# Efficiency Analysis of Regional Innovation Development Based on DEA Malmquist Index

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## Abstract

**:**

## 1. Introduction

**Hypothesis 1 (H1).**

**Hypothesis 2 (H2).**

**Hypothesis 3 (H3).**

- Methodological approaches for the analysis of the innovative development dynamics were determined, and new DEA-based instruments for its assessment were developed.
- Indicators characterizing the cost-effectiveness and results of innovative activities in the Russian regions were collected and analyzed.
- A cluster model for selecting regions relevant for the analysis of innovative development was built, and a research sample on the basis of Russian regional data was formed.
- Various models to evaluate the direct and indirect effects of innovation at the regional level were developed.
- The Malmquist Productivity Index was calculated to assess the dynamics of innovative development over three periods.
- The developed instruments to evaluate the dynamics of the development effectiveness of regional innovative systems in Russia from 2006 to 2017 were implemented.

## 2. Theoretical Framework

#### 2.1. Literature Review

#### 2.2. Development of Approaches to Assess the Innovative Dynamics of Regions

#### 2.3. Indicators and Description of Variables

- R & D personnel is research and development personnel.
- R & D finance is all domestic current and capital costs for research and development.
- Registered patents are granting patents and certificates for the intellectual activity outcomes.
- R & D companies are innovative enterprises, and, in the constituent documents of which, one of the types of economic activity is indicated as “Research and Development” in official statistics.

- The volume of innovation goods is volume of innovative goods, works, and services of organizations by economic activity.
- Hi-tech share in GRP is the share of value-added of high-tech and knowledge-intensive industries in the GRP of Russian regions.
- Investment in fixed assets is the ratio of investments in fixed capital to GRP; it characterizes the investment activity of the Russian regions. The acceleration of investment growth in fixed capital in the economy is an important indicator for the Russian Federation Government.
- Used patents are patents that have been used and commercialized in real businesses.

#### 2.4. Models for Assessing Innovative Growth

- The choice of a non-specific set of indicators (inputs and outputs parameters) reflecting the effects of innovations that would be available in Russian statistical databases and would be statistically significant and accessible for researchers.
- Building two relevant DEA models that reflect the specified approach with underlying direct and indirect indicators of innovative development.
- Selecting regions to be subject to cluster analysis.
- Taking the time lag between the investing resources and the results obtained from innovation into account.

- Model 1 reflects the immediate direct effects of innovation policy—the volume of innovative products as the main indicator of innovation dynamics (Table 1).
- Model 2 depicts indirect effects—so called spillover effects—accompanying the innovations diffusion processes and characterizing the level of effectiveness of innovation policy through the creation of general conditions for innovative susceptibility, the growth of investment indicators, the patents used, and, as a result, structural changes and increases in the volume of industries with high-tech development in regional economies (Table 2).

## 3. Methods for Evaluating Changes in Technical Efficiency

#### 3.1. Data Preprocessing by Cluster Analysis

- Partitional (k-means, k-medoids, k-mode, Clustering LARge Applications (CLARA) and Clustering Large Applications based on RAN-Domized Search (CLARANS).
- Hierarchical (agglomerative and divisive).
- Density-based spatial clustering of applications with noise.
- Distribution-based statistical clustering model (expectation-maximization clustering).
- Fuzzy analysis clustering (c-means).
- Self-organizing maps.

- Input: dataset A of L data points, number of clusters k.
- Output: partition the data points from A into k clusters $\mathrm{C}=\left\{{\mathrm{C}}_{1},{\mathrm{C}}_{2},\dots ,{\mathrm{C}}_{\mathrm{k}}\right\}$.
- Initialization: randomly select the k of the L data points for the medoids set M.
- Build-step: determine the closest medoid m for each point a∈A.
- Swap-step: for each medoid m∈M and each data point a associated to m, swap m and a and calculate the value of the intercluster distance d as the average dissimilarity of a to all the data points associated to m. Select the medoid a with the minimum cost of the configuration distance d.
- Repeat steps 2 and 3 until the medoids do not change or other termination criteria are met.

- Mixed measures (mixed Euclidean distance).
- Nominal measures (Nominal distance, Dice similarity, Jaccard similarity, Kulczynski similarity, Rogers Tanimoto similarity, Russell Rao similarity, and simple matching similarity).
- Numerical measures (Euclidean distance, Camberra distance, Chebychev distance, correlation similarity, cosine similarity, Dice similarity, and Jaccard similarity).
- Bregman divergences (generalized divergence, Itakura–Saito distance, Kullback–Leibler divergence, and Mahalanobis distance).

