1 2 3 4 5 6 7 8 Ц2.19 Ц2.02 Ц1.20 Ц0.77 Ц0.02 Ц0.75 Ц0.09 Ц0.Republic of Udmurtia 4.48 2.66 1.36 1.33 0.09 1.24 Ц0.34 2.Ц3.44 Ц3.30 Ц1.54 Ц1.70 Ц0.25 Ц1.45 Ц0.20 0.Ulyanovsk oblast 4.30 Ц0.60 0.40 Ц0.99 Ц0.18 Ц0.81 Ц0.39 5.Ц1.20 Ц0.16 Ц0.03 Ц0.10 Ц0.10 Ц Ц1.13 0.Khabarovsk krai 8.45 1.62 1.48 0.14 0.14 Ц Ц0.17 7.Ц8.02 Ц1.13 Ц0.36 Ц0.63 Ц0.07 Ц0.56 Ц0.22 Ц6.Chelyabinsk oblast 5.45 Ц1.42 0.54 Ц1.97 0.06 Ц2.03 Ц0.25 7.Ц11.14 Ц4.02 Ц3.87 Ц0.14 Ц0.14 Ц Ц0.86 Ц6.Chita oblast 6.72 1.49 1.53 Ц0.03 Ц0.03 Ц Ц1.10 6.Ц7.36 Ц1.41 Ц1.11 Ц0.28 Ц0.15 Ц0.13 Ц0.13 Ц5.Republic of Chuvashia 3.87 2.58 1.36 1.18 Ц0.05 1.23 Ц0.62 1.Ц2.06 Ц1.70 Ц0.93 Ц0.68 Ц0.22 Ц0.46 Ц0.27 Ц0.Yaroslavl oblast 7.85 2.86 0.78 2.09 0.08 2.01 Ц0.20 5.Table 3.Decomposition of Growth in the RegionsТ Output in 1997Ц1999 and 2000Цof which I.1. EmI. Fac- Labor ploy- II. ReI.LoadGRP tor employ ment mainFixed Capital ing inputs ment) struc- der assets rate ture 1 2 3 4 5 6 7 8 Ц2.91 Ц1.13 0.14 Ц1.27 Ц0.30 Ц0.97 Ц0.99 Ц0.Bryansk oblast 7.90 1.47 0.44 1.06 Ц0.18 1.23 Ц0.56 6.Republic of Ц1.69 0.15 Ц0.28 0.43 Ц0.15 0.58 Ц0.69 Ц1.Karachaevo10.39 1.09 1.43 Ц0.55 Ц0.10 Ц0.44 Ц0.71 10.Cherkessia Ц9.01 Ц4.24 Ц3.72 Ц0.52 Ц0.05 Ц0.47 Ц0.63 Ц4.Magadan oblast 3.10 Ц2.84 Ц0.73 Ц2.13 Ц0.09 Ц2.04 0.37 5.Ц3.40 Ц0.25 Ц0.13 Ц0.12 Ц0.12 Ц Ц1.62 Ц1.Altay Republic 7.29 0.45 0.25 0.15 0.15 Ц 0.02 6.1 2 3 4 5 6 7 8 Ц7.24 Ц0.59 Ц0.19 Ц0.41 Ц0.41 Ц Ц3.76 Ц2.Republic of Ingoushetia 3.33 2.26 3.55 Ц0.36 Ц0.36 Ц41.65 0.79 0.Ц2.03 Ц2.17 Ц1.11 Ц1.06 0.02 Ц1.08 Ц0.76 0.Republic of Komi 4.47 1.32 0.58 0.76 0.29 0.47 Ц0.09 3.Ц3.20 Ц15.45 Ц0.06 Ц15.39 Ц0.12 Ц15.28 Ц0.77 13.Republic of Khakassia 2.53 17.86 0.76 15.92 Ц0.12 16.04 Ц0.58 Ц14.Ц3.49 Ц0.47 Ц0.90 0.42 Ц0.13 0.56 Ц0.85 Ц2.Tula oblast 5.11 Ц0.03 Ц0.36 0.36 Ц0.01 0.36 0.13 5.Chukotka Ц14.52 Ц5.99 Ц5.65 Ц0.34 Ц0.34 Ц Ц0.36 Ц8.autonomous 21.22 Ц0.82 Ц0.72 0.01 0.01 Ц5.83 0.32 21.okrug In most regions whose dynamics of output o display the existence of the two periods undergo the following situation: the main reason for the drop in their output at the stage of decline is formed by basic factors Ц that is, labor and capital, while in the period of growth the remainder begins to prevail. An analogous result was found in the course of analysis of their annual growth rates.
