1. Spatial externalities of technological innovation
IARIW-HSE Conference
Spatial externalities of technological innovation
and economic growth
Ekаterina Kadochnikova, Kazan Federal University
Moscow, HSE

2. Table of Contents
1. Introduction
2. Literature
3. Methodology
4. Data & Variables
5. Estimation results
6. Conclusions

3. Motivation
The main source of growth is technological progress [Barro, 2004], the cost of inventing a new product is reduced as the number of ideas grows [Romer, 2009]
Technology transfer ensures sustainable macroeconomic growth with competitive imports from low-cost territories [Romer, 2010]
Total factor productivity in the region (TFP) depends on both the equity of knowledge and the interregional redistribution of knowledge [Fischer et al., 2009]
The growth of the service sector makes the modern digital economy less tangible and easier to measure through GDP, so it is difficult to assess the growth in the quality of goods, services and productivity in the economy, manifested in innovation [Coyle, 2014]

4. Objectives:
Compare the rate of β-convergence, short-term spatial externalities (effects) of annual growth rates of technological innovations and gross regional product for empirical testing of theoretical conclusions, reflected in [Coyle, 2014]
Check whether we get the same conclusions about the growth of the economy, measuring the GRP and measuring innovation?
Check whether the regions aspire to the same or to their own sustainable state
Show the extent to which the level of economic development, the stock of human capital, the number of granted patents for inventions, the development of the Internet affect the convergence of growth rates in the regions

5. Literature
Machlup F. (1962): Costs and number of employees in five groups of economic activities called “The sphere of production and dissemination of knowledge" are measured
Robbins (2006): Empirical findings on the uneven impact of knowledge across the US economy
Kuo, Yang (2008): Positive impact of knowledge capital on economic growth in China, the assumption of "spillovers" of knowledge between provinces
Fischer et al. (2009): Impact of interregional knowledge redistribution on overall factor productivity in the region
Cuaresma, J. C. et al. (2014): assessment of the determinants of economic growth in terms of intercountry and intercountry convergence, taking into account spatial effects
Kolomak (2010): Positive spatial externalities of economic growth rates prevail in the Western regions, negative ones – in the Eastern regions
Balash (2012): Impact of fixed capital investment in β-convergence models, evidence of spatial externalities of growth
Demidova, Ivanov (2016): Heterogeneity of regions in terms of conditions for interaction with other regions

6. Methodology (1) Data & Variables:
83 regions, Russia. From 2010 till 2016
Dependent variables:
- the natural logarithm of GRP growth rate per capita
- the natural logarithm of expenditure on technological innovation growth rate per capita
Сontrol variables:
- the investments volume in fixed capital per capita, thousand rubles
- the number of Universities students, thousand people
- the number of patents granted for inventions, pcs.
- the use of the Internet in organizations, %

7. Methodology (2) Spatial correlation and clustering of regions:
- the global Moran's I (Anselin L., 1995)
where N – number of regions, X – the logarithm of expenditure on technological
innovation growth rate per capita, the logarithm of GRP growth rate per capita,
wij - weight boundary matrix elements.
- the local Moran's I (Anselin L., 1995)

8. Methodology (3) Model specification:
Linear regression model without spatial effects (ОLS)
Spatial lag model (SLM)
Spatial Error model (SEM)
Spatial Durbin model (SDM)
Spatial Durbin Error model (SDEM)
Model with spatial autoregressive lag and spatial interaction in errors (SAC)
Models with spatial lags of independent variables (SLX)
General nesting spatial model (GNS)

9. Methodology (4) - The model GNS - The model SAC
where yi,t – GRP per capita or the cost of technological innovation per capita, in region i at time t; α - parameter to be estimated; β - convergence coefficient; W -boundary weighting matrix; ρ - spatial autoregressive coefficient for the dependent variable; θ1, θ2 — vectors of spatial coefficients for independent variables; λ - spatial autocorrelation coefficient for shock, εit – random errors.

10. Methodology (5) Marginal effects
where M(Xr)total - total marginal effect, M(Xr)direct – direct marginal effect,
M(Xr)indirect – indirect marginal effect, N – number of observations, Sr(W) –
higher order weighing matrix, In – n-dimensional identity matrix,
ρ – spatial autoregression coefficient, β - regression coefficient for Xr,
r- independent variable number, tr(Sr(W)) - matrix trace Sr(W)

11. Methodology (6) The basic hypothesis Check
H1: the rate of β-convergence of technological innovation growth rates in the modern economy is higher than the rate of β-convergence of economic growth rates
Comparison of the coefficients of β convergence and speed of convergence in the models for the different dependent variables
H2: short-term spatial externalities of technological innovation growth rates and spatial externalities of economic growth have different effects on β-convergence processes
Comparison of spatial externalities "other region - given region" on the basis of spatial autoregressive ρ coefficients.
Comparison of spatial externalities “given region – other region" on the basis of indirect marginal effects
The conclusion on statistically significant difference is proposed to be formulated on the basis of model values confidence interval boundaries comparison: if the intervals intersect, there are no differences between the coefficients

