The algorithm of decision supporting procedure based on Data Envelopment Analysis (DEA) along with the Malmquist Productivity Index is suggested in the paper. The procedure's core consists of evaluations complex for preliminary data processing and adjustment as well as creating of analytic materials in the field of regional strategy planning. The crucial study issue is to define boundaries of DEA applicability in this field and to eliminate DEA shortcoming, such as the scores dependence on a set of inputs and outputs. The efficiency scores of Russian regional agrarian sector are obtained in order to verify the procedure and add knowledge to current indicators' systems of regional economic efficiency by improving approach objectiveness. It is shown how obtained results can be applied in the strategic planning to increase effectiveness of state regional policy activity.
Theoretical model of this study is based on the Pareto-Koopmans concept (1951) [
DEA is a non-parametric frontier approach for comparative efficiency measurement in which a set of similar objects with multiple inputs and outputs is analyzed. The aim of this study is to suggest the procedure for providing strategy planning by analytical reports based on DEA scores implementation.
It is obvious that productivity analysis by DEA has at least three current issues. The first is to define a set of objects which will be compared in the study. The second is to formulate convenient conditions for concrete models’ modifications using. The third issue is to improve discrimination capability. Therefore, efficiency assessment procedure by DEA is primarily based on the following grounds: the formation of objects’ set to be compared, identification of inputs and outputs, and model selection.
Taking into account issues mentioned above, it is necessary to adapt basic DEA models and its implementation. Furthermore, DEA procedure is considered as a core of the evaluation of regional economy efficiency scores.
This paper consists of five parts. We state the main issues in this, first, part. This study’s background is presented in the second part. Part 3 deals to description of suggested evaluation procedure. The applying of investigation of the Russian regions agrarian sector to management tasks by using the procedure is reported in the part 4. We make conclusions in the last part. 2
DEA application has a big number of advantages. First of all, a calculation of an integrated assessment is produced for each region reflecting the efficiency of input factors using for output products. Besides, the Pareto-optimal set of efficient regions in the multidimensional space of inputs and outputs is being obtained. Secondly, it is unnecessary to attract an expert knowledge in a priori assignment of weights for variables corresponding to inputs and outputs. Despite of this, using of additional data on region external factors is helpful for creating the right model. Thirdly, it is very important that there are no restrictions on the functional form of the relation between inputs and outputs.
The study is carrying out with the hypothesis that DEA implementation needs the formal procedure in order to obtain stable scores and apply research results to analytic background of current regional strategic planning.
The multilateral and penetrating analysis of DEA possibilities and its application’s
restrictions are presented in Dyson et al. (2001), Cook and Seiford (2009) [
The application possibilities of Malmquist Productivity Index in different
intertemporal comparisons are described in the research of Färe and Grosskopf (1996)
[
According to review presented in [
Different levels of the regional economy scale and the return to scale effect are considered as a reason of inequality between regional output performances. That is why the model with variable return to scale is suggested for this study. This model was introduced by Banker et al. (1984).
Data for a research by DEA is presented by a number of indicators in form of the matrix of inputs Xt={xtij} and matrix of outputs Yt={ytkj}. The efficiency criterion for a multidimensional assessment of an object is to assign some input and output parameters for all objects, some weights and then to calculate and maximize the ratio for each object: where: j – index of the estimated production facility, j=1…, n; xij – matrix of input parameters that reflect the system resources, i=1,…,m; ykj – matrix of outputs which reflect the products of system, k=1,…,s; ui /wk – weights for outputs/inputs.
According to the DEA framework, this function should be maximized under restrictions for all objects:
The Malmquist Productivity Index is calculated using such DEA efficiency scores for evaluation of total factor productivity change:
The suggested procedure for regional efficiency assessment has the complex of procedures for preliminary data processing and adjustment (fig.1). (1) (2) (3) The dual linear program model for evaluation the criterion given above is: (4) where: η – comparative efficiency score of region j (j=1…, n); λj – dual model variables.
