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Finding empirical assessments of g necessitates the knowledge of values of marginal products FK and FL. In an assumption of constant returns to scale and competitive markets for inputs and the final product, marginal products can be assessed on the basis of observed:

w price of labor services, R rental price of capital.

In this event the total factor productivity growth index is computed as follows:

At Yt Lt Kt L ln = ln - ln +K ln, (3.3) At-1 Yt-1 Lt-1 Kt- where and values of shares of the respective factors in output L K averaged over two periods:

L(t) + L(t -1) wL L = ; L =, (3.4) 2 Y (t) + (t -1) RK K K = ; =.

K K 2 Y Different papers on decomposition of growth provide various definitions of the remainder: while Solow (1957) considers it measure of technical progress, Harberger (1998) views it as real cost reduction, Abramovitz (1993) notes that the remainder comprises totality of unmeasured sources of growth and call it some sort of measure of ignorance.

In the general case of the neoclassical production function, the equation is met approximately, while a precise equation is possible only for the translogarythmic production function. (Diewert, 1976).

The computation of the weights is based upon the condition:

Y = R K + w L or K + = 1, which is met providing the whole L output is conditioned solely by factors included in the production function (i.e. it suggests constant return to of scale).

3.2.1. Assessing Output The indicators that mirrors changes in output can be represented by volume of output (volume of production of goods and services), national income (NI), and gross domestic product (GDP). While opting for a certain measure of output, a researcher, as a rule, is guided by research objectives and models he deals with, on the one hand, and on-hand statistical data, on the other.

The choice between national income and gross domestic product appears rather conditional. The differences between TFP assessments received basing on the indicators are determined by changes in the volume of consumption of fixed assets. While on the one hand, if the major purpose of an analysis is to expose causes and potential possibilities for boosting output, the change in the volume of consumption of fixed assets should be ignored, while building the TPF assessments (Denison (1972)). On the other hand, the preference of net output generates differences in identification of the basic factors whole under the assessment of factor services capital consumption is excluded, the depreciation of labor, which appears an indeterminable value in the general case, is included in the volume of labor services (Griliches, Jorgenson (1967)).

The employment of every single indicator as a measure of output imposes its constraints on production function and, consequently, on an interpretation of TFP. For example, differences in assessments of TFP received on the basis of final output and other indicators is determined by the volume of intermediate consumption and the output prices to intermediate consumption ratio (thus, under the constant proportion of intermediate consumption Y (N / Y = n = const) TFP growth rates on the basis of final output appear times greater than assessments received on the basis of GVA 1- n (Bruno (1982)).

In international practice (OECD (2001a, 2001b)), assessments of TFP on the basis of final output are used, as a rule, under the analysis of changes in productivity on the industry or sectoral levels. The definition of productivity on the basis of value added is more frequently employed to analyze connections on the micro- and macrolevels for instance, to study the contribution of individual industries to the change in TFP by an economy as a whole, and to study structural changes.

The present paper considers gross regional product (GRP) as a measure of output, while to build assessments on the industry level (the industrial sector), the authors employ volume of industrial output (VIO).

For the sake of decomposition of growth, the respective indicators should be translated into comparable prices. The process of computation of deflators forms a separate complex task and because of the absence of the necessary volume of statistical information, it is not considered in the present paper. Let us just note that from the theoretical perspective, the computation of the respective deflators should involve hedonic indices that consider change in the quality of a given produce and inputs over time.

The Russian Statistical Service (Rosstat) provides the indicator of growth in the physical volume of regions GRP (GVA). To compute GRP, regional statistical bodies employ a uniform approved methodology. Regretfully, the information of a real growth of regions GRPs is available only starting from 1997, which considerably shortens the interval for the research. Let us note that results of decomposition of growth appear extremely sensitive to the choice of deflators. In the situation when information of compo nents of output and prices is unavailable, the official statistics on the real dynamics of GRP form a priority (at least, for the purpose of decomposition of growth).