12. The nominal growth rate of gross regional product per capita (2016/2010)
The nominal growth rate of cost on technological innovation per capita (2016/2010)

13. The real growth rate of gross regional product per capita (2016/2010)
The real growth rate of expenditure on technological innovation per capita (2016/2010)

14. Spatial Correlation Indices from 2011 to 2016
Table – The global Moran's I
Indicator
2011
2012
2013
2014
2015
2016
GRP per capita growth rate
0,027
-0,008
0,159**
0,225***
0,132**
0,098*
Expenditure on technological innovation per capita growth rate
0,069
0,136**
0,129**
0,152**
0,234***
0,220***
Table – The speed and time of β-convergence of economic growth rates
Models and specifications
2013
2014
2015
2016
SAC – speed of β-convergence , in fractions of pc
0,13737
0,135581
0,094001
0,090387
SAC – time of β-convergence , in years
5,04585
5,11242
7,37385
7,66863
GNS – speed of β-convergence , in fractions of pc
0,407925
0,328431
0,238784
0,215331
GNS – time of β-convergence , in years
1,69920
2,11048
2,90281
3,21899

15. Spatial correlation of GRP growth rates
  per capita from 2011 to 2016

16. Spatial correlation expenditure on technological
innovation growth rate per capita from 2011 to 2016

17. Estimation results
Table – Estimates of spatial models of unconditional β-convergence
Models and variables
Years
2013
2014
2015
2016
Y = the natural logarithm of GRP growth rate per capita
SAC:
Convergence coefficient
-0.03**
-0.04*
-0.02
-0.03
Spatial lag dependent variable
0.64***
0.61***
0.58**
-0.58*
Shock spatial lag
-0.78***
-0.57*
-0.53
Intercept
0.32**
0.38**
0.35*
1.13***
Test: p-value LR
0.13
0.10
0.22
GNS:
-0.15
-0.15*
-0.11
-0.19
-0.59**
Spatial lag of GRP per capita in 2010
-0,12
-0,104
-0,016
0,28
-0.56*
0.01
0.004
0.003
0.03
0.23
0.18
0.39
0.27

18. Table – Estimates of spatial models of conditional β-convergence
Models and variables
Years
2013
2014
2015
2016
Y = the natural logarithm of GRP growth rate per capita
SAC:
Convergence coefficient
-0.17***
-0.18**
-0.12**
-0.12***
Investments
0.00***
0.00**
Number of students
0.00*
0.00
Internet development
-0.00
Number of patents granted
Spatial lag dependent variable
0.11
-0.08
-0.53*
-0.55*
Shock spatial lag
-0.01
0.36
0.69***
0.72***
Intercept
1.05***
1.30***
1.40***
1.44***
Test: p-value LR
0.74
0.17
0.01
GNS:
-0.80***
-0.68**
-0.46*
-0.44*
0.74***
0.68***
0.65***
0.63**
0.28*
0.14
0.27*
0.20
-0.07
-0.12
-0.17
-0.09
-0.02
-0.23
-0.27*
-0.49
-0.47
-0.42
Spatial lag of GRP per capita in 2010
-0.39
-0.18
0.40
Spatial lag of investment in 2010
-0.15
-0.41
-0.76
-0.89
Spatial lag of students in 2010
-0.24
-0.37
0.59*
Spatial lag of Internet development in 2010
-0.37*
-0.52**
-0.34
-0.25
Spatial lag of the number of patents granted in 2010
0.65
0.39
0.38
0.49
Shock spatial lag
0.52*
0.62***
0.66***
0.07
0.06
0.04
0.03

19. Table - The speed and time of β-convergence of economic growth rates

20. Table – Estimates of spatial models of unconditional β-convergence
Models and variables
Years
2013
2014
2015
2016
Y = the natural logarithm of expenditure on technological innovation growth rate per capita
SAC:
Convergence coefficient
0.82***
0.81***
0.86***
0.68***
Spatial lag dependent variable
0.18
0.04
0.40**
0.58***
Shock spatial lag
-0.28
0.00
-0.31
-0.63***
Intercept
1.42***
1.67***
0.87***
0.63***
Test: p-value LR
0.32
0.91
0.02
GNS:
0.76***
0.64***
0.54***
0.25
0.43**
Spatial lag of expenditure on technological innovation per capita in 2010
0,14
-0,15
-0,03
-0,13
-0.22
-0.35
-0.73***
-0.01
-0.002
-0.02
0.47
0.97
0.05

