# Green Economy and Waste Management as Determinants of Modeling Green Capital of Districts in Poland in 2010–2020

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Materials and Methods

- Determination of the set of diagnostic variables and the study area.
- Reduction in the space of diagnostic variables (elimination of almost constant variables) verification in terms of statistics and content.
- Normalization of variables—method of unitarization to zero and determination of the direction of preferences of variables in relation to the main criterion.
- Determination of the value of the synthetic measure based on the formula selected for the aggregation of the diagnostic variables.
- The linear arrangement of objects. Identification of typological classes for the whole range of variability of the synthetic measure, measures of descriptive statistics, and values of measures of similarity (similarity/dissimilarity matrix) were determined (Table 1, Table 3 and Table 4).

Stage | Description of Stage | |
---|---|---|

stage 4 | The Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method is a reference method in which two reference points are determined—the standard and the anti-standard. Determining the Euclidean distances of objects from the pattern and anti-pattern, according to the formulas: - (a)
- object distances from the pattern (=1):
| |

${d}_{i}^{+}=\sqrt{\frac{1}{n}{\displaystyle {\displaystyle \sum}_{j=1}^{m}}{\left({z}_{ij}-{z}_{j}^{+}\right)}^{2}},$ | (8) | |

- (b)
- distances of objects from the anti-pattern (=0):
| ||

${d}_{i}^{-}=\sqrt{\frac{1}{n}{\displaystyle {\displaystyle \sum}_{j=1}^{m}}{\left({z}_{ij}-{z}_{j}^{-}\right)}^{2}},$ | (9) | |

where n—denotes the number of variables forming the pattern or anti-pattern, ${z}_{ij}$—denotes the unitized value of the j-th feature for the tested unit (or the normalized value of the j-th variable of the object), ${z}_{j}^{+}/{z}_{j}^{-}$—denotes the template or anti-template object. Determining the synthetic measure (according to the TOPSIS method) according to the formula: | ||

${q}_{i}=\frac{{d}_{i}^{-}}{{d}_{i}^{-}+{d}_{i}^{+}},gdzie0\le {q}_{i}\le 1,i=1,2,\dots ,n,$ | (10) | |

wherein: ${q}_{i}$ ∈ [0; 1]; ${d}_{i}^{-}\u2014$means the distance of the object from the anti-pattern (from 0), ${d}_{i}^{+}$ means the distance of the object from the pattern (from 1). A higher value of the measure indicates a better situation of an individual in the analyzed area [52,53,54,63,65]. | ||

stage 5 | Division of the studied units into typological groups. The first, second and third quartiles were adopted as threshold values. The size of the synthetic measure in the first group means a better unit, and in the following groups—weaker units. The similarity matrix was determined in the PQStat program. The Euclidean distance is a metric and is given by the formula: | |

$d\left(A,B\right)=\sqrt{\left({x}_{1A}-{y}_{1B}\right)+\left({x}_{2A}-{y}_{2B}\right)+\dots +\left({x}_{nA}-{y}_{nB}\right)},$ | (11) | |

where A = (x _{a}, y _{a}), B = (x _{b}, y _{b}).Distance equal to 0 when they are identical. The farther away the objects are, the more dissimilar they are (=1). The similarity matrix was determined in the PQStat program. For the analysis and evaluation of the strength of the relationship between the variables and the synthetic measure of the studied areas, Pearson’s linear correlation coefficients (performed in the Grtel program) were used, expressed by the formula: | ||

${r}_{xy}=\frac{{{\displaystyle \sum}}_{i=1}^{n}\left({x}_{i}-\stackrel{\leftharpoonup}{x}\right)\left({y}_{i}-\stackrel{\leftharpoonup}{y}\right)}{\sqrt{{{\displaystyle \sum}}_{i=1}^{n}{\left({x}_{i}-\stackrel{\leftharpoonup}{x}\right)}^{2}{{\displaystyle \sum}}_{i=1}^{n}{\left({y}_{i}-\stackrel{\leftharpoonup}{y}\right)}^{2}}},$ | (12) | |

where, r _{xy}—Pearson’s linear correlation coefficient, x and y are measurable statistical features x = (1,2,… n), y = (1,2,… n), and
$\stackrel{\leftharpoonup}{x},\stackrel{\leftharpoonup}{y}$
are the arithmetic means of the features x and y.The Gini coefficient is a measure of the inequality of the distribution of the examined variable, it takes a value between 0 and 1 (the concentration coefficient was calculated in the Ststistica program). The Gini coefficient is expressed by the formula: | ||

