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Table 3.Results of Assessments of Growth Rates in Output and Average Annual Number of Employment by Federal Okrugs 1997GRP growth Labor reserves Labor reserves growth rate as Federal okrug rate growth rate % of the GRP growth rate Far-Eastern 4.80 1.93 40.Volga 2.63 0.98 37.North-Western 3.22 1.31 40.Siberian 6.69 1.71 25.Ural 2.92 1.07 36.Central 0.12 0.60 496.Southern 3.66 1.53 41.1999Far-Eastern 4.60 0.69 15.Volga 5.52 0.80 14.North-Western 7.46 0.67 8.Siberian 5.60 0.63 11.Ural 6.22 0.71 11.Central 7.72 0.63 8.Southern 8.17 1.34 16.1997Far-Eastern 1.37 0.19 13.Volga 2.73 0.20 7.North-Western 3.77 0.00 0.Siberian 1.33 0.16 11.Ural 3.08 0.11 3.Central 5.13 0.22 4.Southern 4.07 0.38 9. Overall, employment ensured rather a small proportion of GRP growth rates over 19972002, with the rise in output in the FaEastern and Siberian okrugs being accompanied by contraction in the average annual number of employees.

The structure of labor resources in regions changes over time.

As the volume of output produced by unit of labor input (i.e. the quality of labor) varies across groups of labor resources, one cannot help but being taken into account while building TFP assessments.

The assessment of the impact of structural changes is based upon the assumption that the average wages in each group is proportional to the marginal labor product per employee (in the case for assessment of labor reserves) or per worked hour (in the case for assessment of labor services (Denison, 1967).

The building of the assessment of labor input that considers differences in the structure of labor resources involved in the production process necessitates data on distribution of employees across the groups. In the absence of the respective statistics, all kinds of labor inputs, regardless of their classification, are aggregated on the Lj Rj basis of the overall proportion of labor input in output.

Y The assessment of total factor productivity in this case takes the Lj L & wj form: TFP = gY -K gK -. As a result, the bias Y L of such an assessment from the one that considers differences in the structure of labor resources makes up:

& Lj L Lj & wj TFP - gTFP = -. For example, in the L j Y L Lj case two groups of employees are singled out & & L1 L2 L1 + L2 L1 L TFP - gTFP = (w1 - w2) L1 + L2 L1 + L2 Y L1 + L2 L1 + L2, & & L1 Li.e. if w1 > w2, >, then TFP > gTFP.

L1 + L2 L1 + LConsequently, the assessment of total factor productivity appears overvalued, as it comprises the effect from the rise of the employees qualification (Barro (1998)) in the event of singling out groups of employees by age, gender, educational level, or the impact of a redistribution of resources in the event of singling out groups of employees by kinds of job, industry.

The assessment of labor input on the basis of the indicator of the overall number of employees in region Ni suggests that all the employees in the region form a homogenous group. Lifting this restriction suggests the transition to disaggregated assessments:

wij i i i N Nind = N, (3.5) j wi j where wij labor compensation of j category of employees in i region, wi average wages in i region, Nij the number of employees of j category in i region.

i i A transition from N to Nind 31 does not lead to substantial changes in the dynamics of the labor input index. The employment index with account of sectoral variations (Fig. 3.6) for most federal okrugs demonstrates decline in 19971998 (except for the FarEastern okrug where the decline was over in 1999 and the Ural one According to the statistics available, employees in a region are divided into categories only according to their sectoral attribution.

in which it did not occur at all). Given that, in all the federal okrugs, except the Ural one, the consequent rise in the employment index with account of sectoral differences proved to be lower than the rise in the employment index.

1996 1997 1998 1999 2000 2001 Far-Eastern Volga North-Western Siberian Ural Central Southern Fig. 3.6. The Dynamics of Employment Indices of the Federal Okrugs with Account of Sectoral Differences (1996 = 100%) A less notable fall in the assessment of labor input with account of sectoral structure (Fig. 3.6) vis--vis employment-based assessment (Fig. 3.5) in a number of okrugs evidences that in the okrugs there happened an intense redistribution of labor force between sectors. Thus, the Ural okrug has not practically seen reduction of labor input, while employment had been contracting there by 1998.