21. Table - Estimates of spatial models of conditional β-convergence

22. Table - The confidence intervals of the spatial autoregression coefficient in 2015
and 2016
Models
GRP per capita growth rate
The growth rate of cost on technological technological innovation per capita
Unconditional β-convergence models
SAC, 2015
[0,1915**; 0,9680**]
[0,1598**; 0,6322**]
SAC, 2016
[-1,1312*; -0,0360*]
[0,4007***; 0,7583***]
GNS, 2015
[0,1777**; 0,9783**]
[0,1683**; 1,0387**]
GNS, 2016
[-1,1191**; -0,0744**]
[0,4284***; 0,9253***]
Conditional β-convergence models
[-1,0009*; -0,0617*]
[0,2097***; 0,6491***]
[-1,004*; -0,0987*]
[0,4698***; 0,7677***]
[-1,0176; 0,0726]
[0,2884**; 0,9479**]
[-0,9904;0,1438]
[0,4345***; 0,8746***]

23. Table – Confidence intervals of indirect marginal effects in β-convergence
models in 2015 and 2016
Models and Variables
GRP per capita growth rate
The growth rate of expenditure on technological technological innovation per capita
Unconditional β-convergence
Conditional β-convergence
Unconditional β-convergence IL IU
SAC, 2015
grp_ln
-0.16
0.01
7,7e-03**
9,8e-02**
innov_ln
0.20*
1.10**
0,24***
1,14***
invest
-6,6e-07**
-5,7e-08**
0,00
stud
-1,9e-04*
-9,1e-06*
inter
-0,02
0,03
pat
SAC, 2016
-0.01
0.06
0,01**
9,24**
0.54***
1.59***
0,51**
1,30**
-7,0e-07**
-9,8e-08**
1,2e-06**
8,1e-06**
-2,0e-04**
-2,0e-05**
8,4e-04*
7,2e-03*
-0,03
0,04

24. Table – Confidence intervals of indirect marginal effects in β-convergence
models in 2015 and 2016
Models and Variables
GRP per capita growth rate
The growth rate of expenditure on technological technological innovation per capita
Unconditional β-convergence
Conditional β-convergence
Unconditional β-convergence IL IU
GNS, 2015
grp_ln
-1.13
0.68
-0,41
1,06
innov_ln
0.03
1.25
-0,28
0,67
invest
-1,76**
-0,14**
-0,43
1,03
stud
-0,85**
-0,01**
0,03
1,65
inter
-0,57
0,07
-0,07
1,04
pat
-0,63
1,43
-0,55
2,87
GNS, 2016
-0.19
0.83
-0,19
1,32
0.26
1.54
0,10**
1,01**
-1,92**
-0,20**
-0,67
0,69
-1,03**
-0,16**
1,15
-0,54
0,16
-0,26
0,80
1,55
-0,10
3,17

25. Conclusions (1)
Positive spatial autocorrelation of the regions is increasing and spatial effects need to be taken into account in econometric studies of the growth rates of the modern digital economy in the Russian regions.
The speed of β-convergence of economic growth in the regions is slowing down, there is a process of β-divergence of costs growth rates for technological innovations in the regions
In the direction of "other region – given region" there are no statistical differences between the effect of positive spatial externalities of the technological innovation growth (cooperation of regions) on the β-divergence of its rates and economic growth negative spatial externalities (competition of regions) on its β-convergence rates.
In the direction "given region – other region" statistically different predominance of spatial externalities of technological innovations costs over economic growth externalities was found
Thus, the conclusion [Coyle, 2014] about the impossibility of unambiguously assessing productivity growth in the modern economy, manifested in innovation, based on the measurement of GDP, is confirmed.

26. Conclusions (2)
The positive relationship of the variable "volume of investments in fixed capital per capita, rubles" with the rate of economic growth in most models of conditional β-convergence from 2013 to 2016 were confirmed, as well as the rate of growth of technological innovation costs in the GNS models of conditional β-convergence for 2015, 2016, which is consistent with [Balash, 2012]
Variable "Internet usage in organizations, %" connection is not confirmed and, unlike [Fischer et al., 2009; Scherngell et al., 2014], variable "number of granted patents for inventions, pcs." with the rate of economic growth and the rate of growth in the cost of technological innovation
The ambiguity of the results in the regressions of unconditional and conditional β-convergence of growth rates in the regions is shown, which is consistent with [Glushchenko, 2010; Kolomak, 2014]
Finally, the ambiguity results of short-term spatial externalities from cross-sectional data for Russian regions due to small samples, previously obtained in [Demidova, 2014], speaks in favor of identifying long-term spatial externalities on panel data analysis models