A Fuzzy Approach to the Measurement of Employment and Unemployment

Bruno Cheli, Alessandra Coli and Andrea Regoli

Introduction

Analyses of the labour force are traditionally based on a clear-cut distinction between those who are employed and those who are unemployed, which form complementary sets. However, this distinction appears too rigid because it obscures all the nuances between people who are fully employed and those who work only occasionally but need to, or wish to, work more. Furthermore, this way of proceeding involves a significant loss of statistical information which could be used for portraying and measuring the phenomenon more accurately.

In our view, employment should be considered not as a simple condition that is either present or absent but, rather, as a matter of degree. In logical terms, this implies moving from a Boolean conception to a ‘fuzzy’ one.

Fuzzy-set theory (Zadeh, 1965) has been applied in a wide variety of research fields. For what concerns socio-economic studies, it has been successfully used in the measurement and analysis of poverty (Cerioli and Zani, 1990; Cheli and Lemmi, 1995; Betti et ah, 2008; Betti and Lemmi, 2013). To date, however, it has not been applied to analyses of the labour force.

The goal of this chapter is to define fuzzy measures of employment and unemployment using available information on the weekly number of hours worked and on the desire or need of workers to work more hours.

Employment and Unemployment in Official Statistics

According to the International Labour Organisation directives (ILO, 1982), the population of working age (people aged 15 and older) can be divided into three mutually exclusive groups: those who are employed, those who are unemployed and those who are inactive (those who are retired, unable to work and for whatever reason are not seeking work). The first two groups constitute the labour force.

These three groups are identified on the basis of information collected in surveys of the labour force in a hierarchical process, which first identifies the employed, then the unemployed and then those considered inactive.

According to the European Union Labour Force Survey (EU-LFS), those who are employed are at least 15 years old and meet one of the following conditions: (1) over the course of a week, they perform some work - even if for just one hour - for pay, profit or family gain; or (2) if they were not at work during that week, they had a job or business from which they were temporarily absent.

Those who are unemployed are of working age and: (1) did not work during the survey period; (2) are currently available for work and have taken concrete actions over that period to seek paid employment or self- employment. Finally, those who are considered inactive are of working age and have not been classified as either employed or unemployed.

The way in which the employed, unemployed and inactive population groups are identified affects the value of employment and unemployment rates. The unemployment rate is defined as the share of the total labour force that is unemployed, whereas the employment rate is the share of the working age population that is employed.

Fuzzy Measures of Employment and Unemployment:

A Methodological Proposal

The fuzzy measure of employment is intended to avoid the sharp distinction between the employed and the unemployed. The application of fuzzy-set theory (Zadeh, 1965) to employment rejects the binary division between these two labels, which considers the employed to designate every individual who performed some work during a particular week, regardless of the number of hours worked. Instead, we define a membership function (MF) pt in the fuzzy subset E of the employed, which is measured on a scale from 0 to 1, in which 1 means full membership in the set of the employed and 0 means full non-membership.

A fuzzy measure of employment reflects the unmet need among the employed for working additional hours, thus accounting for labour underutilisation. The concept of labour under-utilisation encompasses both time- related underemployment and involuntary part-time employment. These categories refer to people who share some characteristics with the unemployed even though they are officially considered to be employed. In the fuzzy approach that we propose, we treat them as employed to a certain degree: the less the time they work, the lower their degree of employment.

Contextually, we define MF in the fuzzy subset U of the unemployed. Among those in the labour force, we assume that the fuzzy set U of the unemployed is complementary to the fuzzy set £ of the employed: therefore, the MF in the fuzzy set U is given by pv = 1 - pE. According to the ILO/EU employment categories, those who are inactive are not considered to be in the labour force; therefore, they are assigned a value of MF pE and pv that equals 0. For those who are employed (according to ILO/EU employment categories), we calculate the value of the MF pE following the assumptions illustrated in Figure 16.1.

The value of цЕ depends on the number of hours worked by a person and on whether that person is satisfied with it. We define an upper bound (threshold) for the number of hours worked weekly. This threshold acts as a limit set by statutory or collectively agreed standards and approximately corresponds to the number of hours worked on average by full-time workers. Obviously, the threshold takes different values in different countries.

MF ftE = 1 (and therefore jtu = 0) for: (1) full-time workers with a number of hours worked that is not lower than the threshold; (2) full-time workers who do not wish to work more, even if they are employed for less than the specified threshold; and (3) people working part-time voluntarily.

The value of iv is greater than 0 and less than 1 for underemployed workers, which are made up of: (1) involuntary part-time workers, i.e. people who could not find a full-time job; (2) full-time workers who work less than the threshold number of hours and are willing to work additional hours. For both categories of underemployed workers, the MF is defined as the ratio of the hours actually worked to the threshold value. Finally, individuals classified as unemployed based on ILO/EU criteria are assigned the values цЕ = 0 and J4U = .