#### 3.2. DEA Malmquist Index Modeling

_{o}greater than 1 indicates positive TFP growth from period t to period (t + 1). A value of M

_{o}less than 1 indicates a TFP decline. If M

_{o}= 1, there is no progress or regression in period t ratio to (t + 1).

_{o}is the geometric mean of two TFP indices. The first is evaluated with respect to period t technology, and the second is evaluated with respect to period (t+1) technology. An equivalent decomposed form of the TFP index [44,45] is:

_{i}, i = 1, …, N, use P inputs to produce S outputs. In a particular time period t, the following definitions hold:

- y
_{i}is a S×1 vector of output quantities for the DMU_{i}. - x
_{i}is a P×1 vector of input quantities for the DMU_{i}. - Y is a N×S matrix of output quantities for all N DMU
_{i}. - X is a N×P matrix of input quantities for all N DMU
_{i}. - λ is a N×1 vector of weights.
- $\phi $ is a scalar.

## 4. Results

#### 4.1. Clustering of Regions According to the Level of Innovative Development

- High-tech share in GRP, %.
- Investment share in fixed assets, %.
- Volume of innovation goods, rubles.
- Internal R & D costs, million rubles.

#### 4.2. Analysis of Malmquist Productivity Index

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

DEA | data envelopment analysis |

R & D | research and development |

MPI | Malmquist Productivity Index |

GRP | gross regional product |

DBI | Davies–Bouldin Index |

DMU | decision-making units |

CRS | constant return to scale |

VRS | variable returns to scale |

TFP | total factor productivity |

EC | efficiency change |

TEC | technological change |

SEC | scale efficiency change |

PEC | pure efficiency change |

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DEA VARIABLES | |
---|---|

INPUTS | OUTPUTS |

R & D personal, 100 pers. | Volume of innovation goods, % |

R & D finance, 100 mln rubl. | |

R & D companies, units | |

Registered patents, units |

DEA VARIABLES | |
---|---|

INPUTS | OUTPUTS |

R & D personal, 100 pers. | Hi-tech share in GRP, % |

R & D finance, 100 mln rubl. | |

R & D companies, units | Used patents, units |

Registered patents, units | Investment share in fixed assets, % |

k | Davies–Bouldin Index (DBI) |
---|---|

2 | 1.355 |

3 | 0.785 |

4 | 0.941 |

5 | 2.185 |

6 | 2.054 |

7 | 1.810 |

8 | 1.661 |

9 | 1.658 |

10 | 1.465 |

**Table 4.**The division of the initial 80 constituent entities of the Russian Federation into clusters.

Clusters | Regions |
---|---|

Cluster 0 | Arhangelsk Region, Belgorod Region, Vladimir Region, Voronezh Region, St. Petersburg, Kirov Region, Krasnodar Region, Kursk Region, Moscow Region, Nizhny Novgorod Region, Novosibirsk Region, Penza Region, Perm Region, Republic of Bashkortostan, Mari El Republic, Republic of Mordovia, Republic of Tatarstan, Rostov Region, Ryazan Region, Samara Region, Sverdlovsk Region, Stavropol Region, Tomsk Region, Tula Region, Udmurt Republic, Ulyanovsk Region, Khabarovsk Region, Chelyabinsk Region, Chuvash Republic, and Yaroslavl Region |

Cluster 1 | Altai Region, Altai Republic, Amursk Region, Republic of Buryatia, Astrakhan Region, Republic of Dagestan, Bryansk Region, Republic of Ingushetia, Volgograd Region, Republic of Kalmykia, Vologda Region, Republic of Karelia, Jewish Autonomous Region, Komi Republic, Transbaikal Region, Republic of Sakha (Yakutia), Ivanovo Region, Republic of North Ossetia-Alania, Irkutsk Region, Tyva Republic, Kabardino-Balkarian Republic, Republic of Khakassia, Kaliningrad Region, Saratov Region, Kaluga Region, Sakhalin Region, Kamchatka Region, Smolensk Region, Karachay-Cherkess Republic, Tambov Region, Kemerovo Region, Tver Region, Kostroma Region, Tyumen Region, Krasnoyarsk Region, Chechen Republic, Kurgan Region, and Chukotka Autonomous |