G(y) = $\frac{{{\displaystyle \sum}}_{i=1}^{n}\left(2\mathrm{i}-\mathrm{n}-1\right){y}_{i}}{{\mathrm{n}}^{2}\overline{y}},$ | (13) | |

where y_{i} is the value of the ith observation and a $\overline{y}$ is the average value of all y_{i} observations [69]. |

## 4. Results

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Research area—districts in Poland. Source: own study. Districts in Poland—380 (total); terrestrial districts—314; cities poviats—66.

**Figure 2.**Synthetic measure waste management and green economy in districts in Poland (in 2010, 2015, 2019, and 2020). Source: own study.

**Figure 3.**Spatial differentiation, waste management and green economy in districts in Poland (in 2010, 2015, 2019, and 2020). Source: own study based on the BDL CSO data.

**Figure 4.**Distribution diagram of the synthetic measure, waste management and green economy in districts in Poland (in 2010, 2015, 2019, and 2020). Source: Own study.

**Figure 5.**Diversity (spread) of the synthetic measure, waste management and green economy in districts in Poland (in 2010, 2015, 2019, and 2020). Source: Own study.

**Figure 6.**Relation of the synthetic measure, waste management and green economy in districts in Poland (in 2010, 2015, 2019, and 2020). Source: own study based on the BDL CSO data.

**Figure 7.**Relation of the synthetic measure, waste management and green economy and their changes in districts in Poland. Source: own study based on the BDL CSO data.

**Figure 8.**Interdependence of the synthetic measure of waste management and green economy of districts in relation to the years 2020-2019-2015 and 2020-2019-2010. Source: own elaboration based on BDL GUS data.

**Figure 9.**Concentration of the synthetic measure, waste management and green economy of districts (index Gini, for 2010–2020). Source: own study based on the BDL CSO data.

Stage | Description of Stage | |
---|---|---|

stage 1 | A set of tested, multidimensional objects | |

Y = {Y _{1},… Y _{n}} | (1) | |

where n is the number of test objects. A set of diagnostic variables | ||

X = {X _{1},… X _{m}} | (2) | |

where m is the number of studied variables, assuming that m ≥ n. Observation matrix (selected diagnostic variables) X _{ij}: | ||

${\mathrm{X}}_{\mathrm{ij}}=\left[\begin{array}{cccc}{\mathrm{x}}_{11}& {\mathrm{x}}_{12}& \dots & {\mathrm{x}}_{1\mathrm{m}}\\ {\mathrm{x}}_{21}& {\mathrm{x}}_{22}& \dots & {\mathrm{x}}_{2\mathrm{m}}\\ \dots & \dots & \dots & \dots \\ {\mathrm{x}}_{\mathrm{n}1}& {\mathrm{x}}_{\mathrm{n}2}& \dots & {\mathrm{x}}_{\mathrm{nm}}\end{array}\right]$, | (3) | |

where: ${\mathrm{X}}_{\mathrm{ij}}$—denotes the values of the j-th variable for the i-th object, matrix of dnaych objects, i—object number (i = 1, 2,..., n), j—variable number (j = 1, 2,..., m) [47]. | ||

stage 2 | Determination of the coefficient of variation, written by the formula: | |

${\mathrm{V}}_{\mathrm{i}}=\frac{{\mathrm{S}}_{\mathrm{i}}}{\stackrel{-}{\mathrm{x}}},$ | (4) | |

where, V _{i}—coefficient of variation for the i-th variable, S _{i}—standard deviation for the i-th variable, $\stackrel{-}{\mathrm{x}}$ is the arithmetic mean of the i-th variable. From the set of variables, features meeting the inequality $\left|{\mathrm{V}}_{\mathrm{i}}\right|\le {\mathrm{V}}^{*}$ (critical value of the coefficient of variation = 0.10 were eliminated.Inverted matrix and correlation coefficient analysis, threshold value r* = 0.75 [48,49]. The selection of variables was also based on a factor analysis performed in the Statistca program. |