Empirical Application Based on Italian Labour Force Data

We used the fuzzy approach to measure employment and unemployment using 2018 annual Italian data from the EU-LFS (Eurostat, 2019),1 focusing

Specification of the membership function /< for individuals who are employed according to ILO/EU criteria

Figure 16.1 Specification of the membership function /<y for individuals who are employed according to ILO/EU criteria.

on people between 15 and 64 years old. The upper bound of hours worked is set at 40 weekly hours for full-time workers in the private sector (employees, self-employed and family workers) and at 36 weekly hours for full-time public sector employees. These values coincide with the modes of the corresponding distributions in the Italian LFS data. Because the modes and medians are about equal in the two groups, we consider the mode a suitable measure of the central tendency.

Table 16.1 shows the composition of people who are employed according to the five categories described above and referred to in Figure 16.1. More than two-thirds (67.88%) are employed full-time, with the number of hours worked not less than the fixed upper bound. By contrast, about 13.38% are employed full-time, work less than the fixed threshold and declare themselves satisfied with this situation. The percentage of those who work less than the threshold and wish to work more is negligible (0.42%). Finally, voluntarily part-time workers account for 6.29%, which is approximately half the share of involuntary part-time workers (12.02%).

In summary, people who have full membership in the employed fuzzy set are about 88% of the employed.

Analysing the differences in the values of the MF pE by occupational criteria (Table 16.2a), we find that the share of people who have full membership in the employed fuzzy set is close to 90% for self-employed, family workers and employees with a permanent job. On the other hand, it shrinks to about 75% for employees with a temporary job. The share of the employed with pE values of less than 2/3 ranges from 6.34% for the self- employed to 19.29% for temporary employees.

Our analysis by the type of occupation (ISCO code, see Table 16.2b) shows that the share of people who partially belong to the fuzzy set of the employed (0 < pt < 1) ranges from about 6% for high-skilled non-manual occupations to approximately 30% for basic occupations.

The fuzzy rate of employment is calculated as the arithmetic mean of the individual MF pE using survey sample weights across all the individuals of working age (between 15 and 64 years old).2 As such, it can be compared

Table 16.1 Composition of employed based on the criteria in Figure 16.1

Employment Category

Composition (%)

Full-time workers whose hours worked are not lower than the threshold

67.88

Full-time workers whose hours worked are lower than the threshold, but do not want to work more hours

13.38

People working part-time voluntarily

6.29

People working part-time involuntarily

12.02

Full-time workers whose hours worked are lower than the threshold and are willing to work more hours

0.42

Total

100.00

Table 16.2a Distribution of ILO/EU employed by membership values and professional status (15-64 years) (in %)

Membership function //,

Self-employed

Employees with a permanent job

Employees with a temporary’ job

Working for a Family business

Total

employment

0 < pf

2.25

1.13

3.98

1.34

1.74

1/3 E<213

4.09

6.47

15.31

5.94

7.16

2/3 F

2.05

3.16

7.09

1.98

3.45

М.= 1

91.62

89.24

73.62

90.74

87.65

Yotal

100.00

100.00

100.00

100.00

100.00

Table 16.2b Distribution of ILO/EU employed by membership values and ISCO code (15-64 years) (in %)

Membership function //,

High-skill non-manual occupations (ISCO codes 1 to 3)

Low-skill non-manual occupations (ISCO codes 4 to 8)

Basic

occupations (ISCO code 9)

Total

employment

0 < //F

1.09

1.26

6.24

1.74

1/3

3.20

7.94

17.03

7.16

2/3 F

2.09

3.93

5.93

3.45

1

93.62

86.87

70.80

87.65

Total

100.00

100.00

100.00

100.00

with the traditional employment rate (Table 16.3). The results show that, among the total population between 15 and 64 years old, the fuzzy employment rate is 55.2%, which is 5.6% less than the official rate (T = 58.5%). The downward correction (calculated as (F/T^lOO - 100) is more marked among females (9.3%) than males (2.8%), meaning that the unmet need for working more hours is greater by far among female workers than male workers. Young adults (less than 35 years old), foreign-born individuals and workers with a low education level are the groups of workers who are the most severely affected by labour under-utilisation. In terms of the geographic area of residence, the downward correction of the fuzzy measure is slightly above average in southern Italy and the Islands and slightly below average in northern Italy. In contrast, no substantial difference emerges in terms of the degree of urbanisation.

Now let us shift our attention to unemployment. The weighted mean of the MF nv across individuals in the labour force provides the fuzzy rate of unemployment, which is compared with the conventional measure in Table 16.4. For all the people in the labour force aged 15 to 64, the fuzzy

Table 16.3 Comparison of traditional and fuzzy employment rates (workers 15-64 years old) (%)

Traditional measure (T)

Fuzzy

measure (F)

(F/T)*100

Total

58.5

55.2

94.4

By gender

Male

67.6

65.7

97.2

Female

49.5

44.9

90.7

By age group

15-24 years

17.7

15.8

89.3

25-34 years

61.7

57.3

92.9

35-44 years

73.4

69.4

94.6

45-54 years

72.3

68.6

94.9

55-64 years

53.7

51.4

95.7

By country of birth

Native born

58.1

55.2

95.0

Foreign born

60.9

55.5

91.1

By education level

Lower secondary

43.8

40.7

89.3

Upper secondary

64.3

60.9

92.9

Third secondary

78.7

75.4

95.8

Bv regional group ' (NUTS 1 code)

