiency of production or distribution, or by introducing a new product" 3 . The economy's long-term ability to create and commercialise a stream of brand-new ideas and solutions known as its capacity for innovation is strongly and reciprocally related to the level and/or speed of its development. An important role in this process is played by research and development (R&D) activity, which is usually defined as "creative work undertaken on a systematic basis in order to increase the stock of knowledge, including knowledge of man, culture and society, and the use of this stock of knowledge to devise new applications" 4 . The stock of knowledge capital available to the economy is determined by scientific knowledge accumulated through R&D and the knowledge possessed by the society (its level of educational attainment).
One characteristic feature of knowledge is its ability to spread across an economic system (diffusion of knowledge, transfer of knowledge). The process can take place at every level of the system: between enterprises, between sectors (intersectoral diffusion of knowledge), as well as between regions or countries (interregional or international diffusion of knowledge). Two types of knowledge transfers are usually referred to in the literature irrespective of the level of detail of the conducted analysis 5 : -a product-embodied knowledge transfer which occurs when an economic entity concludes a formal sale-buy transaction to purchase a new or considerably improved product, thus formally acquiring the knowledge the product contains. In this case, the embodied knowledge spreads with the flows of intermediate and investment goods, imports, foreign direct investments, patents and licences, etc., -a disembodied knowledge transfer, i.e. via informal contacts between economic agents. This type of transfer is related to observation, learning, and the copying of generally accessible knowledge.
The assessment of the benefits that knowledge transfers bring to the economy is very difficult to perform. The selection of the measurement methods is determined, inter alia, by assumptions that have been made about 1) the type of the transfer (embodied or disembodied), 2) the channels of knowledge diffusion (e.g. flows of raw materials inside or between economies, flows of investment goods, import, FDI, flows of patents, etc.), and 3) the level of the analysis itself (microeconomic, macroeconomic, sectoral, regional). The very measurement of the economy's stock of knowledge is not easy to make either.
This article concentrates on the methods used to measure the amount of economy's benefits from the transfer of knowledge "embodied" in domestic intermediate goods. The transfer takes place at the industry level and the carriers of knowledge are domestic intermediate goods flowing between industries. The factor stimulating knowledge flows in the economy is final demand for domestic goods from particular institutional sectors. An assumption is made that the knowledge stock of particular Polish industries is determined by their expenditures on research and development activity (R&D) 6 . While being only one aspect of enterprises' innovative activity, R&D 7 seems to be indispensable for creating a stock of knowledge. Hence, in this analysis, R&D externalities will be understood as an increase in R&D expenditures in the economy determined by greater domestic final demand for some groups of products.
The analysis presented below makes use of embodied innovation flow matrices constructed for the Polish economy 8 . The matrices and the selected elements of multiplier analysis allow indicating groups of products that embody the most of domestic R&D expenditures, so an increase in final demand for these products contributes the most to increasing R&D activity in the country. The matrices also enable domestic R&D expenditures to be disaggregated into final demand categories, i.e. to determine the role of particular institutional sectors as the stimulants of domestic R&D.
The article is structured as follows. Section 1 presents the construction of an innovation flow matrix, the interpretation of its particular elements, and R&D multipliers. Section 2 provides some comments on the statistical data underpinning the analysis. Section 3 discusses the results of empirical research. The last section 4 presents the conclusions from the analysis.

The methodology of constructing an innovation flow matrix
The construction of an innovation flow matrix starts with a standard input-output (I-O) model defined as: Model (1) can alternatively be written as domestic output: Vectors k x and k y denote, respectively, domestic gross output and final demand for domestic products, and the k k By solving model (2) with respect to domestic gross output we obtain: Hence the notion of a so-called total (direct and indirect) increase in the gross output of industry i caused by a unit increase in final demand for industry j's output is frequently used.

Another important element of the input-output analysis is the sums of the elements in the
Leontief-inverse matrix columns, which are called simple output multipliers 10 . The multipliers' values for the j-th industry determined from the matrix in equation (3), i.e.
how much gross domestic output will increase in the economy because of a unit increase in the final domestic demand from the j-th industry.
The construction of the flow matrix of innovations embodied in domestic intermediate goods starts with the determination of the direct coefficients of domestic R&D expenditures known as R&D intensive coefficients. Assuming that the proxy of the industry's capacity for innovation 11 is the amount of its R&D expenditures (BR i ), the R&D intensive coefficients for industry i (r i ) can be written as: The value of this coefficient indicates the value of industry i's domestic R&D expenditures per a unit of its gross domestic output.
Using relations (3) and (4), total R&D expenditures in the economy can be presented as: Hence, the element j of vector ñ , i.e. j ρ , shows the value of domestic R&D expenditures per a unit of final demand for domestic products of industry j, or -in marginal terms -an increase in domestic R&D expenditures caused by domestic final demand of industry j increasing by a unit. Accordingly, j ρ can be called an R&D multiplier for industry j 12 .
Equation (5) written with the appropriate diagonal matrices provides more detailed information on the level of industry i's R&D expenditures that is required for industry j to satisfy its final demand for domestic goods. Because of that, the matrix: where: is therefore the total amount of (domestic) R&D expenditures involved in a unit of final demand for domestic products. In other words, the sum is identical with the earlier defined R&D multiplier for industry j, i.e.: By multiplying matrix H by the diagonal matrix of domestic final demand we arrive . the sum of the j-th column elements of this matrix stands for the value of R&D expenditures that the whole the economy must make to satisfy industry j's final demand for domestic products.

