Can a Neighbouring Region Influence Poverty? A Fuzzy and Longitudinal Approach

Gianni Betti, Federico Crescenzi and Francesca Gagliardi

Introduction

One of the most important goals in the 2030 UN Agenda for Sustainable Development is to ‘eradicate poverty, in all its forms and dimensions' (UN, 2015). This has been particularly necessary since 2008, when the global financial crisis started, and 2015, with the failure to meet the Millennium Development Goal of halving extreme poverty in the world.

The European Union (EU) has also expressed the need to reduce poverty and launch anti-poverty programmes and policies in its Europe 2020 Strategy (European Commission, 2010), which consists of a series of policy objectives called ‘headline targets’ meant to be achieved by 2020. These targets include the reduction of the at-risk-of-poverty rate (ARPR, known in the literature as the headcount ratio, or FGT(0), following Foster et al., 1984) and of the at-persistent-risk-of-poverty rate in a longitudinal context to monitor poverty over time. Moreover, poverty measures are most useful to policymakers and researchers when they are finely disaggregated so that they can represent geographic units smaller than entire countries. This is the purpose of the DG Regional Policy of the European Commission, which employs sub-national/regional-level data (NUTS 2)1 for the social indicators used for monitoring the ‘headline targets’ at the regional level.

To provide a comprehensive response to the needs mentioned above, in this chapter we adopt a longitudinal measure proposed by Verma et al. (2017), which is based on the fuzzy-set approach to multi-dimensional poverty: the ‘fuzzy at-persistent-risk-of-poverty rate’. Then we estimate this measure at the regional level with small area estimation (SAE) techniques by introducing a spatial correlation model. In this way, we take into account whether a neighbouring region can influence poverty in all its forms and dimensions: the multi-dimensional dimension, the regional dimension and the longitudinal dimension.

The chapter is organised into six sections. Following this introduction, the second section models fuzzy measures of poverty and deprivation, covering both monetary and non-monetary aspects from cross-sectional and longitudinal perspectives. The third section presents the most important characteristics of the spatial empirical best linear unbiased predictor (SEBLUP), which is the small area technique that we believe is the most appropriate for estimating poverty at the regional level in the EU, because it includes correlations of poverty among neighbouring regions. The forth section describes the micro-dataset used and the construction of computational units for variance estimation. We briefly describe the EU survey on the statistics on income and living conditions (EU-SILC), a large-scale microdatabase, from which we use a subset in our analysis. Empirical results are reported in the fifth section: fuzzy monetary and non-monetary longitudinal estimates are compared and discussed. Finally, the last section offers our concluding remarks, indicating fruitful directions for further research.

Cross-Sectional and Longitudinal Measures of Fuzzy Poverty

This section gives a mathematical description of cross-sectional and longitudinal measures of fuzzy and multi-dimensional poverty'.

The fuzzy-set approach treats poverty' as a matter of degree, replacing a simple dichotomy in the traditional approach in which the observations of individuals or households are divided into {0,1}. However, in principle, all individuals are liable to poverty but at varying degrees; so, each individual has a certain propensity towards poverty across the range [0,1].

Treating poverty' as a matter of degree, applicable to all members of the population, has several advantages over using a simple ‘yes-no’ state. They are summarised by Verma et al. (2017) as follows:

  • 1. Non-monetary poverty depends on barriers to access to various services or things that determine basic living conditions. An individual might have access to some of them but not others. Hence non-monetary poverty is inherently a matter of degree; therefore, a quantitative approach is essential.
  • 2. The fuzzy approach provides more robust indicators of poverty in the longitudinal context. The conventional approach measures mobility simply in terms of movement across some designated poverty line and does not reflect the actual magnitude of the changes affecting individuals at all points in the distribution. Consequently, the degree of mobility of persons near this line tends to be over-emphasised, while that of people far from that line is largely ignored.

Apart from the various methodological choices involved in the construction of conventional poverty measures, the introduction of fuzzy measures includes additional factors on which choices have to be made. The fundamental factor concerns the choice of membership functions, meaning a quantitative specification of the propensity towards poverty of each person given the level and distribution of income of the population.

Cross-Sectional Fuzzy Membership Function

Betti and Verma (2008)2 have proposed two fuzzy membership functions, based on the seminal contributions of Cerioli and Zani (1990) and Cheli and Lemmi (1995).

These are elaborated in Betti et al. (2015); in the generalised form, these membership functions are defined for any individual i as follows:

where X is the equivalised income in monetary poverty or the overall score s in non-monetary poverty, w„ is the sample weight of an individual with rank у (у = l,...,w) in the ascending distribution, and aK (K = 1,2) are two parameters that correspond, respectively, to the monetary and non-monetary dimensions of poverty.