North-West

66.8

63.5

95.1

North-East

68.1

65.0

95.4

Central

63.2

59.0

87.0

South

44.9

41.9

93.3

Islands

43.7

40.3

92.2

By degree of urbanisation

Cities

58.9

55.3

93.9

Towns and suburbs

58.2

55.2

94.8

Rural areas

58.5

55.3

94.5

measure is 15.8%, 46.3% higher than the traditional rate (T = 10.8%). The fuzzy approach reveals that the gender gap in the unemployment rate is wider than is shown by the traditional approach. The gap between those born in Italy and foreign-born migrants also increases when the unemployment rate is derived through the fuzzy method. As for other classifications, we find that the largest upward corrections are in the categories that are less affected by unemployment, namely, the highest age groups, highly educated individuals and those who live in the Northeast or in rural areas. Moreover, we can observe that the gap in the unemployment rate shrinks slightly when we use a fuzzy measurement rather than the traditional one. For example, the unemployment rate for the age group 15-24 is 5.6 times higher than that of the age group 55-64 using the traditional approach and four times higher using the fuzzy approach.

Conclusions

The division of the working-age population into three mutually exclusive and exhaustive groups of those who are employed, unemployed and

Table 16.4 Unemployment rates (15-64 years) (%)

Traditional measure (T)

Fuzzy

measure (F)

(F/T)*100

Total

Total

10.8

15.8

146.3

By gender

Male

10.0

12.6

126.0

Female

11.9

20.1

168.9

By age group

15-24 years

32.2

39.2

121.7

25-34 years

15.9

21.9

137.7

35-44 years

9.3

14.2

152.7

45-54 years

7.7

12.4

161.0

55-64 years

5.7

9.7

170.2

By country of birth

Italian born

10.3

14.8

143.7

Foreign born

13.7

21.4

156.2

By education level

Lower secondary

14.9

21.0

140.9

Upper secondary

10.2

15.0

147.1

Third secondary

6.1

10.1

165.6

Bv regional 'group (NUTS 1 code)

North-West

7.1

11.7

164.8

North-East

6.1

10.3

168.9

Centre

9.6

15.1

157.3

South

18.1

23.4

129.3

Islands

20.1

26.3

130.8

By degree of urbanisation

Cities

11.6

17.0

146.6

Towns and suburbs

10.5

15.2

144.8

Rural area

10.1

15.0

148.5

Note: For definitions, see Table 16.3.

economically inactive conceals relevant grey areas among them, such as underemployment and marginal labour force attachment, which deserve special attention.

In this chapter, we focused on people in between employment and unemployment. Using a fuzzy approach, we introduced the concept of being ‘employed to a certain degree’. Our methodological proposal considers both the number of hours actually worked and the fact that a person might wish/ need to work more.

The results of our empirical application to 2018 data on the Italian labour force reveal to what extent our fuzzy measures of employment and unemployment differ from the traditional ones. The fuzzy employment rate of the total population is 55.2%, which is 5.6% lower than the official rate. We observe the largest downward correction for female workers, young workers, foreign-born workers and workers living in central Italy.

The fuzzy measurement of unemployment is 15.8%, which is 46.3% higher than the traditional rate. The largest upward correction is seen among female workers, workers between 55 and 64 years old, foreign-born workers, third-secondary educated and those living in the North.

Moreover, the fuzzy approach amplifies the disadvantages of female and

foreign-born workers with respect to both employment and unemployment.

Notes

  • 1 All conclusions drawn from the data are entirely those of the authors.
  • 2 As specified, inactive people are assigned a pt value of 0.

References

Betti G., Cheli B., Lemmi A., Verma V. (2008) The fuzzy set approach to multidimensional poverty: the case of Italy in the 1990s, in N. Kakwani, J. Silber (eds.), Quantitative Approaches to Multidimensional Poverty Measurement, Palgrave MacMillan, London, pp. 30-48.

Betti G., Lemmi A. eds. (2013) Poverty and Social Exclusion: New Methods of Analysis, Routledge, London.

Cerioli A., Zani S. (1990) A fuzzy approach to the measurement of poverty, in C. Dagum, M. Zenga (eds.), Income and Wealth Distribution, Inequality and Poverty, Springer, Berlin, pp. 272-284.

Cheli B., Lemmi A. (1995) A ‘totally’ fuzzy and relative approach to the multidimensional analysis of poverty. Economic Notes 24, 115-134.

Eurostat (2019) EU Labour Force Survey Database UserGuide, November, Publications Office of the European Union, Luxembourg.

ILO (1982) Statistics of Labour Force, Employment, Unemployment and Underemployment, Report II of the 13th International Conference of Labour Statisticians, Geneva.

Zadeh L.A. (1965) Fuzzy sets. Information and Control 8, 338-353.

17 The Relationship Between

 
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