Nr | Diagnostic Variables | Units | S/D |
---|---|---|---|

waste management | |||

X1 | Division 900—Municipal Management and Environmental Protection | pln/pc | S |

X2 | Total waste generated during the year per 1000 inhabitants | thousand t | D |

X3 | recovered per 1000 inhabitants | thousand t | S |

X4 | neutralized together per 1000 inhabitants | thousand t | S |

X5 | Waste previously stored (accumulated) in own facilities in total per 1 km^{2} | thousand t | D |

X6 | share of recovered waste in the amount of waste generated during the year | % | S |

X7 | total per capita/Mixed waste collected during the year in total | kg | D |

X8 | Landfills/active landfills where municipal waste is neutralized—as of 31 December | pcs | D |

X9 | Non-reclaimed waste storage area per 1 km^{2} | ha | D |

X10 | area of active landfills where municipal waste is neutralized—as of 31 December | ha | S |

X11 | wild landfill area per 100 km^{2} in total | pcs | D |

X12 | municipal waste collected during the liquidation of illegal landfills—during the year | vol | D |

Green economy | |||

X13 | Expenses in Division 851—Health care | pln/pc | S |

X14 | Division 900—Municipal Management and Environmental Protection | pln/pc | S |

X15 | electricity consumption per capita/Electricity in households in cities | kWh | D |

X16 | electricity consumption per capita/Electricity in households by location of the recipient in the countryside | kWh | D |

X17 | waterworks Users of installations in% of the total population | % | S |

X18 | sewers | % | S |

X19 | Distribution network per 100 km^{2}… water supply network | km | S |

X20 | sewage network | km | S |

X21 | gas network | km | S |

X22 | Yearly sales of heat energy by location, total residential buildings offices and institutions (per 1 inhabitant) | GJ | S |

X23 | The area of forest land in the total area | % | S |

X24 | water consumption per capita/Water consumption for the needs of the national economy and population during the year in total | m^{3} | D |

X25 | share of industry in total water consumption | % | D |

X26 | total treated to total discharge Waste water treated during the year | % | S |

X27 | discharged per capita/Sewage treated during the year | dam^{3} | D |

X28 | Population using sewage treatment plants in % of the total population | % | S |

X29 | share of recovered waste in the amount of waste generated during the year | % | S |

X30 | total per capita/Total mixed waste collected during the year | kg | D |

X31 | Municipal sewage treated per 100 km^{2} | dam^{3} | D |

X32 | Share of legally protected areas in the total area | % | S |

Stage | Description of Stage | |
---|---|---|

stage 3 | The normalization of diagnostic variables was performed depending on their types of variables, X j ∈ S according to the formula: | |

${\mathrm{Z}}_{\mathrm{ij}}=\frac{{\mathrm{x}}_{\mathrm{ij}}-{\mathrm{min}}_{\mathrm{i}}{\mathrm{x}}_{\mathrm{ij}}}{{\mathrm{max}}_{\mathrm{i}}{\mathrm{x}}_{\mathrm{ij}}-{\mathrm{min}}_{\mathrm{i}}{\mathrm{x}}_{\mathrm{ij}}}$, Z _{ij} = 0 ⇔ x _{ij} = min _{i} x _{ij}; Z _{ij} = 1 ⇔ x _{ij} = max _{i} x _{ij}.
| (5) | |

for the variable X j ∈ D, | ||

${\mathrm{Z}}_{\mathrm{ij}}=\frac{{\mathrm{max}}_{\mathrm{i}}{\mathrm{x}}_{\mathrm{ij}}-{\mathrm{x}}_{\mathrm{ij}}}{{\mathrm{max}}_{\mathrm{i}}{\mathrm{x}}_{\mathrm{ij}}-{\mathrm{min}}_{\mathrm{i}}{\mathrm{x}}_{\mathrm{ij}}}$, Z _{ij} =0 ⇔ x _{ij} = max _{i} x _{ij}; Z _{ij} =1 ⇔ x _{ij} = min _{i} x _{ij},
| (6) | |

where: Z _{ij} ∈ [0; 1], max _{i} x _{ij} ≠ min _{i} x _{ij}, max _{i} x _{ij} > min _{i} x _{ij}, S-stimulant, D-destimulant, i = 1, 2… n (number of selected variables for analysis); j = 1, 2… m (number of random values of the variable), max_{xij}—the maximum value of the j-th variable, min_{xij}—the minimum value of the j-th variable, x _{ij}—means the value of the j-th variable for the th object [48,50].Value matrix of unitary features ${\mathrm{Z}}_{\mathrm{ij}}$: | ||

