natural increase of population (the difference between birth and mortality rates). We used these data to estimate the adjusted working age population as working age population minus the net migration inflow, which in turn was estimated as natural increase subtracted from total population increase. This method assumes that all migration inflow is of working age, which is a conservative approach.<sup>12</sup> But using both adjusted and non-adjusted measures of working age ratio allows us to estimate an upper bound for adjustment. The results of estimating the contribution of adjusted working are ration growth to GDP per capita growth are shown in Column (2) of Table 1. We do not find significant differences compared to the unadjusted model except the growth of the working age ratio. The contribution of the growth rate of this factor is significant in the adjusted model. It means that the bias caused by possible migration into faster growing regions could be significant.

To verify this result, we used another approach estimating dynamic panel developed by Arellano and Bond (1991). This method is based on GMM estimation, where current values of contemporaneous or predetermined values of regressors are instrumented by their lagged values.<sup>13</sup> In theory, this method should provide consistent estimations without any systematic bias.

The results of the estimation is presented in column (3) and (4) of the Table 1. We would like to pay attention that coefficient for the growth rate of real GDP per capita _ρ_ +1. To compare the results with first column one should subtract 1 from the value of the coefficient. Column (3) represents the results for not adjusted working age ratio, while column (4) is for adjusted. As we mentioned before, in theory the Arellano-Bond approach should lead to consistent estimates and there is no need for additional adjustment. In practice, we estimated both models – with and without the adjustment of working age ratio growth to be on the safe side because we reduced the number of instruments significantly. The quantitative results of column (3) and (4) are very close to each other and to the general panel regression ((1) and (2)). We conclude that there is negative significant contribution of the former level of GDP per capita showing convergence. The positive effect of working age growth and level in previous period (�� and ��) is still significant for adjusted for migration model that confirms tested hypothesis that demographics have a signification impact on growth.

Following Aiyar and Mody (2011), we split our sample into time periods. In principle, a decade might seem appropriate for demographic changes. However, in view of the small time period, we use 5-year periods. This approach can be justified for the case of Russia, as our sample period coincided with fast demographic changes in Russia. For growth rate within the 5-year period, we use the average of annual growth rates and for initial level – the value in the first year of the period. For control variable, we also calculated the time means. In this case, the equation for estimation is modified slightly. The only difference lies in the initial

> 12 This adjustment is relevant only for working age ratio growth. While the initial (previous) level of working age ratio could also be affected by migrants who came earlier, we cannot distinguish between them and natural population of the region. However, this indicator is not contemporaneous with current level of GDP and that is why it bias of the coefficients should be smaller.

> 13 The method is based on the property that past value of dependent variable and regressors are not contemporaneous with the error term and can therefore be used as instruments. They correlate with the current levels of regressors and that is why could be strong enough instruments. The idea is to use as many instruments as possible. In our case the contemporaneousness of regressors limit the amount that could be used. We could use only lagged levels of dependent variable as well as regressors, while in standard Arellano-Bond approach all regressors (including future) are used as instruments.

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