The aK parameters are estimated such that the mean of the corresponding membership function equals the ARPR, which is calculated based on the official poverty line. Betti and Verma (2008) call the monetary-based indicator fuzzy monetary (FM) and the non-monetary indicator fuzzy supplementary (FS).

Construction of the FS Measure

Betti et al. (2015) proposed a step-by-step procedure for measuring the FS measures, as follows.

First, we identify the items to be included in the index or indices, which should be the most meaningful and useful (see Eurostat 2000,2002). In fact, it is desirable to avoid items for which issues of choice, in terms of possession versus non-possession, cannot be satisfactorily resolved, for which possession is relatively rare (i.e. possession of a boat), or for which the degree of comparability among regions or countries is not sufficient.

Then, for each item, we determine a quantitative deprivation indicator in the range [0,1]: these indicators are used in a first exploratory factor analysis to identify the ‘dimensions’, which are distinct groups of items of non-monetary poverty, ideally independent of other dimensions and which describe a particular facet of living conditions. After this first exploratory factor analysis, we rearrange some items in the dimensions to create more meaningful groups: to test the goodness of fit of this final grouping, we conduct a confirmatory factor analysis, as proposed by Betti et al. (2015).

The weights to be assigned to each item are determined within each dimension; they are based on two elements: the dispersion of the item (prevalence weights) and the correlation with other items in the same dimension (correlation weights). For a detailed description of the weight construction, see Betti and Verma (2008).

Although the score sjh within each dimension b is calculated as a weighted mean of items in that dimension, the overall score st is defined as the simple average of the dimension scores sjh, thus giving the same importance to all the dimensions, i.e. the several faces of non-monetary (supplementary) poverty. Finally, as explained above, the membership function FS is defined in Equation (4.1).

The positive results achieved while applying this methodology to fields other than poverty (see e.g. Aassve et al., 2007; Betti et ah, 2011, 2016; Belhadj, 2015; Betti, 2017) demonstrate its applicability and robustness.

Longitudinal Measures of Fuzzy and Multi-Dimensional Poverty

In this section, we describe the construction of the fuzzy longitudinal poverty measures, which aim to estimate occasional, persistent, or chronic concepts of poverty. In the fuzzy literature, these measures are defined as: (1) anytime, for individuals who are members of fuzzy-set poverty for at least one in four years; (2) continuous, for those who have membership in all four years; and, we add a definition proposed by Verma et al. (2017), (3) the ‘fuzzy at-persistent-risk-of-poverty’, which refers to people who are members of the fuzzy set in the most recent year and in two or three years in the last three years. This third measure is the fuzzy counterpart of the Eurostat ‘at- persistent-risk-of-poverty rate’, one of the most important Laeken indicators.

From a mathematical point of view, we let be the series of T = 4 membership functions over the four periods, and then we define fuzzy measure 1 as a fuzzy union over the periods, which consists of the maximum T values:

In the same way, the continuous fuzzy measure is defined as the fuzzy intersection over the periods, which consists of the minimum T values as:

The definition of the fuzzy at-persistent-risk-of-poverty is much more complex; for a full and detailed description, see Verma et al. (2017).

Model-Based Small Area Estimation

Sample sizes of surveys such as the EU-SILC, designed to be representative at the national level, are frequently too low to obtain efficient estimates of indicators at the small area level, such as NUTS 2. In other words, the measures calculated from such small sub-samples - called ‘direct estimators’ in the related literature - have variances that are too large. SAE theory is concerned with resolving these problems.

Often some additional information can be used to define estimators for small areas:3 in some cases, they are values of the variable of interest in other, similar areas or past values of this variable in the same area or values of other variables that are related to the variable of interest. Estimation approaches based on using this information are called ‘indirect or model based’. Henderson (1950) developed the best linear unbiased prediction (BLUP), which assumes that the variances associated with the model are known. In practice, of course, these variance components are unknown and have to be estimated from the data. The predictor obtained from the BLUP when unknown variance components are replaced by associated estimators is called the empirical best linear unbiased predictor (EBLUP; Fay and Herriot, 1979), defined as:

where dj (i = 1,2,...,m) are the specific parameters of areas or domains of a population (i.e. regions), and they are assumed to be linearly related to a vector of p-area specific auxiliary variables xt = {xuxli,...,xjT-, where v; are independent area-level random effects, independent of et; tney are the sampling errors for each area, independent of one another.

This classic Fay and Herriot model in Equation (4.4) can be extended by considering that vector v follows a simultaneously autoregressive (SAR) process with spatial autoregressive coefficient p and proximity matrix W (Cressie, 1993). In this way, the model with spatially correlated random effects is:

The estimator is unknown because it depends on unknown parameters, such as p. By substituting them with consistent estimators, a two-stage estimator called a spatial EBLUP is obtained (for further details, see Pratesi and Salvati, 2007).