188.8.131.52. Decomposition of Growth with Account of Worked Time As noted above, assessment of labor input on the basis of the employment indicator suggests that the volume of output is equal for all the employees, regardless of the length of the workday. A more accurate assessment of labor input is built upon the total number of hours worked by all the employees. In this case changes in labor input (the aggregate worked time) are determined by two components: changes in the number of the employed and changes in the average length of the workday per employee (an average worked time):
i i i i N Nh = N H, (3.10) i where H Ц the time worked by a employee in i region.
The index of the averaged worked time was built on the basis of the data on the average actual length of the working week37. In the assumption that the number of working weeks in the year is constant, the index of time worked by an individual employee in a year coincides with the index of actual length of the working week 1999 2000 2001 Far-Eastern Volga North-Western Siberian Ural Central Southern Fig. 3.14. The Dynamics of Indices of the Average Worked Time for the Federal Okrugs (1999 = 100%) By contrast to the number of the employed, whose dynamics for most of regions and federal okrugs displays growth over the whole period between 2000 and 2002 (Fig. 3.14), the dynamics of the average worked time lacks such an explicitly manifested tendency.
The rise of the working time of the employed in 2000 was followed by a fall in the indicator in 2001 (for all the federal okrugs, except the Siberian one).
Source: The GKSТ collection of surveys УPopulation Surveys on Employment ChallengesФ.
Having transformed the expression for assessing the contribution of labor input in the rise in output in i region, one can proceed to the sum of two components: namely, 1) change in the number of i the employed (LgN ), and 2) change in the length of the working i i week ( gH ):
i L i i i gN = gN H = (gN + gH ). (3.11) i i i i i L L L h While building assessments of the contribution of labor input in the growth of output, proceeding from the available statistical data, we have taken into account changes in the structure of the employed in terms of gender. The respective index is built in an assumption that the average hourly wages in each group are proportional to the marginal labor product per one worked hour.
i i wm Hm wif H i f i i i i Nh Nhg = N H +, (3.12) i i i i w H w H where i wm Ц menТs average monthly wages in i region, wif Ц womenТs average monthly wages in i region, i w Ц average monthly wages of the employed in i region, i Hm Ц menТs average actual length of the working week in i region, i H Ц womenТs average actual length of the working week in i f region.
Having transformed the expression to assess of the contribution of labor input with account of changes in gender structure of the employed to the rise in output in i region and denoted i i wm Hm wif H i f Stri = +, i i i w H wi H we receive:
i i i gN = gN H Stri = (gN + gH + gStr ). (3.13) i i i i i i L L L hg Table 3.Results of Assessment of Output Growth Rates and Contribution of Labor Input by the Federal Okrugs Growth rates As % of the GRP growth rates Aver- AverFederal Number Number age Gender Labor age Gender Labor okrug of the GRP of the worked structure input employed worked structure input employed time time 2000ЦFar0.81 Ц0.24 1.55 2.12 4.13 19.48 Ц5.75 37.51 51.Eastern Volga 0.38 0.06 0.34 0.78 5.71 6.65 1.02 5.92 13.North0.42 0.25 Ц0.36 0.31 7.56 5.52 3.33 Ц4.75 4.Western Siberian 0.27 0.10 0.01 0.38 6.03 4.45 1.60 0.24 6.Ural 0.36 0.31 0.87 1.54 7.39 4.92 4.14 11.74 20.Central 0.14 Ц0.06 1.28 1.37 8.26 1.75 Ц0.69 15.55 16.Southern 0.84 Ц0.22 0.02 0.63 8.11 10.33 Ц2.77 0.22 7.Computations evidence (Table 3.11) that the adjustment of the assessment of labor with account of changes in the worked time has led to a rise in the proportion of the output growth rates explained by changes in the labor input for most federal okrugs in the period of growth of 2000Ц02 (except for the North-Western and Southern ones). Computations for regions are given in the Annex 2, Table A2-12).
Results of the decomposition of the regionsТ growth output with account of worked time are presented in Table 3.12.
Table 3.Decomposition of the GRP Growth by the Federal Okrugs for the period 2000ЦFar- North Volga Siberian Ural Central Southern Eastern Western GRP 4,13 5,71 7,56 6,03 7,39 8,26 8,I. Factor inputs 1,80 1,52 1,41 1,33 3,39 3,12 1,I.1 Labor 2,12 0,78 0,31 0,38 1,54 1,37 0, Employment 0,81 0,38 0,42 0,27 0,36 0,14 0,Worked time Ц0,24 0,06 0,25 0,10 0,31 Ц0,06 Ц0,Structure 1,55 0,34 Ц0,36 0,01 0,87 1,28 0,I.2 Capital Ц0,32 0,74 1,10 0,95 1,85 1,75 0,Fixed assets 0,06 0,32 0,21 Ц0,18 0,63 0,36 0,Loading rate Ц0,39 0,43 0,89 1,13 1,22 1,38 Ц0,II. Remained 2,34 4,19 6,16 4,70 4,00 5,14 7, The Solow re3,26 5,01 6,94 5,94 6,39 7,76 6,mainder In the period between 2000 and 2002, the remainder growth rates were positive in all the federal okrugs. However, despite the fact that the conducted adjustment of the assessment of labor input has led to a fall in the proportion of the output growth rates unexplained by the basic factors, it still exceeds the explained proportion. The proportion of the output growth rates generated by the growth of the remainder for all the federal okrugs changes within the range 40 to 80%. Results of the decomposition of the regionsТ growth are given in the Annex 2 (Table A2-13).