Statistical data used in the research
The innovation flow matrix for the Polish economy was constructed with the symmetric input-output tables of inter-sectoral flows for domestic products. The data on R&D expenditures made in 2000 and 2005 were obtained from the OECD database (STAN). The database was selected because its data show R&D expenditures made by both manufacturers and service providers (the national data from these years are quite comprehensive regarding the R&D expenditures of manufacturers, but rather fragmentary with respect to service providers). The data (available at the second and sometimes also at the third level of the Statistical Classification of Economic Activities in the European Community, NACE) were transformed into a product-based system using a supply matrix as described by Przybyliński (2012, p. 70). The values of R&D expenditures were additionally converted into PLN using the average USD exchange rate.

The results of empirical research
The structures of R&D expenditures made by the manufacturing sector in both analysed years were not considerably different from each other (a similarity rate of around 83%). In both 2000 and 2005, most expenditures were made to manufacture goods, mainly machinery and equipment (respectively 11% and 9.5%), chemicals and chemical products (9.8% in both years), motor vehicles, trailers and semi-trailers (6.7% and 10.2%), other transport equipment (7.1% and 6.4%), and electrical machinery and apparatus (5.1% in both years). In the services sector, R&D services (2.8% in 2000 and 2.5% in 2005) are worth noting, as well as computer and related services the importance of which was considerably greater in 2005 (increasing from 0.1% to 3.9%). The changes are also reflected in the R&D multipliers (see Table 1) determined from formula (5).  intensive. It is worth noting, though, that while these groups of products embody a significant proportion of the domestic expenditure on R&D, their role in stimulating domestic R&D activity decreases, as proven by the diminishing values of multipliers for the majority of the aforementioned groups of products. An exception is computer services for which the multiplier increased more than fourfold. This increase was driven by growing demand for this type of service from final users (mainly households) and more than a tenfold increase in R&D expenditure on these services.
Higher values of the multipliers of domestic R&D expenditures were also noted in the case of financial and insurance services and machinery and equipment rental services.
With the innovation flow matrix derived from relation (6), R&D expenditures were decomposed into final demand categories (see Figure 1). The graph shows exports to embody the greatest proportion of domestic R&D expenditures. An increase in the importance of export as the stimulant of domestic R&D activity is also noticeable. Slightly more than 30% of R&D expenditures in the country are allocated to domestic products addressed to households. This rate was stable in both investigated years.
Another observation is a minor decrease in domestic R&D expenditures resulting from less active government consumption and investment processes.

Conclusions
The above analysis of the externalities generated by enterprises' innovation activities was undertaken to identify the role of final demand for domestic products as a stimulant to research and development activity in the country. The analysis was based on the multipliers of domestic R&D expenditures and the flow matrices of innovations embodied in domestic intermediate products. The results of this study point to a diminishing effect of final demand for domestic products on domestic R&D activities. Lower values of the R&D multipliers (in the case of some products they are several times lower) are caused by decreasing domestic R&D expenditure and its unfavourable structure -the business sector's contribution is relatively small compared with that in the technologically advanced countries. The trend is particularly marked in manufacturing (lower multiplier values for all manufacturing products). Conclusions must be formulated with caution, though, because the balanced input-output tables become available with a delay. The changes that have been observed in the R&D sphere in recent years, such as increased expenditures on R&D activity, seem to promise that despite the structure of the expenditures being still unfavourable from the perspective of their effectiveness the role of domestic R&D will increase.
As found, the R&D activity in Poland is mainly stimulated by exports and household final demand. The analysis of domestic demand for particular groups of products that aimed to determine their effect on domestic R&D activity has revealed the central role of demand for knowledge-intensive products and services. The stable structure of R&D expenditures made by institutional sectors indicates that the main drivers of domestic R&D will be exports (particularly of medium-and high-tech manufacturing products) and household consumption.
The analysis is part of author's research into inter-sectoral diffusion of knowledge in Polish economy.