Estimating the spatial EBLUP models requires having the standard errors of the direct estimator 0. Because the poverty measures adopted in the present chapter are quite complex (e.g. the ‘fuzzy at-persistent-risk-of-poverty rate’)4 and are calculated on the basis of a very complex survey, such as the EU-SILC, we estimate their standard errors with jack-knife repeated replication (JRR) as in Verma and Betti (2011).5

The Dataset: EU-SILC in Spain

The reference data in the present work are based on a subset of microdata from the EU-SILC survey, which is the major source of comparative statistics on income and living conditions in Europe. The survey is conducted annually in each participating country. The EU-SILC covers data and data sources of various types: cross-sectional and longitudinal, household and individual level, on income and social conditions, and from registers and interview surveys, depending on the country. A standard integrated design has been adopted by nearly all EU countries. The design recommended by Eurostat involves a rotational panel in which a new sample of households and individuals is introduced each year to replace a quarter of the existing sample. Each individual enumerated in each new sample is followed up in the survey for four years, along with that individual’s entire household.

Construction of Computational Units for Variance Estimation

Variance estimation of measures from surveys such as the EU-SILC based on complex sample designs requires full information on the sample structure. Implementing practical variance computation procedures such as the one adopted here and based on JRR (Verma and Betti, 2011), requires information at a minimum including specification at the micro-level of: (1) sample weights, (2) stratum and (3) primary sampling unit (PSU). In addition, it is necessary to have a detailed description of the actual sample selection procedures used so that the micro-level information on PSUs and strata can be correctly interpreted and used to construct ‘computational’ PSUs and strata for variance estimation.

Although this type of information on sample structure is collected in all the EU-SILC surveys, not all of it is included in the micro-data in the public domain. This restriction on the availability of essential information results from various policy considerations, some justifiable, but not all. In any case, the absence of this information in complex samples makes it impossible to compute valid estimates of the sampling error.

Thanks to research cooperation with the Organisation for Economic Co-operation and Development (OECD) (Piacentini, 2014), we gained access to the public cross-sectional 2011 EU-SILC data (UDB) and the nonpublic variables concerning the sample structure on Spain: the code for regions at the NUTS 2 level (DB040), sampling strata (DB050) and PSUs (DB060).

Generally, the EU-SILC national surveys are designed with a focus on the production of reliable estimates at the national level. In fact, although the EU-SILC survey has a very large sample in Spain (13,109 households and 34,756 individuals for 2011), the regional sub-samples are very heterogeneous in size, so in some NUTS 2 regions, the estimates are not significant.

The Spain EU-SILC 2011 Intermediate Quality Report (INE, 2012) provides us with a detailed description of the sample design, which is important for understanding whether regions form independent sampling domains and for the construction of the ‘computational’ PSUs and strata.

DB040 and DB050 define unique strata within each region separately. The use of the sample description and of the three variables makes it possible to define the computational strata and PSUs for variance estimation.

Empirical Analysis

Using the data described above, this section analyses the direct estimates and their relative sampling errors for the poverty and deprivation variables. The results for each of the 19 regions in Spain can be entered into the Fay and Herriot (FH) and the SEBLUP models. The following statistics are considered in turn in a longitudinal context: the FM poverty rate and the FS deprivation rate. For each of these statistics, the longitudinal measures are as described above: any-time poverty, continuous poverty and the at-persis- tent-risk-of-poverty rate.

Table 4.1 reports the outcomes related to the FM fuzzy at-persistent- risk-of-poverty rate; the first set of values comprise direct estimates and the direct standard errors and the second set shows the FH estimates, the FH standard error and the gain of such model, reported in the percentage of reduction of direct standard errors, and the last set of measures report the values in the SEBLUP model.

Two aspects should be considered in this analysis: the substantive results at the regional level and the gain in precision using both the FH and SEBLUP models.

The highest measures of the fuzzy at-persistent-risk-of-poverty rate are found in Extremadura, Andalucfa and Castilla-La Mancha, whereas Navarra, Pais Vasco, Madrid, Aragon, Balears and Cataluna are better off, with a fuzzy measure below 10%. Melilla has a low percentage according to the direct estimate (7%); however, because of the small sub-sample size, this measure is not significant. The results obtained by both the FH and SEBLUP models severely reduce the standard errors, but the more precise measure is much higher.

The results concerning standard errors show that both FH and SEBLUP are lower than the direct estimates. In general, we have a mean reduction in the standard error for FH of 18% and for SEBLUP of 26%. The largest reduction in standard errors is in regions with small sub-samples, such as Melilla, Ceuta and Rioja.

However, for the purpose of this chapter, it is quite interesting to observe the larger gain in spatial EBLUP over FH; the geographic information in the w matrix for vicinity clearly contributes added value, indicating that an increase in poverty in a neighbouring region affects the region under investigation as well.