Cluster_2 | Moscow City |

Attribute | Cluster 0 | Cluster 1 | Cluster 2 |
---|---|---|---|

Hi-tech share in GRP, % | 0.017 | 0.009 | 0.014 |

Investment share in fixed assets, % | 0.009 | 0.010 | 0.007 |

Volume of innovation goods, % | 0.025 | 0.003 | 0.007 |

Intramural R & D costs, million rubles | 0.007 | 0.000 | 0.352 |

**Table 6.**Malmquist Productivity Index

**(**${M}_{o}$

**)**decomposition for model 1. EC: efficiency change; TEC: technological change; SEC: scale efficiency change; and PEC: pure efficiency change.

Region | EC | TEC | PEC | SEC | ${\mathit{M}}_{\mathit{o}}$ |
---|---|---|---|---|---|

Arhangelsk Region | 3.479 | 1.463 | 1.245 | 2.794 | 5.088 |

Krasnodar Region | 2.098 | 1.973 | 1.000 | 2.098 | 4.138 |

Kursk Region | 1.747 | 1.374 | 0.995 | 1.755 | 2.400 |

Khabarovsk Region | 1.722 | 1.337 | 0.928 | 1.856 | 2.302 |

Mari El Republic | 1.167 | 1.854 | 1.000 | 1.167 | 2.163 |

Voronezh Region | 1.027 | 1.969 | 1.503 | 0.684 | 2.022 |

Sverdlovsk Region | 1.046 | 1.834 | 1.143 | 0.914 | 1.918 |

Tomsk Region | 0.899 | 2.116 | 0.966 | 0.930 | 1.902 |

Moscow Region | 0.691 | 2.495 | 0.693 | 0.997 | 1.724 |

Yaroslavskaya Region | 1.025 | 1.644 | 1.096 | 0.935 | 1.685 |

Republic of Bashkortostan | 1.402 | 1.103 | 1.502 | 0.934 | 1.547 |

Rostov Region | 0.762 | 2.011 | 0.805 | 0.947 | 1.534 |

Udmurt Republic | 1.189 | 1.177 | 0.861 | 1.382 | 1.400 |

Perm Region | 1.000 | 1.369 | 1.000 | 1.000 | 1.369 |

Vladimir Region | 1.099 | 1.243 | 1.328 | 0.827 | 1.366 |

Nizhny Novgorod Region | 0.585 | 2.234 | 0.510 | 1.147 | 1.307 |

Republic of Mordovia | 1.000 | 1.270 | 1.000 | 1.000 | 1.270 |

Chelyabinsk Region | 0.827 | 1.404 | 0.778 | 1.063 | 1.161 |

Chuvash Republic | 1.181 | 0.954 | 0.938 | 1.259 | 1.127 |

St. Petersburg | 0.828 | 1.335 | 1.011 | 0.818 | 1.105 |

Tula Region | 0.665 | 1.654 | 0.733 | 0.907 | 1.099 |

Samara Region | 0.549 | 1.976 | 0.534 | 1.029 | 1.085 |

Republic of Tatarstan | 0.618 | 1.610 | 0.615 | 1.005 | 0.996 |

Ryazan Region | 0.848 | 1.156 | 0.806 | 1.053 | 0.980 |

Belgorod Region | 0.561 | 1.664 | 0.762 | 0.736 | 0.934 |

Novosibirsk Region | 0.740 | 1.232 | 0.863 | 0.857 | 0.912 |

Kirov Region | 0.871 | 0.910 | 1.000 | 0.871 | 0.793 |

Moscow City | 2.223 | 0.336 | 2.081 | 1.068 | 0.748 |

Stavropol Region | 0.978 | 0.735 | 1.116 | 0.876 | 0.719 |

Penza Region | 0.868 | 0.653 | 1.000 | 0.868 | 0.567 |

Ulyanovsk Region | 0.553 | 0.963 | 0.593 | 0.932 | 0.533 |

Period | EC | TEC | PEC | SEC | ${\mathit{M}}_{\mathit{o}}$ |
---|---|---|---|---|---|

2011–2014 | 0.597 | 2.407 | 0.653 | 0.914 | 1.436 |

2014–2017 | 1.657 | 0.763 | 1.344 | 1.233 | 1.263 |

Mean | 0.994 | 1.355 | 0.937 | 1.061 | 1.347 |

Region | EC | TEC | PEC | SEC | ${\mathit{M}}_{\mathit{o}}$ |
---|---|---|---|---|---|

