Resilience and vulnerability of regional labour markets: principal component analysis of labour market efficiency in the EU

Figures & data

Table 1. Basic statistical parameters of nine labour market efficiency (LME) indicators.

Indicator/parameter	N	Mean	Median	SD	Minimum	Maximum
Employment rate	268	63.7	65.6	10.46	35.3	82.1
Labour productivity	268	94.8	95.8	29.76	30.4	203.8
Long-term unemployment	259	4.4	2.8	4.41	0.6	21.3
Unemployment	267	9.1	7.0	6.20	2.4	31.6
Gender balance unemployment	265	1.9	1.1	2.48	0.1	15.2
Gender balance employment	268	10.2	8.9	5.13	0.9	25.9
Female unemployment	265	9.6	7.0	7.50	2.3	39.3
NEET	263	11.5	10.6	5.61	3.6	33.7
Involuntary part-time/temporary employment	262	12.1	10.7	7.92	0.5	39.6

Note: Mean = arithmetic mean; SD, standard deviation; NEET, not in education, employment or training.

Table 2. Principal component analysis (PCA) of nine labour market efficiency (LME) indicators.

Component	Initial eigenvalues			Extraction sums of squared loadings
	Total	% of Variance	Cumulative %	Total	% of Variance	Cumulative %
1	5.837	64.851	64.851	5.837	64.851	64.851
2	1.168	12.983	77.834	1.168	12.983	77.834
3	0.775	8.610	86.444
4	0.531	5.902	92.346
5	0.375	4.164	96.509
6	0.158	1.755	98.265
7	0.126	1.400	99.665
8	0.027	0.299	99.964
9	0.003	0.036	100.000

Figure 1. Principal components plot of nine labour market efficiency (LME) indicators.

Figure 2. Dependence of the regional competitiveness index (RCI) 2019 on the resilience principal component (RPC), including the linear regression line and prediction intervals.

Figure 3. Dependence of the regional competitiveness index (RCI) 2019 on the vulnerability principal component (VPC), including the linear regression line and prediction intervals.

Table 3. Equality of slopes test in the linear regression model between the regional competitiveness index (RCI) 2019 and resilience principal component (RPC) for the first fixed categorical factor – development phase of regions.

Source	Type III sum of squares	d.f.	Mean square	F	p
Corrected model	97.628	3	32.543	517.228	0.000
Intercept	0.544	1	0.544	8.640	0.004
Development phase	0.117	1	0.117	1.863	0.173
RPC	35.531	1	35.531	564.729	0.000
Phase*RPC	0.105	1	0.105	1.666	0.198
Error	16.610	264	0.063
Total	116.648	268

Table 4. Equality of slopes test in the linear regression model between the regional competitiveness index (RCI) 2019 and vulnerability principal component (VPC) by development phase of regions.

Source	Type III sum of squares	d.f.	Mean square	F	p
Corrected model	89.791	3	29.930	323.205	0.000
Intercept	16.154	1	16.154	174.440	0.000
Phase	22.873	1	22.873	246.997	0.000
VPC	13.171	1	13.171	142.224	0.000
Phase*VPC	0.367	1	0.367	3.964	0.048
Error	24.448	264	0.093
Total	116.648	268

Table 5. Parameters of linear regression model between the regional competitiveness index (RCI) 2019 and the vulnerability principal component (VPC) by development phase of regions.

Development phase fixed categorical factor		Unstandardized coefficients		Standardized coefficients	t	p
		B	SE	Beta
Post-socialist	(Constant)	−0.715	0.052		−13.620	0.000
	VPC	−0.724	0.120	−0.631	−6.036	0.000
Capitalist	(Constant)	0.062	0.020		3.113	0.002
	VPC	−0.517	0.018	−0.893	−28.608	0.000

Figure 4. Dependence of the regional competitiveness index (RCI) 2019 versus the vulnerability principal component (VPC) with the linear regression line in both development phase groups of regions.

Figure 5. Classification and regression tree (CART) decision tree of regions with positive (black) versus negative (grey) values of the regional competitiveness index (RCI) 2019, using the resilience principal component (RPC), vulnerability principal component (VPC) and both fixed categorical factors.

Table 6. Relative importance of variables in the classification and regression tree (CART) decision tree of the regional competitiveness index (RCI) 2019 value.

Independent variable	Importance	Normalized importance
RPC	0.394	100.0
VPC	0.282	71.7
Development phase factor	0.095	24.2
Capital region factor	0.009	2.2

Note: RPC, resilience principal component; and VPC, vulnerability principal component.

Table 7. Classification matrix of the classification and regression tree (CART) decision tree of the regional competitiveness index (RCI) 2019 sign by the resilience principal component (RPC) and vulnerability principal component (VPC).

Observed	Predicted
	Negative	Positive	% Correct
Negative	127	5	96.2%
Positive	7	129	94.9%
Overall %	50.0%	50.0%	95.5%

Figure 6. Scatterplot of the vulnerability principal component (VPC) against the resilience principal component (RPC) with some partition values of the classification and regression tree (CART) decision tree.

Figure 7. Classification and regression tree (CART) decision tree of regions with positive (black) values of the regional competitiveness index (RCI) 2019 versus negative (grey) values of the RCI 2019, using labour market efficiency (LME) indicators and two fixed categorical factors.

Table 8. Classification matrix of the classification and regression tree (CART) decision tree of the regional competitiveness index (RCI) 2019 performance by labour market efficiency (LME) indicators.

Observed	Predicted
	Negative	Positive	% Correct
Negative	126	6	95.5%
Positive	4	132	97.1%
Overall %	48.5%	51.5%	96.3%

Figure 8. Scatterplot of labour productivity versus employment rate with partition values of the classification and regression tree (CART) decision tree.

Table 9. Importance of variables in the classification and regression tree (CART) decision tree of regional competitiveness index (RCI) sign by labour market efficiency (LME) indictors.

Independent variable	Importance	Normalized importance
Labour productivity	0.288	100.0
Employment rate	0.270	93.6
Gender balance employment	0.249	86.4
NEET	0.199	69.0
Female unemployment	0.171	59.3
Long-term unemployment	0.168	58.3
Involuntary part-time/temporary employment	0.159	55.2
Unemployment	0.145	50.1
Development phase factor (one FCF)	0.140	48.5
Gender balance unemployment	0.135	46.8
Capital region factor (two FCF)	0.002	0.8

Note: FCF, fixed categorical factor; NEET, not in education, employment or training.

Figure 9. Scatterplot of the resilience principal component (RPC) and vulnerability principal component (VPC).

Figure 10. Spatial distribution of the proposed operational framework for resilience and vulnerability of regional labour markets in the EU.

Notes: RPC, resilience principal component; and VPC, vulnerability principal component. Quadrant 1: RPC+, VPC+; quadrant 2: VPC+, RPC–; quadrant 3: VPC–, RPC–; and quadrant 4: VPC–, RPC+. Readers of the print article can view the figures in colour online at https://doi.org/10.1080/00343404.2022.2042507

Figure 11. Operational framework for improving the resilience and reducing the vulnerability of regional labour markets.