Table 4.2 reports the outcomes related to the FS fuzzy at-persistent-risk- of-poverty rate; the three sets of values are the same as those in Table 4.1. The highest measures of the FS fuzzy at-persistent-risk-of-poverty rate are now in Galicia, Andaluda and Ceuta, whereas Melilla, Aragon, Asturias,

Direct

SE

FH

SE

Gain FH

SEBI.UP

SE

Gain SEBI.UP

Galicia

12.32%

1.25%

12.55%

1.19%

95.45%

12.81%

1.18%

94.40%

Asturias

10.18%

2.27%

10.57%

1.91%

84.04%

10.73%

1.62%

71.44%

Cantabria

10.87%

2.32%

10.35%

1.95%

83.79%

10.37%

1.72%

73.90%

Pais Vasco

7.39%

1.72%

6.85%

1.60%

93.19%

6.29%

1.48%

86.04%

Navarra

3.87%

1.39%

4.66%

1.32%

94.78%

5.37%

1.27%

91.19%

Rioja

17.33%

3.69%

13.43%

2.44%

66.19%

11.53%

1.89%

51.23%

Aragon

8.08%

1.96%

8.46%

1.73%

88.42%

8.17%

1.47%

74.98%

Madrid

8.21%

1.15%

7.67%

1.12%

98.04%

7.76%

1.17%

102.28%

Castilla у Leon

13.77%

2.87%

12.81%

2.19%

76.21%

13.76%

1.56%

54.25%

Castilla-La Mancha

19.83%

2.78%

17.92%

2.19%

78.80%

18.80%

1.70%

61.11%

Extremadura

24.96%

2.49%

22.58%

2.13%

85.84%

23.04%

1.92%

77.10%

Cataluna

9.06%

1.27%

9.48%

1.21%

95.19%

9.39%

1.17%

92.68%

Comunitat Valenciana

12.17%

1.54%

12.41%

1.43%

92.74%

12.37%

1.32%

86.00%

Balears

8.02%

1.53%

9.29%

1.42%

92.95%

8.65%

1.51%

98.95%

Andalucia

20.06%

1.79%

19.07%

1.63%

91.32%

19.61%

1.54%

85.95%

Murcia

15.29%

3.21%

15.61%

2.35%

73.40%

16.88%

1.89%

58.77%

Ceuta

17.05%

8.69%

18.90%

3.18%

36.55%

14.98%

2.62%

30.14%

Melilla

6.99%

6.23%

12.70%

2.79%

44.77%

9.55%

2.40%

38.44%

Canarias

12.56%

2.48%

13.77%

2.04%

82.25%

11.68%

2.01%

80.78%

81.78%

74.19%

Direct

SE

EH

SE

Gain EH

SEBLUP

SE

Gain SEBLUP

Galicia

19.88%

2.36%

17.28%

1.98%

83.70%

17.22%

2.09%

88.62%

Asturias

7.90%

1.37%

7.80%

1.31%

95.48%

8.01%

1.34%

97.80%

Cantabria

13.21%

3.08%

11.35%

2.30%

74.60%

11.02%

2.41%

78.16%

Pais Vasco

8.08%

1.71%

8.75%

1.56%

90.94%

8.80%

1.60%

93.31%

Navarra

10.36%

2.87%

9.25%

2.25%

78.51%

8.70%

2.35%

81.84%

Rioja

9.07%

1.59%

9.47%

1.47%

92.21%

9.38%

1.50%

94.55%

Aragon

6.80%

1.39%

6.97%

1.32%

95.16%

7.03%

1.35%

97.67%

Madrid

8.95%

1.32%

9.94%

1.26%

95.49%

9.93%

1.28%

96.96%

Castilla у Leon

9.00%

1.65%

9.16%

1.51%

91.89%

9.11%

1.59%

96.63%

Castilla-La Mancha

11.73%

2.16%

11.91%

1.86%

85.79%

11.74%

1.96%

90.52%

Extremadura

12.83%

1.86%

12.10%

1.67%

89.38%

12.08%

1.72%

92.41 %

Cataluna

11.00%

1.59%

10.49%

1.48%

92.78%

10.47%

1.52%

95.22%

Comunitat Valenciana

13.90%

1.78%

13.39%

1.60%

90.25%

13.45%

1.66%

93.56%

Balears

12.78%

4.35%

14.80%

2.75%

63.15%

14.75%

2.77%

63.74%

Andalucia

20.98%

2.00%

20.16%

1.87%

93.35%

20.32%

1.92%

95.82%

Murcia

14.35%

3.22%

14.19%

2.37%

73.59%

14.49%

2.46%

76.42%

Ceuta

18.75%

9.38%

13.44%

2.97%

31.70%

13.22%

2.99%

31.91%

Melilla

5.26%

0.66%

5.53%

0.65%

98.78%

5.52%

0.66%

99.16%

Canarias

17.86%

2.82%

16.57%

2.25%

79.62%

16.48%

2.27%

80.64%

84.02%

86.58%

Navarra, Pais Vasco, Madrid, Castilla у Leon, Rioja and Cataluna are better off, with a fuzzy measure below or around 10%.