By contrast, according to the assessment based on sectoral differences, in the Far-Eastern okrug the fall in labor input was yet more visible than the contraction in employment.

Having transformed the expression for assessing the contribution of labor reserves to the rise in output in i region, we arrive at:

i & L i i i i = gN = g = g + g (3.6) i i i i i L L L L i w N w N ind j j j i L N j i j wi j wi N Table 3.Results of the Assessment of Output growth Rates and Contribution of Components of the Assessment of Labor Reserves across the Federal Okrugs Growth rates As % of the GRP growth rates Federal okrug Number of Structure of Number of Structure of Labor input GRP Labor input employed employed employed employed 1997Far-Eastern 1.93 0.51 2.44 4.80 40.15 10.70 50.Volga 0.98 0.08 1.06 2.63 37.40 3.05 40.North-Western 1.31 0.19 1.12 3.22 40.71 5.78 34.Siberian 1.71 0.34 2.05 6.69 25.50 5.07 30.Ural 1.07 0.88 0.19 2.92 36.58 30.11 6.Central 0.60 0.07 0.53 0.12 496.82 59.72 436.Southern 1.53 0.51 2.04 3.66 41.77 13.97 55.1999Far-Eastern 0.69 0.33 0.36 4.60 15.08 7.17 7.Volga 0.80 0.30 0.50 5.52 14.42 5.45 9.North-Western 0.67 0.04 0.63 7.46 8.93 0.48 8.Siberian 0.63 0.45 0.18 5.60 11.23 8.05 3.Ural 0.71 0.29 0.42 6.22 11.39 4.67 6.Central 0.63 0.43 0.20 7.72 8.15 5.62 2.Southern 1.34 0.52 0.82 8.17 16.42 6.42 10.1997Far-Eastern 0.19 0.39 0.58 1.37 13.77 28.64 42.Volga 0.20 0.23 0.02 2.73 7.32 8.32 0.North-Western 0.00 0.04 0.04 3.77 0.08 1.01 1.Siberian 0.16 0.41 0.57 1.33 11.75 31.08 42.Ural 0.11 0.10 0.22 3.08 3.66 3.17 7.Central 0.22 0.27 0.04 5.13 4.24 5.18 0.Southern 0.38 0.52 0.14 4.07 9.22 12.76 3. Thus the contribution of labor reserves to the output growth rates in i region can be presented in the form of two components:

i (1) LgN that considers the impact of changes in the number of i i employees and (2) Lg that determines the impact of changes i wij N j i j wi N i in the structure of employees. Given the above, coefficient L remains unchanged for the whole period.

The calculations witness (Table 3.3) that the changes in the sectoral structure of the employed have resulted in the rise in the proportion of the output growth rates explained by changes in labor input in most federal okrugs over the 199798 period of decline.

The period of growth of 19992002 displays an opposite situation:

most federal okrugs saw the contribution of labor input to the output growth rate lessen.

The percentage of output growth rates explained by changes in labor input Fig.3.7. Bar Chart of the Percentage of the Output Growth Rates Explained by Changes in the Average Number of Employed in Regions with Account of Sectoral Differences (for the Period of 19972002) Number of Regions ) ;0) 80) 60) 40) 20) ;

;40) ;80) ;;100) 0;0;(er 40;60) ( ( ( ( -der 100;( (( (ov ( un The percentage of the output growth rate explained by changes in labor input varies substantially across regions. For some of them, the direction of changes of the output growth rate appears opposite to the direction of changes in the labor input growth rates (negative values in the Bar Chart). However, for most regions changes in the average number of the employed with account of industry-specific differences explain from 20% to 20% on average of the GRP growth rates (see Fig. 3.7). A great percentage of negative assessments of the contribution of labor input to growth testifies either to an insignificant role played by the labor factor in the regional growth over the period in question, or a poor accuracy of measure of the respective indices. Yet another reason for the presence of negative assessments lies with the fact that one can single out two stages of the time interval in question that concern both the dynamics of output and employment: namely, decline and growth stages.

