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N. Mikheeva studied issues of differentiation of indices of the Russian regions socioeconomic positions in 199096. The author assessed volumes of gross regional products in constant prices and Granberg, Zaitseva (2003).

Mikheeeva (2000).

the populations real incomes. An empirical analysis of the interregional differentiation was conducted on the basis of the regression analysis of panel data. Basin on her assessments, the author concludes that the interregional differentiation of the populations incomes and the average GRP per capita intensified over the period in question. In addition, the author attempted to conduct a quantitative assessment of the impact of a number of factors (initial conditions of development, production structure, orientation towards exports, inflation rates, investment, and regional budget expenditures) on the dynamics of interregional biases. The respective outputs allow the author to argue that it is current economic indices (inflation, export, changes in the share of the services sector and the agrarian sectors) that provide a major contribution to the interregional differences, while possibilities for economic policy to influence the differentiation of regions socio-economic positions are fairly limited.

The above review of research outputs presented in the national economic literature allows the following conclusions on the extent to which the issue of regional growth is examined therein:

1. Most papers essentially contain legal provisions regarding regional development policy options basin on the authors personal views. Their empirical evaluations is mostly based upon a description of initial statistical data and parameters of dispersion of evaluated indices. In many cases, the authors fail to directly test, by using the available data, their economic policy conclusions and recommendations.

2. A number of papers describe the regions development record and the dynamics of interregional differences, or they specify and correct the initial Goskomstat data. However, they fail to consider causes for such differences and factors underlying the dynamics of the respective indices, or they refer to them proceeding from general economic considerations, without a quantitative anaylis.

3. While N. Mikheeevs paper appears most close to ours by its objectives and the degree of the empirical development of the issue, nonetheless, the period it covers (199096) falls under the first stage of reforms (the transformational slump). By contrast, at present we are keen to examine the regions development at the stage of transition to growth and an initial stage of recovery growth.

2. The Concept of Convergence and Its Application to the Evaluation of Economic Growth in the RF Regions 2.1. The Convergence Theory The neoclassical model of economic growth bears an important specific feature: that is, it predicts the existence of conditional convergence, or the concept that forecasts a positive correlation between growth rates of a given economy and the difference between the current and equilibrium income level in the economy (steady state). The concept of conditional convergence appears different from the concept absolute convergence concept. The latter implies that poorer economies grow at a pace greater than richer ones (i.e., catching up with them). It may become possible that two economies meet the condition of conditional convergence (the economys growth rates fall under the diminishing bias of the income level from its equilibrium state), but they fail to meet conditions of absolute convergence (the richer economies may grow at a higher pace than poorer, if the former find themselves farther from the steady state). The concepts would be identical only provided the steady state is identical fro both of them).

It rather frequently happens that the convergence hypothesis of the neoclassical growth rate is tested against the example of regions of the same country. Despite the regions may differ by the level of technological development, preferences, economic institutions, etc., the differences would be substantially less great than those between the countries. That is why the probability of the presence of an absolute convergence between the regions is substantially higher visa-vis that between different countries. However, the employment of regions for testing the absolute convergence hypothesis breaks an important prerequisite of the neoclassical model of growth: that is, the closeness of an economy. Obviously, cultural, linguistic, institutional and formal barriers to the moving of factors proves to be less significant for a group of regions of the same country. However, it was proved that even in the event the factors were mobile and, consequently, prerequisites of the original model were broken, a closed economy and the one with a free capital movement would bear similar dynamic features13.

The theory suggests that the initial differentiation forms an effect form exogenous shocks and an imperfect adjustment mechanism. In accordance with the convergence hypothesis, in the event at the initial moment the economy of a given country (region) is farther from the steady equilibrium state, its growth rates would be greater than those in the economy that finds itself closer to the equilibrium. Accordingly, in the longer run the differentiation should disappear. The convergence hypothesis is mostly frequently used for examining differences in, and the dynamics of the level of per capita GDP (GRP).

It should be noted, however, that there is no sole definition of the notion of convergence in the economic literature. Rather, research papers refer to several concepts of the hypothesis, with two ones being most popular: these are the so-called - and -convergences14.

While the concept of - convergence15 define convergence as a catch-up process, wherein poor countries or regions enjoy higher economic growth rates, the concept of convergence16 is under Barro, Sala-i-Martin (2004).

For a more detailed review of convergence hypotheses and their empirical testing see: Barro, Sala-i-Martin (2004) and Le Pen (1998).

The term -convergence originates from the letter that denotes the coefficient under the initial per capita GDP in an assessed equilibrium. The term was introduced by Barro, Sala-i-Martin (1990).

The term -convergence was introduced by Sala-i-Martin (1998).

stood as a diminishment over time of the dispersion of distribution of the per capita GDP or any other income index applied to a sample of countries or regions.

The hypotheses of - convergence and -convergence appear interrelated, albeit not equivalent. A number of papers17 demonstrate that convergence does not directly follow from convergence. Henin, Le Pen (1995) suggested an interpretation of a correlation between an absolute convergence and convergence.

The former convergence points to the existence of a trend to reduction in the gap in the GDP per capita, while random shocks that affect countries (regions) economies can counteract this particular trend and temporarily increase the dispersion of the distribution of GDP per capita.