To extend a possible interval of research, we have tried to approximate the dynamics of the real volume of GRP on the basis of the GDP deflator and the regions consumer price index (CPI). In the former case, there appears the necessity to introduce a prerequisite of GRP deflators being equal for all the regions, which appears poorly matched to the reality. The employment of regional CPIs as GRP deflators leads to lowering the assessment of GRP growth rates vis--vis the official data on the dynamics of the physical volume of GRP. The comparison of results of the computations based on both methods with the official data on growth rates for the federal districts are given in Table 3.1. The comparison of results of the computation of the index of output across regions is given in Annex (table A2-3). Because of a great discrepancy between assessments, in the paper below, the decomposition of growth was conducted for the period between 1997 and 2002, on which the official statistics on the dynamics of regional output are available.

For most federal okrugs (Fig. 3.1) the dynamics of the output (GRP) index are similar to those of GDP index for Russia as a whole. The indices sunk in 199798 (with the greatest decline in the Siberian okrug whose 1998 output fell by 12.5% vs. the one). The trend changed in 199899 (with the output rising constantly in all the federal okrugs). In the Central okrug, during the whole period in question the output remained at a level greater than its 1996 index, while the Volga, North-Western and Southern okrugs managed to reach the 1996 level as early as in 1999, the Ural in 2000, and the Far-Eastern and Siberian ones only in 2001.

The dynamics of regional indices (see Annex 2, Table A2-4) likewise allow singling out two stages: namely, the fall in output and its rise (Fig. 3.2). In some regions, the change of the trend occurred earlier than in 1999: thus, in Astrakhan and Orel oblasts, the rise in output is noted through the whole period of 1997200; in Republic of Kabardino-Balkaria, Republic of North-Ossetia Alania, Tver oblast, the rise in output started yet in 1998. By contrast, in Bryansk, Magadan, Tula oblasts, Republic of Karachaevo-Cherkessia, Altay republic, republics of Ingoushetia, kalmykia, Komi, Sakha and Khakassia, the change of the periods occurred in 2000.

Table 3.Results of Computations of GRP Growth Indices by Federal Okrugs on the Basis of Different Deflators The 2002 GRP Index Value (1996. = 100) Variant 2: Variant 3:

Variant1: Index Computation Variation (as % computation on Variation (as % Federal Okrug of physical on the basis of of variant 1) the basis of of variant 1) volume of GRP GDP deflator regions CPI FarEastern 109.33 96.35 11.88 104.87 4.Volga 118.87 95.23 19.89 87.57 26.NorthWestern 126.45 114.22 9.67 114.72 9.Siberian 109.48 84.22 23.07 91.64 16.Ural 121.31 105.80 12.79 97.94 19.Central 137.32 146.57 6.74 135.37 1.Southern 129.01 108.46 15.93 104.77 18.Across RF as a 123.95 111.61 9.95 106.33 14.whole In Belgorod, Moscow, Murmansk, Perm, Tambov oblasts, city of Moscow, Republic of Mordovia, despite decline in their output in 1998, its values have not ever sunk below the 1996 level, while the Jewish autonomic oblast, Irkutsk, Kamchatka, Magadan oblast, republics of Adygea, Mary-El, Khakassia by 2002 have failed to reach the 1996 level.

1996 1997 1998 1999 2000 2001 Far-Eastern Volga North-Western Siberian Ural Central Southern GDP, total Fig. 3.1. The Dynamics of Indices of Output across Federal Okrugs (1996 = 100%) up to 1996 1997 1998 1999 the trend is not no te d T he last year of the fall in output Fig. 3.2. Bar Chart of the Moment of the Change of the Trend in the Dynamics of Regions Output The pictorial rendition of the regional differentiation of the change in output volumes can be represented by means of Sun-rise diagram28 (see Fig. 3.3 and 3.4). As Fig. 3.3 and 3.4 show, in 19972002 the rise in GDP across the federal okrugs can be considered relatively more even than across regions. This is determined by the fact that all the federal okrugs demonstrated positive growth rates over the period in question, while there are regions with negative growth rates (republics of Adygea, Khakassia, Mary El, Ingoushetia, Jewish autonomic oblast, Irkutsk, Magadan, Kamchatka oblasts). The contraction of the regions GRPs (given that in the initial period (1996) their share in GDP had accounted roughly for 3.9%) made up 1.7% of the aggregate rise in GDP.

