A knowledge-based economy: new directions of macromodelling.

Issues concerning the absorption of foreign R&D cumulative expenditures were also raised. They indicated the important role that the expanding domestic stocks of R&D capital play in the foreign R&D stocks absorption and the role of growing human capital, especially consequential in the developing counties, that limits the application of foreign technologies. (see Benhabib and Spiegel 1994, Krueger and Lindahl 2001, Fuente de la 2004).

A few authors distinguished a separate spillover channel - Foreign. Direct Investment (FDI) (Cincera and van Pottelsberghe de la Potterie 2001). This separate treatment of the impact of FDI inflows related to the activities of multinationals is disputable, as the results of FDI flows are partly represented by the addition of

When the R&D effects are considered with respect to sectors and branches, it is also necessary to analyse the impacts of knowledge capital accumulated in the complementary sectors or branches.

Summary and Related Issues

The above relations are multiplicative in nature. For that reason, when the relation for R&D is examined, we obtain

ln [A.sub.t.sup.k] = [[beta].sub.l]ln [BRK.sub.t.sup.K] + [[beta].sub.2] ln BR[K.sub.t.sup.M] (7)

In the discussed context, the adequacy of using information on innovation outlays as an alternative to R&D expenditures also has to be investigated, particularly when research assumes disaggregations into sectors and branches.

It should be added that Barro's proposals (1999) to expand the range of new quality products and to analyse the impact of returns to scale (Peretto and Smulder 2002) have not been given sufficient attention in empirical research.

Impact of Human Capital Growth and Applications

The Concept of Human Capital

The way human capital growth influences economic growth remains a highly controversial issue. Let us recall that, following Lucas, human capital is frequently viewed as an independent production factor and excluded from the TFP notion. In our opinion, this approach is not legitimate as human capital per employee represents the quality of labour input and should not be separated. According to Nelson and Phelps approach, it may also show a positive relationship with the absorption of foreign capital (cumulated R&D).

Notwithstanding, the issue of measuring and explaining human capital dynamics requires an extended scope of research. Many researchers still operate primitive approaches and only use data on the share of employees with higher education among the economically active, or even on graduates/school-leavers or students attending secondary schools or academic institutions, even though global measures of human capital per worker have been developed.

Very broadly, human capital can be presented as a weighted sum of the number of economically active persons by level of education ([N.sub.it]):

[H.sub.t] = [summation][[mu].sub.i][N.sub.it], (8)

where

i educational level (for instance: primary, secondary, tertiary)

[mu]i weight attached to educational level i

The weights may represent (a) the standard number of school years; hence the right-hand side stands for total school years of the active population; (b) average wages earned by persons with different educational level; (c) average educational costs.

The Empirical Results

The first approach frequently used in investigations takes advantage of the cross section international data and for many years it has not brought convincing results (Benhabib and Spiegel 1994 and followers), mainly because of the international databases' shortcomings. The most recent research results based on improved data samples show that such measurement of the impact of human capital (mainly treated as a separate regressor) provides statistically reliable and convincing results (Fuente de la 2004).

Let us reproduce Fuente's results provided in his paper, setting them against the previous estimates of output elasticities with respect to human capital (per employee). The results were based on a Cobb-Douglas production function with constant returns to scale and obtained, with different specifications and schooling years, for the OECD countries in years 1960-1990 (see Fuente de la (2004), Table 4, 103).

The results below were calculated using both levels and first differences in logs. The most important are (t-statistics in brackets):

Levels First difference Nehru et al. (1995) 0.078 (2.02) 0.079 (0.70) Barro and Lee (1996) 0.165 (4.82) 0.083 (1.47) Cohen and Soto (2001) 0.397 (7.98) 0.525 (2.57) Fuente de la and Domenech (2000) 0.407 (7.76) 0.520 (2.17)

All the estimates using levels were statistically significant. However, earlier studies indicate much lower impact, whereas estimates based on first differences were significant only in the latest studies and showed much stronger impact not essentially exceeding that obtained for levels.

All the studies do not explicitly account for the impact of R + D spillovers (5). As we already mentioned, all specifications use the average number of schooling years as a proxy for the stock of human capital.

The second approach on our list has a deeper theoretical underpinning. Wage relations among employees with different levels of education reflect, of course, the differences in schooling years as Mincer suggested (Krueger and Lindahl 2001, 1003-1007). In the first place, however, they represent the market efficiency of different educational levels.

The choice of the above variables in not a purely academic issue. The empirical results of comparisons of human capital dynamics for Poland show large variations. In the period 1991-1998, the average annual rate of human capital growth per employee was 0.54% for wage ratios and 0.78% for schooling years (Welfe Ed. 2001, 163).

Let us note that the composition of employees can be extended even further. In the industrial studies employees can be subdivided using gender, age, position, etc. (for the USA, see Jorgenson and Stiroh (2000)). The feasibility of this method depends on the availability of detailed and updated databases on changes in employment structures that individual countries started to build only recently.

The third approach accentuating differences in educational costs is rarely used, mainly because of the scarcity of more detailed data. The approach has an obvious advantage-it enables a direct linkage between investments in human capital and the total educational expenditures (Welfe 2005).

Human Capital per Capita: Its Links to Educational Expenditures

Human capital per employee [h sub t] is obtained by dividing the total human capital by the total number of employees([N sub t]):

[h.sub.t]=[H.sub.t]/[N.sub.t] (9)

The human capital dynamics is defined by a balance equation:

[H.sup.t]= [H.sub.t-1]+ [HI.sub.t] [deltha][H.sub.t-1] (10)

where

[HI sub t] investments in humans capital (fixed prices)

[delta] rate of knowledge depreciation

A particularly difficult task is how to relate investments in human capital to expenditures on education (BDE.sub.t). A relevant submodel has to be constructed for this purpose (Welfe et al. 2002).

The measures discussed above are not perfect, because they disregard postgraduate education, effects of learning by doing, consequences of the rising level of culture (e.g. the scale of readership), population's health condition, the effects of economic migration and many other factors (see Benabou 2002). The issues deserve possibly full treatment on a macro scale, leading to the development of new methodological solutions incorporating the indicated broad aspects of expanding human capital.

Applications

We hope that the research conducted at the Lodz academic centre will contribute to an enhanced description of the effects of technological progress as a result of their inclusion into an updated version of model W8D. Prior to that, many methodological issues will have to be resolved, in addition to the suitable extension of the model's database. Let us note that direct introduction to the production function of many new variables that are proposed would require a substantially extended sample. Using the time series alone (for a single country) does not solve the problem, as going beyond 40 annual observations is quite difficult. A feasible approach is an analysis based on the cross-section-time series data, either regional or international, followed by the calibration of parameters. Hence, the scope of research will have to be considerably expanded.

After the model extension, a variety of scenario analyses can be run. They may investigate issues such as the effects of growing R&D expenditures, scenarios devised by the former State Committee for Scientific Research (Strategia 2004) and the conditions of their realization, the effects of growing educational outlays and the conditions of their increase, especially regarding higher and post-graduate education (see Welfe (Ed.) 2004b).

The Concept of Macromodels for the Sectors of Research and Education

The Research Sector Model

The presented macromodel extension cannot be expected to solve all fundamental problems that appear when research tools needed to examine the characteristics of a knowledge-based economy are being enhanced. It becomes therefore necessary to construct special submodels focused on the growth of knowledge capital.