The results for standard errors have a smaller reduction than the corresponding FM measure: 16% for FH and 13% for SEBLUP. In this case, the effect of the geographic information in the vicinity matrix does not contribute added value.

Table 4.3 shows the results for the FM any-time poverty rates; the highest values are in Extremadura, Castilla-La Mancha and Andalucia, whereas the lowest are in Navarra, Aragon and Baleares. The average gains in standard errors for FFI and SEBLUB are similar to those for the FM at-persistent-risk- of-poverty rate. Again, the largest reductions are in the smallest regions, Melilla and Ceuta.

The results for the FS any-time poverty rate are in Table 4.4, showing the highest values are in Galicia, Andalucia, Canarias and Murcia, and the lowest are in Melilla, Navarra, Aragon and Pais Vasco. Again, the average gains in standard errors for FH and SEBLUB are similar to those for the FS at-persistent-risk-of-poverty rate. The largest reduction is in the smallest region, Ceuta.

Table 4.5 reports the FM continuous poverty rates; the highest values are in Extremadura, Ceuta, Castilla-La Mancha, Andalucia, Murcia and Rioja, and the lowest are in Navarra, Pais Vasco, Asturias, Madrid and Melilla. In this case, the average gain in the standard error is larger than in all the other measures, with a mean reduction of about 20% for FH and 24% for SEBLUP.

Finally, Table 4.6 reports the FS continuous poverty rates, for which the highest values are in Ceuta, Andalucia and Galicia, and the lowest are in Melilla, Aragon and Asturias. Again, the average gains in the standard errors for FH and SEBLUB are similar to those for the other measures.

Concluding Remarks and Further Considerations

In this chapter, we propose a series of mathematical procedures to estimate longitudinal poverty and deprivation at the regional level. First, we consider direct estimates of poverty and deprivation measured by means of fuzzy-set theory. In particular, we take into account a new measure, the ‘fuzzy at-persistent-risk-of-poverty rate’, proposed by Verma et al. (2017); then, we employ JRR for the first time in the version of this measure in Verma and Betti (2011) to estimate the standard errors of these fuzzy direct estimates.

The primary result obtained is the extension of variance estimation to go beyond measures of monetary longitudinal poverty, specifically using a fuzzy formulation of those measures and, as a corollary, multi-dimensional measures of longitudinal deprivation, which by their nature are a matter of degree - i.e. are fuzzy. To our knowledge, no such extension has been previously presented in the literature. Moreover, we propose the use of SAE