A special case of Lorenz curve. Harberger (1998) employed the definition to analyze the irregularity of real cost reduction in sectoral terms. Such diagrams are built as follows: the horizontal axe (in our case) presents the regional structure of GDP as a cumulative result. Regions are ranked according to their growth rates with the region enjoying the greatest growth rates ranked the first and the one with the smallest rate the last. The vertical axe presents growth rates of the respective regions. The more convex the curve that unites the points is, the more uneven in regional terms growth is. Accordingly, an uneven growth would be represented by a straight line.

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 Structure of GDP by the federal okrugs in the initial period (as of end 1996) Fig 3.3. Sun-Rise Diagram of Growth in GDP (19972002.) at the Level of the Federal Okrugs 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 Regional structure of in the initial period (as of end 1996) Fig. 3.4. Sun-Rise Diagram of Growth in GDP (19972002) at the Regional Level Siberian FO Volga FO Far-Eastern FO _ Ural FO _ (increment in GDP=100%) North-Western FO Southern FO Central FO_ Increment (fall) in the federal okrugs GRPs GRP=100%) Increment (fall) in regions GRPs (increment in 3.2.2. Assessing Labor Input The concept of contribution of the labor factor to economic growth, implies, as a rule, labor services provided by working population. The simplest measure of labor input can be worked manhours. However, it is known that labor forms a nonhomogenous indicator and it depends, as a minimum, on employees qualification and a number of other factors (gender, age, sectoral profile, etc.) In his first papers, Denison (1962) demonstrated that the contribution of labor could change even if the total number of worked manhours was constant. That is why to ensure a more accurate measuring, one needs a detailed breakdown of the used labor by categories, with account of worked hours and marginal productivity.

However, it was just recently that Rosstat has begun providing information of worked hours29 on the regional level, which substantially reduces the horizon of the analysis. It is possible to apply an alternative method of assessing the labor employed in the produci tion process basing on the available employment statistics ( N ).

The dynamics of employment indices by the federal okrugs are given in Fig. 3.4. However, the use of employment instead of worked hours affects the interpretation of the TFP indicator. In the event labor input is assessed on the basis of the indicator of the number of employees, the unexplained by factors growth (assessment of TFP) comprises a component that corresponds to qualitative changes in labor input (changes in the age and gender structure, employees educational level and qualification, distribution of labor resources by sectors, among others).

The comparison of the employment and output dynamics displays that in the period in question (19972002), the range of Obsledovanie naselenia po problemam zanyatosti, Rosstat, 19992002.

changes in the employment index across the federal okrugs did not exceed 12% against the 55% range of changes in GRP (see Fig. 3.and 3.1) 1996 1997 1998 1999 2000 2001 Far- Eastern Volga North-Western Siberian Ural Central Southern By RF, total Fig. 3.5. The Dynamics of Employment Indices by the Federal Okrugs (1996 = 100%) The contribution of labor is computed as a product of multiplication of the labor input weight coefficient by their growth rate; the 19972002 results and two sub-periods are given in Table 3.2.

As the Table shows, it was until 1998 that labor input ensured the greatest contribution to output. Against the background of the declining output, the contraction in labor input has been happening because of an intense discharge of labor force (lay-offs)30. On the contrary, there was no drastic rise in employment over the second period in question. A considerable rise in output was noted under rather a modest growth in employment. That occurred apparently The present paper is not intended to research into the causes for the contraction in employment, which could be initiated by either party.

thanks to a more intense consumption of then remaining labor resources (just a reminder, the indicator of factor input is employment, rather than worked hours, which enables us to advance this assumption).

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