${\mathrm{Z}}_{\mathrm{ij}}=\left[\begin{array}{cccc}{\mathrm{z}}_{11}& {\mathrm{z}}_{12}& \dots & {\mathrm{z}}_{1\mathrm{m}}\\ {\mathrm{z}}_{21}& {\mathrm{z}}_{22}& \dots & {\mathrm{z}}_{2\mathrm{m}}\\ \dots & \dots & \dots & \dots \\ {\mathrm{z}}_{\mathrm{n}1}& {\mathrm{z}}_{\mathrm{n}2}& \dots & {\mathrm{z}}_{\mathrm{nm}}\end{array}\right]$, | (7) | |

where Z_{ij} ∈ { S} ∪ {D}—unitized value of j-th variables for i-th object; i = 1,..., m, j = 1,..., k, are the normalized values of the jth diagnostic variable for this object. |

**Table 5.**Distance between the best and the weakest unit (according to the similarity matrix) for the synthetic measure waste management and green economy of districts.

q Green Economy | q Waste Management | ||||||
---|---|---|---|---|---|---|---|

2010–2015 | |||||||

Bielsko district | Kozienice district | Wolow district | Nowy Sącz district | Bydgoszcz district | Polkowice district | ||

Bielsko district | 0 | 0.16 | 0.13 | Nowy Sącz district | 0 | 0.08 | 0.04 |

Kozienice district | 0.16 | 0 | 0.06 | Bydgoszcz district | 0.08 | 0 | 0.06 |

Wolow district | 0.13 | 0.06 | 0 | Polkowice district | 0.04 | 0.06 | 0 |

2015–2019 | |||||||

Bielsko district | 0 | 0.17 | 0.18 | Nowosądecki district | 0 | 0.11 | 0.17 |

Kozienice district | 0.17 | 0 | 0.01 | Bydgoszcz district | 0.11 | 0 | 0.09 |

Wołowski district | 0.18 | 0.01 | 0 | Polkowice district | 0.17 | 0.09 | 0 |

2019–2020 | |||||||

Bielsko district | 0 | 0.18 | 0.18 | Nowosądecki district | 0 | 0.18 | 0.23 |

Kozienice district | 0.18 | 0 | 0.01 | Bydgoszcz district | 0.18 | 0 | 0.08 |

Wołowski district | 0.18 | 0.01 | 0 | Polkowice district | 0.23 | 0.08 | 0 |

**Table 6.**Statistical characteristics of the synthetic measure waste management and green economy in districts in Poland (in 2010, 2015, 2019, and 2020).

q Green Economy | q Waste Management | |||||||
---|---|---|---|---|---|---|---|---|