Direct

SE

EH

SE

Gain EH

SEBLUP

SE

Gain SEBLUP

Galicia

35.5%

2.81%

34.96%

2.60%

92.58%

33.90%

2.52%

89.67%

Asturias

23.29%

3.20%

25.12%

2.89%

90.14%

26.81%

2.67%

83.24%

Cantabria

29.50%

5.04%

28.44%

3.92%

77.81%

27.44%

3.38%

67.08%

Pais Vasco

25.12%

4.07%

23.53%

3.57%

87.69%

22.03%

3.19%

78.43%

Navarra

16.22%

3.12%

18.55%

2.86%

91.69%

19.61%

2.70%

86.58%

Rioja

34.03%

5.08%

31.89%

3.91%

76.99%

29.07%

3.35%

65.86%

Aragon

21.34%

3.38%

23.01%

3.03%

89.49%

24.01%

2.66%

78.54%

Madrid

27.98%

2.81%

26.00%

2.69%

95.61%

26.27%

2.81%

100.00%

Castilla у Leon

32.62%

4.20%

31.90%

3.50%

83.26%

33.23%

2.77%

65.86%

Castilla-La Mancha

42.09%

3.35%

40.57%

3.01%

90.10%

41.62%

2.67%

79.95%

Extremadura

46.16%

3.93%

44.76%

3.51%

89.14%

46.08%

3.19%

81.13%

Cataluna

29.56%

2.35%

29.71%

2.23%

94.90%

29.26%

2.17%

92.73%

Comunitat Valenciana

34.26%

2.99%

33.91%

2.74%

91.45%

33.79%

2.53%

84.65%

Balears

20.77%

3.28%

24.49%

2.94%

89.75%

23.59%

3.15%

95.97%

Andalucia

43.99%

2.05%

43.16%

1.99%

96.85%

43.33%

1.94%

94.74%

Murcia

36.20%

5.88%

36.61%

4.27%

72.58%

39.50%

3.40%

57.84%

Ceuta

31.50%

13.34%

40.50%

5.60%

41.96%

34.11%

5.01%

37.54%

Melilla

28.12%

25.86%

33.69%

5.32%

20.58%

27.10%

4.78%

18.48%

Canarias

35.43%

5.25%

35.78%

4.02%

76.62%

31.04%

4.01%

76.42%

81.54%

75.51%

Direct

SE

FH

SE

Gain FH

SEBLUP

SE

Gain SEBLUP

Galicia

46.54%

3.79%

41.74%

3.22%

84.89%

42.63%

3.24%

85.52%

Asturias

25.41%

3.95%

28.61%

3.30%

83.65%

27.11%

3.32%

83.95%

Cantabria

35.42%

4.64%

35.09%

3.64%

78.46%

36.61%

3.66%

78.88%

Pais Vasco

24.84%

2.71%

24.89%

2.55%

94.26%

24.62%

2.61%

96.23%

Navarra

24.34%

4.13%

23.79%

3.58%

86.65%

23.84%

3.68%

89.12%

Rioja

29.08%

3.76%

31.48%

3.21%

85.37%

32.39%

3.19%

84.93%

Aragon

24.44%

3.58%

27.23%

3.09%

86.44%

27.80%

3.12%

87.29%

Madrid

28.99%

2.52%

28.21%

2.39%

95.07%

28.61%

2.41%

95.88%

Castilla у Leon

27.74%

3.55%

30.34%

3.09%

86.85%

30.71%

3.13%

88.19%

Castilla-La Mancha

31.03%

3.92%

33.70%

3.33%

84.94%

33.36%

3.36%

85.75%

Extremadura

38.85%

4.02%

39.36%

3.44%

85.54%

39.62%

3.58%

89.00%

Cataluna

31.82%

3.15%

31.25%

2.83%

89.84%

30.82%

2.85%

90.48%

Comunitat Valenciana

39.16%

3.51%

37.80%

3.06%

87.21%

37.76%

3.07%

87.65%

Balears

30.48%

3.69%

31.49%

3.16%

85.61%

31.44%

3.15%

85.49%

Andalucia

45.55%

2.81%

43.55%

2.60%

92.56%

43.45%

2.66%

94.67%

Murcia

42.01%

5.62%

39.78%

4.07%

72.48%

37.74%

4.14%

73.72%

Ceuta

33.92%

13.36%

24.55%

5.33%

39.93%

22.43%

4.58%

34.27%

Melilla

18.95%

5.64%

21.68%

4.24%

75.22%

20.88%

4.03%

71.45%

Canarias

43.40%

3.47%

41.95%

3.08%

88.91%

41.55%

3.11%

89.63%

83.36%

83.79%

Direct

SE

EH

SE

Gain EH

SEBLUE

SE

Gain SEBLUE

Galicia

7.91%

1.14%

8.28%

1.06%

92.82%

8.10%

1.05%

91.59%

Asturias

5.11%

1.03%

5.57%

0.97%

94.00%

5.70%

0.94%

90.98%

Cantabria

7.01 %

1.46%

6.72%

1.28%

88.07%

6.49%

1.21%

83.18%

Pais Vasco

4.43%

1.17%

4.03%

1.10%

94.32%

3.75%

1.06%

91.12%

Navarra

2.13%

0.76%

2.44%

0.74%

97.34%

2.63%

0.73%

96.64%

Rioja

11.24%

3.09%

8.61%

1.88%

60.75%

7.44%

1.58%

51.10%

Aragon

4.77%

1.02%

4.98%

0.96%

94.40%

4.86%

0.93%

91.21%

Madrid

5.59%

0.87%

5.04%

0.85%

97.78%

5.17%

0.88%

101.11%

Castilla у Leon

8.50%

2.07%

8.25%

1.60%

77.02%

9.04%

1.29%

62.42%

Castilla-La Mancha

13.63%

1.96%

12.55%

1.58%

80.65%

13.31%

1.37%

70.07%

Extremadura

19.49%

1.95%

17.04%

1.65%

84.45%

17.07%

1.55%

79.32%

Cataluna

6.18%

0.92%

6.44%

0.88%

95.31%

6.24%

0.87%

94.36%

Comunitat Valenciana

7.86%

1.17%

8.15%

1.08%

92.28%

8.16%

1.04%

88.80%

Balears

6.04%

1.87%

7.57%

1.51%

80.91%

6.98%

1.59%

85.02%

Andalucia

13.80%

1.58%

13.10%

1.38%

87.52%

13.82%

1.33%

83.91%

