Using linear regression with the least squares method to determine the parameters of the Solow model

Abstract

The article shows that a simple method for calculating the values of the coefficients at which the production functions of Cobb-Douglas and Robert Solow best approximate statistical data, as well as determining the accuracy of the model and coefficients, is linear regression using the least squares method. By means of a regression analysis, the parameters of the effect of the introduction of innovative processes and the coefficients of the level of technology, labor elasticity and capital of production functions are determined. The initial statistics for the calculations were taken on the website of the Federal State Statistics Service in the relevant sections. Using the constructed functions, the influence of such factors as labor, capital, innovative processes on the long-term change in the volume of production in Russia was estimated, and the nature of the return on these production factors was determined. It is shown that the considered production functions in relation to real data demonstrate an increasing return on labor and capital. To determine the reliability of the approximation, a linear correlation coefficient (Pearson correlation coefficient) was calculated. As a result of calculations with the formula, the value of the Pearson coefficient r xy = 0.9844 was obtained. From the obtained value, it was concluded that there is a strong correlation between the variables, the variables correlate positively and the reliability of the approximation is high.

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