To analyze the correlation between these tow kinds of convergence, let us consider a fundamental equilibrium of the neoclassical model of growth that correlate the growth rate in the per capita income in economy i over some time interval to the initial income level:

yi,t log( ) = ait - (1- e- ) log(yi,t -1) + ui,t (2.1) yi,t -The theory shows that absolute term ait is a sum of some variable that reflects the technological progress and the value whose multiplier is the logarithm of the equilibrium value of a given countrys or regions income. This is the core of the concept of conditional convergence, as in this particular case one considers the income value that corresponds to a steady state of equilibrium.

While considering regions, it is assumed that absolute term ait is the same for all of them. Given this, if >0, then equation (2.1) For instance, Barro, Sala-i-Martin (2004).

implies that poorer regions would enjoy high rates of economic growth. If on assumes that random ui,t has average zero, dispersion and it dispersed independently of log(yi,t -1) and u u,t j,t for i j, he can arrive to the following expression that allows to track down the correlation between convergences:

2 2 u 0 u e-2 t = + - (2.2) t 1- e-2 1- e- 2 where dispersion log(yi,0 ). It follows from this that 0 t aims at its equilibrium value u, which grows in parallel 1- e-with the increase in, but diminishes with the increase in.

u 2 Over time may grow or fall, depending on whether is t greater or smaller vs. an equilibrium value. So a positive value of coefficient still does not mean a diminishment of, i. e. the t presence of the convergence. But convergence forms a necessary, but not sufficient conditions of the existence of convergence. So, convergence is noted only in the cases when convergence oppresses the impact of such random shocks. Let us also note that Lichtenberg (1994) extended this conclusion onto the conditional convergence as well.

The methodology of empirical testing concepts of convergence requires somewhat more detailed consideration. The most frequently used statistical method to test convergence is the regression of GDP growth rate (the average or accumulated over a given period) to the constant and logarithm of an original per capita GDP (on the basis of the crosssection data). Should the coefficient under the explanatory variable be statistically significant and get the negative sign, the hypothesis of absolute convergence is not rejected. However, there exist a number of problems that under an econometric assessment would lead to a biased assessment of coefficient. More specifically, dispersion log(yi,t ) would appear vulnerable to perturbations that exert a general influence on a group of countries of regions. This would entail an abuse of the prerequisite of shocks ui,t being independent of different countries. In this particular case, such shocks would have a positive, or, on the contrary, negative impact on the countries or regions with a higher or lower income level, which is why the assessment of coefficient would be biased under the regression assessment. To solve this problem, one introduces to the equation additional variables that characterize the impact of these or those shocks. Providing the variable of the starting income level of a given country or region and additional variables, the econometric assessment of coefficient would be valid.

It is also important to note another major advantage of employing regional data to test the convergence hypothesis. As noted above, it mostly frequently happened that an empirical testing of convergence implied particularly assessment of the equation of a correlation between GDP growth rates and its initial level. However, according to the theory, the genuine correlation also comprise a term that considers the income value under the steady state. In other words, once the traditional approach to the assessment is employed, the regression equilibrium appears incorrectly specified. If coefficient has negative sign, the hypothesis of absolute convergence is not rejected. But the problem is if one needs to reject the convergence hypothesis, if he has got a positive assessment of coefficient, for the theory suggests a multiple correlation with the inclusion of a steady state variable.

If countries of regions converge to different states of the steady equilibrium, a regular pair regression appears incorrectly specified, and the member of an equation that reflects an equilibrium income value is included in the regression error. If it in turn is correlated with the variable of the countrys or regions initial income level, the assessment of the coefficient of convergence would appear biased. For instance, should rich countries have a greater value of the equilibrium income, the assessment of the convergence coefficient would shift towards zero, which would entail incorrect conclusions on the absence of convergence, despite the existence of the conditional convergence. This example demonstrates the necessity of inclusion in a pair regression equilibrium of a proxy for the income in the steady equilibrium state to obtain a valid assessment of convergence coefficient. In the event of an error in the regression equilibrium and the initial income level, the assessment of the pair correlation would allow to obtain a valid assessment of. Finally, should all the countries or regions concerned enjoy an equal steady equilibrium state, the term that comprises an equilibrium income level would consequently form a part of the constant and the assessment of appears valid as well.

Hence, there exist two possibilities to obtain a valid assessment of coefficient : the first one is to find a proxy for the equilibrium income level and employ it as an additional explanatory variable, to assess a pair correlation between a given economys growth rate and the income level at the initial moment of time. The other method is to use the data across economies that for sure have an equal equilibrium income level, or, at least, for whom the equilibrium and initial income levels are not correlated. It is the second method in the frame of which regional data appears particularly important.

The contemporary literature has long attempted to assess the convergence hypothesis in respect to various countries or regions of a single one. Thus, Barro and Sala-i-Martin18 provide results of an assessment of convergence for the USA over the period 18802000 for the following equilibrium:

yi,T (1- e- T )T log(yi,0 ) + i0,T (2.3) (1T)log yi,0 = a + Assessments along the whole period and its single sub-periods evidenced the presence of a convergence between different states.

The assessment of coefficients along several subperiods bore the negative sign, but upon introduction of control variables that reflected a given state geographical location and structural shocks, all the coefficients proved to be positive and statistically significant. Overall, it was found out that the convergence pace between different states accounted roughly for 2% annually.

Analogous assessments were carried out basing on the data on Japanese prefectures over the period between 1930 through 1990.

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