Murcia

11.08%

2.96%

11.21%

1.91%

64.37%

11.79%

1.64%

55.29%

Ceuta

14.43%

7.55%

13.95%

2.40%

31.74%

11.83%

2.26%

29.98%

Melilla

5.76%

6.01%

9.23%

2.13%

35.38%

7.68%

2.07%

34.52%

Canarias

9.19%

2.03%

9.99%

1.60%

78.97%

9.02%

1.67%

81.97%

80.43%

76.98%

Direct

SE

FH

SE

Gain EH

SEBLUP

SE

Gain SEBLUP

Galicia

13.55%

1.75%

11.52%

1.48%

84.71%

11.53%

1.55%

88.86%

Asturias

4.34%

0.93%

4.32%

0.90%

96.61%

4.53%

0.91%

98.05%

Cantabria

9.21%

2.59%

7.24%

1.84%

71.09%

6.95%

1.87%

72.30%

Pais Vasco

5.22%

1.68%

5.66%

1.44%

85.35%

5.81%

1.47%

87.09%

Navarra

5.64%

2.12%

5.20%

1.69%

79.80%

4.73%

1.72%

81.22%

Rioja

5.88%

1.29%

6.03%

1.17%

91.30%

5.99%

1.19%

92.86%

Aragon

3.95%

1.16%

4.06%

1.09%

94.12%

4.07%

1.10%

95.14%

Madrid

5.40%

0.82%

5.84%

0.80%

97.15%

5.85%

0.81%

98.20%

Castilla у Leon

5.97%

1.20%

5.92%

1.12%

92.62%

5.95%

1.14%

94.29%

Castilla-La Mancha

5.87%

1.32%

6.27%

1.20%

90.85%

6.20%

1.22%

92.45%

Extremadura

8.72%

1.62%

7.84%

1.40%

86.44%

7.73%

1.45%

89.19%

Cataluna

6.58%

1.09%

6.31%

1.02%

94.39%

6.24%

1.04%

95.81%

Comunitat Valenciana

8.14%

1.29%

7.94%

1.18%

91.19%

7.91%

1.20%

92.94%

Balears

8.58%

3.42%

9.41%

2.12%

62.07%

9.30%

2.16%

63.12%

Andalucia

14.27%

1.75%

13.25%

1.59%

90.41%

13.43%

1.61%

91.91%

Murcia

7.89%

1.56%

8.14%

1.37%

88.09%

8.27%

1.39%

89.18%

Ceuta

16.70%

8.80%

8.45%

2.31%

26.24%

7.95%

2.34%

26.63%

Melilla

1.20%

0.97%

2.03%

0.92%

95.17%

1.97%

0.94%

96.99%

Canarias

9.79%

1.90%

9.63%

1.59%

83.72%

9.52%

1.63%

85.70%

84.28%

85.89%

techniques, such as spatial EBLUP, to further reduce the variability of fuzzy poverty measures at the regional level.

Overall, we conclude that both FH and SEBLUP can reduce standard errors by 20-30% on average, with a rate of 70% in regions with particular small sample sizes. Moreover, a larger gain in spatial EBLUP over FH is evident only for FM longitudinal measures, whereas little gain is achieved for FS measures, which obtain no added value from the geographic information in the w matrix of vicinity. So, in conclusion, neighbouring regions affect poverty only when we adopt a monetary measure, but it is unaffected using the multi-dimensional or non-monetary measure. Further research is necessary to understand the reasons for this outcome.

Notes

  • 1 NUTS is an abbreviation for Nomenclature of Statistical Territorial Units. This is Eurostat’s hierarchical classification of regions, from member states (NUTS 0) to smaller areas.
  • 2 For further details on the contributions of philosophy, mathematics and economics of the fuzzy-set approach to poverty measurement, see also Lemmi and Betti (2006a, 2006b), Cheli and Betti (1999), Betti, Cheli and Cambini (2004), Belhadj (2011, 2012), Alkire and Foster (2011), Belhadj and Limam (2012) and Betti and Lemmi (2013).
  • 3 When additional information comes from the population census, the SAE method is defined as ‘poverty mapping’, and the two seminal papers on it are Elbers, Lanjouw and Lanjouw (2003, 2005).
  • 4 A ‘complex measure’ is an estimator which cannot be expressed in terms of average, total, or a ratio of averages. For instance, fuzzy measures in Equation (4.1), or the fuzzy APRP rate are clearly complex measures.
  • 5 Verma and Betti (2011) demonstrate how a variant of the JRR method can fit better in the case of ‘complex measures’; moreover, Betti et al. (2018) show that the JRR variant in Verma and Betti (2011) is particularly adapted for estimating variance of fuzzy poverty measures.

References

Aassve A., Betti G., Mazzuco S., Mencarini L. (2007), Marital disruption and economic well-being; a comparative analysis, Journal of the Royal Statistical Society, Series A, 170(3), pp. 781-799.

Alkire S., Foster J. (2011), Counting and multi-dimensional poverty measurement, Journal of Public Economics, 95(7-8), pp. 476-487.