Arhangelsk Region | 1.000 | 2.242 | 1.000 | 1.000 | 2.242 |

Rostov Region | 0.649 | 3.265 | 1.640 | 0.396 | 2.120 |

Tula Region | 1.074 | 1.941 | 1.000 | 1.074 | 2.085 |

Udmurt Republic | 0.909 | 2.180 | 1.000 | 0.909 | 1.983 |

Belgorod Region | 1.392 | 1.354 | 1.178 | 1.181 | 1.884 |

Kursk Region | 0.775 | 2.364 | 0.780 | 0.994 | 1.831 |

Samara Region | 0.639 | 2.686 | 1.578 | 0.405 | 1.716 |

Republic of Mordovia | 1.000 | 1.683 | 1.000 | 1.000 | 1.683 |

Sverdlovsk Region | 1.329 | 1.239 | 1.329 | 1.001 | 1.647 |

Mari El Republic | 1.000 | 1.506 | 1.000 | 1.000 | 1.506 |

Stavropol Region | 0.678 | 2.178 | 1.000 | 0.678 | 1.476 |

Moscow Region | 1.335 | 1.042 | 0.750 | 1.781 | 1.391 |

Ryazan Region | 0.833 | 1.585 | 0.778 | 1.070 | 1.320 |

Republic of Bashkortostan | 0.494 | 2.458 | 1.062 | 0.465 | 1.215 |

Chuvash Republic | 0.718 | 1.630 | 1.000 | 0.718 | 1.170 |

Chelyabinsk Region | 0.590 | 1.876 | 0.885 | 0.667 | 1.107 |

Moscow City | 1.283 | 0.862 | 1.253 | 1.024 | 1.106 |

Ulyanovsk Region | 0.536 | 2.045 | 1.000 | 0.536 | 1.096 |

Nizhny Novgorod Region | 1.290 | 0.843 | 1.000 | 1.290 | 1.087 |

Kirov Region | 0.681 | 1.573 | 1.000 | 0.681 | 1.071 |

Krasnodar Region | 0.493 | 2.163 | 0.636 | 0.775 | 1.067 |

Voronezh Region | 0.569 | 1.846 | 1.222 | 0.466 | 1.051 |

Vladimir Region | 0.590 | 1.642 | 0.612 | 0.964 | 0.968 |

Republic of Tatarstan | 1.000 | 0.962 | 1.000 | 1.000 | 0.962 |

Perm Region | 1.000 | 0.923 | 1.000 | 1.000 | 0.923 |

Khabarovsk Region | 0.580 | 1.310 | 0.650 | 0.891 | 0.760 |

Penza Region | 0.531 | 1.427 | 0.566 | 0.939 | 0.758 |

St. Petersburg | 0.742 | 1.014 | 1.000 | 0.742 | 0.753 |

Novosibirsk Region | 0.351 | 2.044 | 0.736 | 0.477 | 0.717 |

Tomsk Region | 0.331 | 1.708 | 0.364 | 0.909 | 0.566 |

Yaroslavskaya Region | 0.355 | 1.003 | 0.447 | 0.794 | 0.356 |

Period | EC | TEC | PEC | SEC | ${\mathit{M}}_{\mathit{o}}$ |
---|---|---|---|---|---|

2011–2014 | 1.098 | 0.888 | 0.992 | 1.107 | 0.975 |

2014–2017 | 0.498 | 2.876 | 0.826 | 0.603 | 1.432 |

Mean | 0.739 | 1.598 | 0.905 | 0.817 | 1.182 |

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**MDPI and ACS Style**

Firsova, A.; Chernyshova, G.
Efficiency Analysis of Regional Innovation Development Based on DEA Malmquist Index. *Information* **2020**, *11*, 294.
https://doi.org/10.3390/info11060294

**AMA Style**

Firsova A, Chernyshova G.
Efficiency Analysis of Regional Innovation Development Based on DEA Malmquist Index. *Information*. 2020; 11(6):294.
https://doi.org/10.3390/info11060294

**Chicago/Turabian Style**

Firsova, Anna, and Galina Chernyshova.
2020. "Efficiency Analysis of Regional Innovation Development Based on DEA Malmquist Index" *Information* 11, no. 6: 294.
https://doi.org/10.3390/info11060294