As before, the percentage of the output growth rates unexplained by the basic factors likewise appears substantially diverse across regions. With account of changes of the worked time, the remainder determines a greater proportion of the output growth rates vs.
labor and capital inputs. There are only 9 regions that made an exception in this respect: (city of Moscow, Tyumen, Yaroslavl, Sam ara, Vologda, Smolensk, Sakhakin and Kamchtka oblast, and Republic of Khakassia).
3.3. The Dual Approach to Decomposition of Growth Whilst conducting a direct decomposition of the regionsТ economic growth, we proceeded from the assumption that the value of output is determined solely by the included in production function factors, i.e.
m n piYi = X, (3.13a) q j j i=1 j=where pi and Yi Ц price for and quantity of i kind of product, q and X Ц price for and quantity of j kind of input.
j j In their paper, Griliches and Jorgenson (Griliches, Jorgenson (1967)) demonstrated that the assumption of the equality between the values of output and inputs allows another way to assess growth rates of total factor productivity which is computed as the total output to total inputs ratio:
n & qj m pi & gTFP = -. (3.14) vj µi qj i=1 pi j =q X piYi j j µi = and v = are the shares of i kind of product j piYi X q j j in the value of total output and the shares of j kind of input in their value of total input, respectively.
Thus, the assessment of the growth of total factor productivity can be made basing on both indices of output and inputs values, and indices of the respective prices. These two methods ensure the same result, providing equality (3.13a) is met. In reality, as demonstrated by Hsieh (2002), this particular precondition appears fairly strict, especially as long as developing economies are concerned. In this paper, we attempt to decompose growth on the basis of the dual approach for the purpose of comparing its results with those of the direct approach. However, the problem with data still persists, which is why all the computations are built on the basis of aggregated indices, while if they are missing,Ц on the basis of estimates and proxy variables.
To measure the price rise of the aggregated outcome we employ the GRP deflator computed basing on the data of the index of physical volume of GRP and volume of GRP in constant prices38.
According to (3.14), the index of total factor productivity (unexplained by the basic factors remainders) on the basis of aggregated price indices is computed by the formula:
At wt rt PtY L ln = ln + K ln - ln, (3.15) At wt -1 rt PtY -1 -1 - where, as before, and Ц average for the two periods values of shares of the L K respective factors in output: (see. (3.4)), w and r Ц aggregated indices of labor and capital prices, PtY Ц aggregated index of output price.
After transforming the above, we receive:
At (w/ PY ) (r / PY ) t t K ln ln = L ln +. (3.16) At (w/ PY ) (r / PY ) -1 t -1 t -The first item in the right part of the expression represents adjusted by the weight coefficient logarithmic growth rates of real Source: УRegiony Rossii. Sotsialno-ekonomicheskie pokazateli Ц 2004 g.Ф Rosstat.
wages, while the other item represents adjusted by the weight coefficient logarithmic growth rates of the real rate of return on capital.
Thus, the TFP growth rates are computed as a weighted sum of the real growth rate of labor and capital costs.
To assess the price index of labor, we employed the index of real average accrued wages (as % to the prior year).
As in the case of assessing TFP by the direct method, the assessment of the capital index likewise forms more complex a task vis--vis an assessment of the labor index. First, this is explained by the absence of necessary statistics and, second, the ambiguity of the finding of technological efficiency of capital of different kinds and generations (vintages). In conjunction with that, the paper suggests two assessments of the price index of capital:
1. on the basis of investment goods prices, and 2. on the basis of prices for real estate on the secondary market.
The assumption that the capabilities of capital to produce output does not change in the process of its ageing and, consequently, the service price of capital do not change with its age suggests a price index for investment goods computed on the basis of index of physical volume of investment and volume of investment in constant prices39 as an acceptable estimate of the price index of capital.
Between 1998Ц2002 facilities and buildings roughly averaged 60% of fixed assets in the industrial sector and 71% in the agrarian sector (Table 3.13). Given that facilities and buildings account for the lionТs share of fixed assets, the assessment of the service price of capital indeed can appear seriously correlated to prices for real estate.
3.3.1. Comparing Assessments Made by Different Methods The 1997Ц2002 unexplained remainder assessment results of the by the basic factors of regionsТ economic growth (TFP) are given in Table 3.14, while those of 1997Ц98 and 1999Ц2000 Ц in the Annex 2(Table 2A-15 and 2A-16).
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