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Weekly UpdatesCalibrating the Elasticities
Secondly, using Eq. 2 we assume that parameter [alpha], i.e. elasticity of production w.r. to fixed capital is known. The parameter's estimate can be obtained by either estimating parameters of the production function (1) or via calibration. In the first case, the TFP explaining function (i.e. [A.sub.t]) needs a more detailed specification, which is discussed below. The other approach, quite common, takes advantage of results provided by the neoclassical theory of production. According to them parameter [alpha] can be approximated using the share of surplus in value added, i.e. by deducting the share of labour costs in value added from one.
This approach, broadly applied in empirical research, is based on an augmented growth accounting framework and also gives rise to doubts, because the share varies in the long term and additionally labour costs definitions are not consistently applied. For instance, various investigations took [alpha] values for Poland from the range 0.25-0.5. The differences produced considerable variations in the estimates of TFP dynamics, because slowly expanding volumes of fixed capital were accompanied by fluctuations in employment and especially its decline in some years (see Welfe 2002).
Potential and Effective Output
Nevertheless, most problems arise because taking actual output ([X.sub.t]) instead of unobservable potential output ([X..sub.t.sup.p]) to calculate TFP based on Eq. 2 leads to biases in the estimates of TFP dynamics. It is so, because a residual determined using Eq. 2 reflects not only the effects of technological progress, but also the varying rate of production capacity utilisation [WX.sub.t].
This rate can be derived from relation [WX.sub.t] = [X.sub.t]/[X.sub.t.sup.p], Rearanging, the identity is estabilished showing the relationship between the effective and potential output:
[X.sub.t] = W[X.sub.t][X.sub.t.sup.p], and then [X.sub.t] = [WX.sub.t]] + [X.sub.t]]
In fact, TFP dynamics should be determined using production function l that assumes full utilisation of the production factors. Then we have:
[A.sub.t]] = [X.sub.t.sup.p]] - [[alpha] [K.sub.t]] + (1 - [alpha])[N.sub.t]]]. (3)
Now, examining Solow residual Eq. 2, when [X.sub.t] is replaced by the term [WX.sub.t] + [X.sub.t.sup.p], we obtain:
RES = W[X.sub.t]] + [X.sub.t.sup.p]] - ([alpha] [K.sub.t]] + (1 - [alpha]) [N.sub.t]]) = W[X.sub.t]] + [A.sub.t]], (4)
Therefore, the residual dynamics represents the dynamics of technological progress only when the rate of capacity utilisation does not change, i.e. [WX.sub.t] = 0. This condition is frequently not met, when TFP dynamics is analysed for countries (areas), where the capacity utilisation rate shows substantial variability. For instance, the residual growth rate overestimates the rate of TFP growth for a long-term increase in capacity utilisation.
In such cases, finding a relevant measure of the capacity utilisation rate is not a routine task. The applied methods differ with respect to their accuracy and depend on data availability. We mean here the direct measurement methods that take advantage of survey data (see Grzeda Latocha 2005), as well as questionable methods analysing deviations from output trends. On the other hand, methods are available that help observe changes in the rate of capacity utilisation via changes in the use of observable production factors.
In principle, we can decompose the rate of capacity utilization into rates to which production factors, i.e. fixed capital and employment, are utilised. This approach proposes to replace total fixed capital by machinery and equipment directly engaged in the manufacturing process, assuming that their use is correlated with employees' working time (or at least with the shifts worked). By introducing hours worked by employees to the production function we can satisfy the call for taking into account the rate of employment utilisation. This requirement, however, cannot be met for Poland due to the unavailability of relevant data (Welfe 1992).
Specification of Equations Explaining TFP Dynamics: The Role of Research and Development
Decomposing of TFP Dynamics
The possibility of modelling the sources of TFP growth is essentially weakly recognised. To explain TFP variations it is usually proposed to decompose growth into the effects of generally available knowledge capital ([A.sub.t.sup.W]), impacts of expanding knowledge capital embodied in fixed capital ([A.sub.t.sup.K]) and increase in knowledge capital embodied in employment i.e. human capital per employee ([A.sub.t.sup.N]). Taking into account production function l, we obtain:
[A.sub.t] = [A.sub.t.sup.W] + [alpha] [A.sub.t.sup.K] + (1 - [alpha])[A.sub.t.sup.N] (5)
The effects of growth of generally available, disembodied knowledge capital ([A.sub.t.sup.N]) are treated as exogenous (usually as an exponential function of time), or attributed to growing human capital.
The Role of R&D
The impacts of expanding knowledge capital embodied in fixed capital are related to the outcome of R&D processes materialised in the number of patents ([PA.sub.t]) or scientific publications ([PU.sub.t]), as well as cumulated R&D expenditures, both domestic ([BRK.sub.t.sup.K]) and transferred from abroad ([BRK.sub.tsup.M]). The latter represent the capital of technological and organizational knowledge (Coe and Helpman 1995).
Cumulative real R&D expenditures change due to the addition of real current expenditures on R&D (R&D investments) and because of the depreciation of this stock of knowledge (the rates of depreciation are estimated at 5-15%).
Transfers of Foreign R&D Capital
The major problems here relate to the construction of measures of foreign knowledge capital stocks, the channels through which they spill over, as well as their absorption. Direct and indirect spillovers are distinguished. As for the latter, it is assumed that foreign technology is transferred via the import of commodities and services. The total foreign stock of knowledge is obtained as a weighted sum of domestic cumulative real R&D expenditures of foreign countries j from which country i derives its imports. We have:
[BRK.sub.i.sup.M] = [summation over (j)] [[omega].sub.ij] [BRK.sub.j.sup.K], (6)
where [[omega].sub.ij] - weights attached to cumulative R&D domestic expenditures of countries j [BRK.sub.J.sup.K] (j [not equal to] i).
Weight [[omega].sub.ij] was initially defined as share of from country j imports in total imports of country i (Coe and Helpman 1995). Lichtenberg and van Pottelsberghe (1998) proved, however, that the measures yield biased results. They suggested to use instead: ratios of imports from particular countries to their total output (i.e. shares of their exports to country i), which better represent the countries' R&D intensities.
The choice of imports' indicator also turned out to be disputable. Initially, Coe and Helpman (1995) proposed to use imports of intermediate inputs representing technology transfers (in their computations they used total imports, however). An alternative approach would assume that the import of investment goods is the major channel through which new technologies are acquired. According to a study by Xu and Wang (1999) who analysed impacts of alternative channels in the OECD countries (for the period 1983-1996), the use of imported capital goods yields superior results and is statistically significant as opposed to the use of import of intermediate goods, or total imports. (4)
Direct and Indirect Spillovers of Foreign R&D
The direct channel of spillovers accounts for the impacts of direct information flows due to telecommunications, patent information, etc. The impacts are stronger in countries with similar industrial structures, exhibiting technological proximities and so forth. Several single indicators (e.g. like the length of telephone lines) or composite indicators were applied. A recent study by Lee (2005) claims that results provided by the introduction of direct channels of spillovers (obtained using several estimation techniques) yield more robust estimates than in the case of indirect channels. This finding needs further verification, as the author used an inferior version of the indirect spillovers, based on weights using intemediate imports related to total imports.
Many international studies, especially those dealing with developing countries, have confirmed that spillovers of the foreign stock of knowledge are the most important source of their economic growth (Bayoumi et.al. 1999; Engelbrecht 1997).
Absorbtion of Foreign R&D Capital: The Role of FDI
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
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