The aggregate production function for the Russian economy (with progress in science and technology considered)

The article discusses the issue of aggregating production functions as models of production processes at the regional and national levels of the Russian economy. The problem of aggregation was first formulated in the 1940s in the academic journal Econometrica, but it still remains unsolved. This problem is a part of a broader research area studying «bridges» between micro and macroeconomics. The article develops a statistical method of production functions aggregation, offered by Perm school of hierarchical analysis of economy, and is aimed at adapting this method for the Russian economy. A modification of the method for the case of unequal allocation of resources among the elements of the economy is proposed. Estimates of the parameters of the «investment» Cobb-Douglas production function for all Russia's regions, obtained on the basis of the «PROGNOZ. SBSP SER» software, are presented. The aggregate production function for the Russian economy is constructed on the basis of the regional production functions. Progress in science and technology is taken into account as a factor of the production function. It was found that the resulting production function provides more accurate forecasts compared with the traditional macroeconomic Cobb-Douglas production function. Basing on the aggregate production function, Russia's GDP for 2015 is calculated, forecast for 2016-2018 is made, and production processes are analyzed as follows: elasticity coefficients with respect to production factors, marginal rate of substitution and elasticity of substitution are calculated. According to the baseline scenario of the forecast obtained for Russia, in 2015 economic contraction by 2,6% is expected, in 2016-2018 the economy will start recovering, its growth rate for this period is expected to be 2-2,5% per year.