Pseudorandom search algorithms in problems of optimal choice of parameters of complex econometric models

T. N. Averina ; N. N. Dobrovol'skii ; I. Yu. Rebrova ; N. M. Dobrovol'skii

Čebyševskij sbornik, Tome 22 (2021) no. 5, pp. 25-43

Résumé

The pseudorandom search method considered in this paper is quite universal and allows solving complex econometric problems using the discrete least squares method. The paper considers the problem of finding the parameters of a linear combination of the Cobb-Douglas-Tinbergen function and the third production function, which is its generalization. If the choice of parameters of the Cobb-Douglas-Tinbergen function, or the third production function after logarithmization and the application of the least squares method is reduced to a linear problem that is solved in the final form, then a linear combination of these two models requires solving an optimization problem of 10 or 11 variables with a transcendental function, which makes the problem difficult to solve. At least 10 different types of classical number-theoretic grids are well known in the literature. From the point of view of the organization of the pseudorandom belt, the grids and LP sequences proposed by I. M. Sobol are the most well studied. Previously, Korobov parallelepipedal grids were used in solving problems of textural analysis in geophysics. 6-dimensional grids were used in these works. In our work, we have to work with 10-dimensional and 11-dimensional grids with a much larger number of points in order to overcome the well-known "curse of dimensionality". It is partially possible to reduce the dimension to the 9th by using the properties of the models under consideration, which are studied in detail in this paper. As a result of the study, it was found that three parameters cannot be determined unambiguously from the original mathematical model. An additional optimization problem arises for the least squares method if we postulate the proximity of technological coefficients. The latter assumption requires additional economic interpretation and will be the subject of further economic research. It would be interesting to compare the results of calculations for different regions of the country and for the country as a whole. The problem is related to the availability of data, but we expect to consider this formulation of the problem in subsequent works.

Détail

Keywords: algebraic lattices, algebraic net, trigonometric sums of algebraic net with weights, weight functions.