If η<1 then the region belongs to inefficient set, otherwise (η = 1) it is a part of Pareto set.
According to procedure carrying out, the result of all evaluations using (3), (4) is a set of regional types by dynamics character.
Generally, the result of DEA application is the set of scores also which shows the ways of comparative efficiency improvement for each inefficient region. Nevertheless, this issue is not treated in this procedure because it requires the special attention and investigation due to its complexity. 4
We examined the issue of inequality of regional economy performance for the period
from 2008 to 2010. Federal State Statistics Data is used from www.gks.ru [
Stage 1. The set of indicators for models consists of resources and results of regional agrarian sector performance. Indicators are reported in Table 1.
Stage 2. Set of model’s variables defined this way: five resources are taken as inputs while three results are taken as outputs. The volume of region population is considered as the special variable for the set’s normalization.
Type Resources Results Variable for Normalization number of cattle, thousand heads (x1) organizations acreage under crops, ha (x2) average number of employees, thousand people (x3) power capacity, thousand horsepower (x4) equipment park (tractors), units (x5) gross grain yield, thousand tons (y1) production of milk, thousand tons (y2) production of livestock and poultry, thousand tons (y3) volume of region population, thousand people
Stage 3. Next, the homogeneity of conditions was checked for all agrarian regional systems, and asymmetry of land’s quality founded out. The input called “organizations acreage under crops” is adjusted by the coefficient of cadastral value of agricultural land. The rule of ratio of variables’ number and objects’ number is kept, therefore, modeling is made for 53 quite similar agrarian Russian regions.
Additional restriction to weights is used in order to improve the discrimination capability of the model. Direct restriction on the ratio of the quantity of employees and the power capacity presented by the following ratios: (5) (6) (7) price_x3 – regions’ average monthly salary; price_x4 – regions’ average energy price; x3, x4 – inputs which are taken in the normalized forms according to the second stage.
Stage 4. According to (3) and (4), the calculation cycle is done, and obtained scores are insensitive regarding the model parameters changes. It was approved by decreasing of the set of analyzed objects. Besides, the Malmquist Indices values are similar to current expert opinion on the character of current tendencies of technological progress changes in the industry for analyzed period.
Stage 5. The quantitative scores combined with qualitative evaluation of risks and conditions of regional development allow finding out the regions taxonomy by using obtained knowledge on type of efficiency dynamics. The procedure has conducted from the first to the fifth stage given in Fig.1.
The most significant agrarian regions of Russia are located on the Southern
territory which consists of two state districts, namely Southern Federal District and
Northern Caucasus Federal District. There are two strategies for these regions: Southern
Federal District Strategy and Northern Caucasus Federal District Strategy [
Although analyzed period covers the crisis years, the agrarian production of the South of Russia shows the reserve of stability. Besides, it is brought out that the Southern regions belong to Pareto-Efficient set of Russian regions.
Thus, only 4 regions among 13 of the South are estimated as having the stable decline. The economic development opportunities of this regions are significant, nevertheless the considerable potential of regions is not using.
Such indicators’ further analysis can be used for adjustment of scenario data tasks in the field of regional development foresight and strategic planning. The obtained results also can be suitable for equalization policy design in order to steady the level of regional efficiency during long-term period. In addition to this, it is important that risks, conditions and possible consequences of the policy should be assumed for each scenario of regional development. 5
The verification of suggested procedure along with the DEA model demonstrates the positive results that approve the possibility of the procedure application to prospective studies in the field of production analysis as well as strategic management.
As it was shown, the obtained results can be part of the quantitative investigations for the current strategies of development policy. In addition to this, the development scores can be used together with regional development risks and opportunities analysis, indicators of economical efficiency, such as gross domestic product per capita, enterprises profitability, etc. Thus, obtained scores will add knowledge to current indicators’ systems of regional economic efficiency and improve approach objectiveness and effectiveness of state regional policy activity.
This article is conducted within Program of the Presidium of Russian Academy of Sciences № 32 “Fundamental Issues of Polyethnic Region Modernization in Terms of Tensions Growth”.