Economic Growth Patterns: Spatial Econometric Analysis for Russian Regions^†

Reviewer #1: The concepts of beta-convergence and sigma-convergence in the beginning of section 2 need to be clarified and better explained, namely the sentence in line 38 “the sigma-convergence implies a decrease in the per capita distribution of gross regional product (GDP)” is confused and not rigorous. Also, the sentence about beta-convergence is confused “the beta-convergence is based on the Solow model [1], which implies a reduction in GDP variance per capita or the same other characteristics of income over time”.

The σ-convergence implies a decrease in differences between regions over time. That is, we can talk about the presence of a trend towards equalization of levels of economic development in a long-term opportunity. Appropriate measurements are used to measure the  σ- convergence of the unweighted ordinary difference, variant coefficient, Gini index, Tail index, etc.  The β-convergence suggests that poor regions grow faster than rich ones and therefore catch up with them.β-convergence is based on the Solow model [1], which implies that production factors tend to have diminishing returns. Thus, the growth process should bring the economies of the regions to a long-term stable state, the growth rates of which depend only on the (exogenous) rates of technological progress and labor force growth.

 Reviewer #1: A. Section 3: lines 113 and 114 – should mention the several criterions that define contiguity. Should mention that the elements in the diagonal of W are equal to zero in order to be consistent with equations that follow

The weights express the neighbor structure between the observations as a n×n matrix W in which the elements w_ij of the matrix are the spatial weights:

W=

The spatial weights  w_ij  are non-zero when i and j are neighbors, and zero otherwise. By convention, the self-neighbor relation is excluded, so that the elements in the diagonal of W are equal to zero.  Which is quite natural, since the weight matrix is designed to reflect the influence of other regions.

In our  analyses we use the spatial weights  in so-called row-standardized form. Row-standardization takes the given weights w_ij (e.g, the binary zero-one weights) and divides them by the row sum:

.

As a result, each row sum of the row-standardized weights equals one. Also, the sum of all weights, S₀=∑_i∑_j w_ij, equals n, the total number of observations  (Anselin, 2014).

Contiguity means that two spatial units share a common border of non-zero length. Operationally, we can further distinguish between a rook and a queen criterion of contiguity, in analogy to the moves allowed for the such-named pieces on a chess board.  The rook criterion defines neighbors by the existence of a common edge between two spatial units. The queen criterion is somewhat more encompassing and defines neighbors as spatial units sharing a common edge or a common vertex. Therefore, the number of neighbors according to the queen criterion will always be at least as large as for the rook criterion.  When constructing a geographic adjacency matrix for regions with a common border, we used queen criterion  (Anselin, 1996}.

Reviewer #1: B. The sentence in lines 169 -171 is confused. What is Z? Should be clarified.

An important step in the analysis of the obtained data is the construction of a spatial Moran scattering diagram. The standardized Z-values of the studied parameter are plotted along the abscissa, and the spatial factor W Z along the ordinates.

The diagram shows the regression line WZ by Z, the slope of which is equal to the coefficient of total spatial autocorrelation I with a standardized matrix of weights. The spatial autocorrelation coefficient shows the degree of linear relationship between the vector Z of centered values of the studied parameter and the vector WZ of spatially weighted centered values of the studied indicator in neighboring territories (areas), which is called the spatially lagged vector.

Reviewer #1: C. The description of a Moran’s scatter is basic and well-known information therefore should be removed.

Moran's scatter description has been removed.

Reviewer #1: D. Line206 – reference is missing in the reference list.

The link is added to the reference list.

Reviewer #1: E. Lines245 and 246 – reference is missing in the reference list.

The link is added to the reference list.

Reviewer #1: F.Tables should include notes about the acronyms used, the meaning of the stars, etc…

For Table 2 added:

 sd is standard deviation

For Table 3-6 added:

p-value 0.1 to 0.05 is *,

p-value 0.05 to 0.01 is **, p-value <0.01 is ***

Reviewer #1: G. The authors should explain why they split the estimations in 2 periods: 2010-2014 and 2014-2017.

Added to section 4.2:

We split the estimations in 2 periods: 2010-2014 and 2014-2017, because we were interested to see how economic sanctions against Russia affected the interaction between its regions.

Reviewer #1: H. When referring to the adjacency matrix the authors should clarify which criterion used (queen, rook?)

Added to section 3:

When constructing a geographic adjacency matrix for regions with a common border, we used queen criterion.

Reviewer #1: I. Clarify the sentence in lines 344 and 345 “then the direct effects turn out to be much more indirect”.

This phrase has been removed.