2010 | 2015 | 2019 | 2020 | 2010 | 2015 | 2019 | 2020 | |

Mean | 0.52 | 0.48 | 0.48 | 0.48 | 0.49 | 0.48 | 0.48 | 0.48 |

Median | 0.53 | 0.48 | 0.48 | 0.48 | 0.49 | 0.48 | 0.48 | 0.48 |

Minimum | 0.43 | 0.44 | 0.38 | 0.39 | 0.42 | 0.42 | 0.42 | 0.43 |

Maximum | 0.61 | 0.56 | 0.55 | 0.55 | 0.55 | 0.55 | 0.55 | 0.56 |

Lower (Quartile) | 0.51 | 0.47 | 0.46 | 0.47 | 0.48 | 0.47 | 0.47 | 0.47 |

Upper (Quart.) | 0.54 | 0.49 | 0.49 | 0.49 | 0.5 | 0.5 | 0.5 | 0.5 |

Gap | 0.18 | 0.12 | 0.17 | 0.16 | 0.13 | 0.13 | 0.13 | 0.13 |

Quartile. (Gap) | 0.03 | 0.02 | 0.03 | 0.02 | 0.02 | 0.03 | 0.03 | 0.03 |

SD | 0.03 | 0.02 | 0.02 | 0.03 | 0.02 | 0.02 | 0.02 | 0.02 |

Coefficient of change | 5.18 | 4.91 | 4.64 | 5.21 | 3.76 | 4.19 | 4.18 | 4.36 |

Skewness | −0.87 | 0.81 | 0.28 | 0.32 | -0.32 | 0.37 | 0.31 | 0.41 |

Kurtosis | 0.85 | 0.33 | 2.33 | 1.86 | 1.04 | 0.39 | 0.26 | 0.26 |

**Table 7.**Coefficients of correlation between the value of the synthetic measure, waste management, green economy and diagnostic variables of their structure for districts in 2020 and 2020.

Diagnostic Variable/Specification | q Green Economy | q Waste Management |
---|---|---|

q waste management | 0.474 | 1.000 |

recovered per 1 km^{2} | 0.188 | 0.230 |

share of recovered waste in the amount of waste generated during the year | 0.496 | 0.757 |

total per capita/Total mixed waste collected during the year | −0.087 | −0.425 |

area of illegal dumps per 100 km^{2} of total area | −0.230 | −0.287 |

q green economy | 1.000 | 0.474 |

expenditure in chapter 90003—Clearing towns and villages | 0.081 | −0.243 |

expenses in chapter 90004—Maintenance of green areas in cities and communes | 0.029 | −0.170 |

expenses in chapter 90015—Lighting of streets, squares and roads | −0.112 | −0.120 |

electricity consumption per capita/Electricity in households by location of the recipient in the countryside | −0.196 | −0.203 |

waterworks Users of installations in% of the total population | −0.039 | −0.162 |

sewers | 0.396 | −0.146 |

gas | 0.381 | −0.094 |

Distribution network per 100 km^{2}… water supply network | 0.254 | −0.005 |

sewage network | 0.543 | 0.012 |

gas network | 0.470 | 0.018 |

The area of forest land in the total area | 0.104 | 0.198 |

water consumption per capita/Water consumption for the needs of the national economy and population during the year in total | −0.208 | −0.024 |

industry share in total water consumption | −0.269 | −0.089 |

total discharged sewage treated during the year/per 1 km^{2} | 0.330 | −0.133 |

Population using sewage treatment plants as a percentage of the total population | 0.413 | −0.133 |

share of recovered waste in the amount of waste generated during the year | 0.496 | 0.757 |

total per capita/Total mixed waste collected during the year | −0.087 | −0.425 |

Municipal sewage treated per 100 km^{2} | 0.330 | −0.133 |

existing area—as of 31 December | −0.248 | −0.249 |

Arithmetic mean of the dependent variable | 0.484904 | Standard deviation of dependent variable | 0.021153 |

Sum of squares residuals | 0.026585 | Residual standard error | 0.009367 |

Coefficient of determination R-square | 0.810173 | Adjusted R-square | 0.803908 |

F(10, 303) | 129.3191 | p-values for F-test | 4.88 × 10³ |

Logarithm of credibility | 1026.613 | Inrom. Crit. Akaike’a | −2031.226 |

Crit. Bayes. Schwarza | −1989.982 | Crit. Hannana-Quinna | −2014.746 |

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## Share and Cite

**MDPI and ACS Style**

Misztal, P.; Dziekański, P. Green Economy and Waste Management as Determinants of Modeling Green Capital of Districts in Poland in 2010–2020. *Int. J. Environ. Res. Public Health* **2023**, *20*, 2112.
https://doi.org/10.3390/ijerph20032112

**AMA Style**

Misztal P, Dziekański P. Green Economy and Waste Management as Determinants of Modeling Green Capital of Districts in Poland in 2010–2020. *International Journal of Environmental Research and Public Health*. 2023; 20(3):2112.
https://doi.org/10.3390/ijerph20032112

**Chicago/Turabian Style**

Misztal, Piotr, and Paweł Dziekański. 2023. "Green Economy and Waste Management as Determinants of Modeling Green Capital of Districts in Poland in 2010–2020" *International Journal of Environmental Research and Public Health* 20, no. 3: 2112.
https://doi.org/10.3390/ijerph20032112