Belhadj B. (2011), A new fuzzy unidimensional poverty index from an information theory perspective, Empirical Economics, 40(3), pp. 687-704.

Belhadj B. (2012), New weighting scheme for the dimensions in multi-dimensional poverty indices, Economic Letters, 116(3), pp. 304-307.

Belhadj B. (2015), Employment measure in development countries via minimum wage and poverty: new Fuzzy approach, Opsearch, 52(2), pp 329-339.

Belhadj B., Limam M. (2012), Unidimensional and multi-dimensional fuzzy poverty measures: New approach, Economic Modelling, 29(4), pp. 995-1002.

Betti G. (2017), Fuzzy measures of quality of life in Germany: a multi-dimensional and comparative approach, Quality and Quantity, 51(1), pp. 23-34.

Betti G., Cheli B., Cambini R. (2004), A statistical model for the dynamics between two fuzzy states: theory and application to poverty analysis, Metron, 62(3), pp. 391-411.

Betti G., D’Agostino A., Neri L. (2011), Educational mismatch of graduates: A multi-dimensional and fuzzy indicator, Social Indicators Research, 103(3), pp. 465^180.

Betti G., Gagliardi F., Lemmi A., Verma V. (2015). Comparative measures of multidimensional deprivation in the European Union, Empirical Economics, 49(3), pp. 1071-1100.

Betti G., Gagliardi F., Verma V. (2018), Simplified jackknife variance estimates for fuzzy measures of multi-dimensional poverty, International Statistical Review,

86(1), pp. 68-86.

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

Betti G., Soldi R., Talev I. (2016), Fuzzy multi-dimensional indicators of quality of life: The empirical case of Macedonia, Social Indicators Research, 127(1), pp. 39-53.

Betti G., Verma V. (2008), Fuzzy measures of the incidence of relative poverty and deprivation: a multi-dimensional perspective, Statistical Methods and Applications, 17, pp. 225-250.

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

Cheli B., Betti G. (1999), Fuzzy analysis of poverty dynamics on an Italian pseudo panel, 1985-1994, Metron, 57, pp. 83-104.

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

Cressie N. (1993), Statistics for Spatial Data, New York: Wiley.

Elbers C., Lanjouw J.O., Lanjouw P. (2003), Micro-level estimation of poverty and inequality, Econometrica, 71(1), pp. 355-364.

Elbers C., Lanjouw J.O., Lanjouw P. (2005), Imputed welfare estimates in regression analysis, Journal of Economic Geography, 5(1), pp. 101-118.

European Commission (2010), Communication from the Commission. Europe 2020. A Strategy for Smart, Sustainable and Inclusive Growth. Brussels, 3.3.2010 COM(2010) 2020.

Eurostat (2000), European Social Statistics: Income, Poverty and Social Exclusion, Luxembourg: Office for Official Publications of the European Communities.

Eurostat (2002), European Social Statistics: Income, Poverty and Social Exclusion, 2"d Report, Luxembourg: Office for Official Publications of the European Communities.

Fay R.E., Herriot R.A. (1979), Estimates of income for small places: an application of James-Stein procedures to census data, Journal of the American Statistical Association, 74, pp. 269-277.

Foster J.E., Greer J., Thorbecke E. (1984), A class of decomposable poverty measures, Econometrica, 52, pp. 716-766.

Henderson C.R. (1950), Estimation of genetic parameters, Annals of Mathematical Statistics, 21, pp. 309-310.

Instituto Nacional De Estadistica (INE), (2012), Intermediate Quality Report, Survey on Income and Living Conditions Spain (Spanish ECV 2011).

Lemmi A., Betti G. eds. (2006a), Fuzzy Set Approach to Multidimensional Poverty Measurement, New York: Springer.

Lemmi A., Betti G. (2006b), Introduction, in Lemmi A., Betti G. (eds.), Fuzzy Set Approach to Multidimensional Poverty Measurement, New York: Springer, pp. 1-7.

Piacentini M. (2014), Measuring Income Inequality and Poverty at the Regional Level in OECD Countries, OECD Statistics Working Papers, 2014/03, OECD Publishing.

Pratesi M., Salvati N. (2007), Small area estimation: The EBLUP model based on spatially correlated random effects, Statistical Methods and Applications, 17(1), pp. 113-141.

United Nations (2015), Transforming our World: The 2030 Agenda for Sustainable Development, A/RES/70/1, United Nations.

Verma V., Betti G. (2011), Taylor linearization sampling errors and design effects for poverty measures and other complex statistics, Journal of Applied Statistics, 38(8), pp. 1549-1576.

Verma V., Betti G., Gagliardi F. (2017), Fuzzy measures of longitudinal poverty in a comparative perspective, Social Indicators Research, 130(2), pp. 435-454.

 
Source
< Prev   CONTENTS   Source   Next >