For most regions and the federal okrugs (see Fig. 3.1 and Fig. 3.6) the 19971998 decline in output was just slightly in excess of the one in employment (at 2% on average), while the consequent rise in output in 19992002 substantially outpaced the rise in employment (by 25% on average). The computed averaged (over the whole period between 1997 and 2002) growth rates of the indicators do not mirror such changes in the dynamics. Meanwhile, for the sub-periods (see Annex 2, Fig. A2-3 and Fig. A2-4) the proportion of the output growth rates explained by changes in labor input has shifted to the area of positive values: while in 199798 it accounted for 2040% on average, in 19992002 020%.

To ensure a more accurate assessment of labor input, one should take into account worked time (thus differing from the number of the employed), the employees gender and age structure, their qualification and education.

3.2.3.Assessing Capital Input Issues associated with capital input assessments pose the greatest problems not only in the framework of Russian statistics but to research into decomposition of growth on the whole.

An assessment of capital input in growth decomposition models gives a rise to a number of issues that concern the methodology of assessment of the input itself and assessment of the measure of its quality. Production capacities of different generations (vintages) are undoubtedly characterized by different productivity rates.

Economists disagree on the issue as to how one needs to exercise the procedure (which indicators to use as weights while building an aggregate assessment) whether they have to employ relative prices or marginal products.

To assess capital input, Denison (1967, 1974) employed the sum of production units weighted on the basis of their relative prices in the basic period, while he regarded the unmeasured improvement of quality of the capital as a component of the contribution by technical progress. His stand (Denison (1978, 1980)) is that while conducting decomposition, one can neglect the embodiment hypothesis, as changes in the equipment age structure have just a minor effect on the output growth rates, even if one considers that all technical progress has found its embodiment in capital. In their paper, Gregory and Denis (1973), as well as Phelps in his theoretical paper (1982), arrive at the same conclusion.

However, models that suggest consideration of technical progress embodied in capital have recently begun earning an increasing popularity. In this particular case, it is assumed that new equipment has a greater productivity than the one placed in operation earlier, and capital index is built on the basis of marginal products, whose approximation is formed by prices of the factors (Griliches, Jorgenson (1967)). The embodiment hypothesis has found its reflection in many papers which regard technical progress as function of the investment rate (Kaldor (1957)); the rate of change of the investment rate (Kaldor, Mirrlees (1962)); as a factor that determines prices of investment goods (Griliches (1961), Brubaker (1968), Hall (1968), Gordon (1990)).

The compromise solution is formed by a model of sources of growth that considers technical progress, both embodied and not embodied in capital. This concept was developed by Nelson (1964), Jorgenson (1966), Hulten (1992) on the basis of assessments of changes in the quality of the basic factors.

The two approaches to interpretation of technological changes suggest different interpretations of capital. In the former case (technical progress is assumed not to be embodied in capital), the differences between production capacities of different generations are limited by some factor associated with the depreciation level, therefore:

t K t = 1- I t -, (3.7) ( ) ( ) ( ) =where deterioration rate (productivity loss in the process of ageing of the equipment).

If investment volumes I t of period t are measured by the ( ) number of production units, then assessment K t received as a ( ) weighted sum of previous investment constitutes the number of production units in an equivalent t.

In the assumption of technical progress embodied in capital, such an assessment leads to the fall of an actual effect from the capital reserves productivity. This defect can be liquidated (Fischer (1965)) by introducing the technical efficiency index whose changes are conceived as qualitative differences between production capacities of different age (Hulten (1992)), i.e. the growth rate of t constitutes the growth rate of technical progress embodied ( ) in capital. In this case t K(t) = ) I (t - )(t - ). (3.8) (1 =Excessive depreciation forms yet another critical source of biases in the course of assessing capital. Numerous empirical research papers note that it is moral ageing of equipment that forms a more important characteristic of depreciation and not its physical depreciation. Economically, capital ages faster than its operational deadline comes, nonetheless the outdated equipment do not fully loose its capability to generate output. So the value of services the capital provides falls over time at a speed different from that of depreciation writeoffs. In the event net investment and depreciation are equal, the net capital formation equals zero, while in the conditions of improvement of the level of technologies, the volume of capital grows (in the frame of the embodiment hypothesis). On the other hand, if one does not consider the rise of efficiency of the capital in conjunction with its age, while assessing capital input, one should also ignore its moral ageing. As a result, the assessment of capital on the basis of net value (less depreciation) that does not consider technical progress embodied in the capital leads to an undervalued assessment of its impact on economic growth rates.

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