Polarization, growth and social policy in the case of Israel, 1997 - 2008

García-Fernándeza, Rosa María; Gottlieb, Daniel; Palacios-González, Federico Working Paper Polarization, growth and social policy in the case of Israel, 1997 - 2008 Economics Discussion Papers, No. 2012-55 Provided in Cooperation with: Kiel Institute for the World Economy – Leibniz Center for Research on Global Economic Challenges Suggested Citation: García-Fernándeza, Rosa María; Gottlieb, Daniel; Palacios-González, Federico (2012) : Polarization, growth and social policy in the case of Israel, 1997 - 2008, Economics Discussion Papers, No. 2012-55, Kiel Institute for the World Economy (IfW), Kiel This Version is available at: https://hdl.handle.net/10419/65680 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. http://creativecommons.org/licenses/by-nc/2.0/de/deed.en Polarization, Growth and Social Policy in the Case of Israel, 1997–2008 Rosa María García-Fernándeza Department of Quantitative Methods for Economics and Business, University of Granada Daniel Gottlieb National Insurance Institute and Baerwald School of Social Work, Hebrew University Federico Palacios-González Department of Quantitative Methods for Economics and Business, University of Granada Abstract In this paper we apply two statistical models to the measurement of polarization to Israeli income data over the past decade in order to empirically detect income classes as sub-populations of incomes concentrated around an optimal number of poles. The statistical models compared are a multi-resolution analysis (MRA) and a log-normal approach (LNA). We find the MRA to be superior to the LNA, by providing a more efficient allocation of households into each of the classes, reducing the overlap between the classes around the cut-values for each class. We then study polarization by use of the MRA in a multinomial logit-analysis by including ethniccultural, individual, family and other characteristics. We use a multiplicative normalized polarization measure developed by Palacios and Garcia (2010) which consists of presenting the interaction of three components, consistent with the axioms spelled out by Esteban and Ray (1994): alienation and identification, the number of income classes and the size distribution of the groups. The strong cultural heterogeneity of Israeli society, the sharp shifts in social policy during the observation period and the generally high quality of yearly Israeli income data render this dataset particularly useful for analyzing polarization. We find polarization to be significantly affected by cultural classes, by social policy and by standard demographic and individual characteristics. A comparison of our results with those of Esteban and Ray and Zhang and Kanbur reveals some similarity with our normalized version of Zangh and Kanbur (2001). JEL H54, I21, I3, J1, O15, O53 Keywords Polarization; poverty; multi-resolution analysis; income distribution Correspondence Rosa María García-Fernándeza, Department of Quantitative Methods for Economics and Business, University of Granada, Spain; e-mail: rosamgf@ugr © Author(s) 2012. Licensed under a Creative Commons License - Attribution-NonCommercial 2.0 Germany Discussion Paper N o. 2012-55 | October 24, 2012 | http://www.economics-ejournal.org/economics/discussionpapers/2012-55 2 1. INTRODUCTION Among 19th century economists the question concerning the partition of the income distribution into income classes was a natural one to ask. In the last two decades the interest in such questions has reappeared, following the contributions of Foster and Wolfson (1992, 2009), Wolfson (1994) and Esteban and Ray (1994). Societies are believed to consist typically of three classes – the poor, the middle class and the rich. However, empirically one may find that the classes vary in number and sizes. In the recent literature the determination of the number of classes itself has been an issue of interest, especially due to the importance of the middle class in securing social stability. The possibility of the vanishing middle class 1 becomes thus not only a theoretical problem but also an interesting empirical question. We focus on detecting empirically the number and sizes of income classes as subpopulations of incomes concentrated around an optimal number of poles by allocating micro data of the Israeli income survey for the years 1997 to 2008 to each of the detected groups. We proceed by calculating a three-pronged polarization index as suggested by Palacios and Garcia (2008, 2010). The index is based on the axiomatic approach of identification and alienation within and between the estimated income groups, their sizes and the number of groups, as laid out in Esteban and Ray (1994). We then identify the variables and characteristics affecting the allocation of households among the classes in a multinomial logit analysis. The Israeli economy is particularly interesting for the study of polarization, due to the cultural heterogeneity of its population, its exposure to various macroeconomic and other shocks, as well as due to its dynamic economic development. The economy experienced sharp economic 1 See a discussion of this phenomenon in Esteban and Ray (1994), Duncan, Smeeding and Rodgers (1993), Horrigan and Haugen (1988), Kosters and Ross (1988), and Atkinson and Brandolini, 2011. 3 fluctuations, from rapid growth to a severe recession, followed by a quick turnaround and a growth period of four and a half years, which was interrupted by the global crisis of 2008/9. During the 1990s there was a large influx of temporary migrant workers, allowed to work only in low-skilled occupations, thus putting downward pressure on wages for low-skilled workers with the effect of crowding them out of the labor market and causing many of them to become recipients of social benefits. During the recession of 2002/3, when the cyclical developments would normally cause an increase in the number of social benefit receivers, two consecutive governments carried out a harsh social policy reform, cutting deeply into the availability of social benefits (especially the size of child benefits and eligibility and size of benefits of unemployment and income support, including a temporary freeze on the indexation of social benefits). This development was accompanied by a small scale pilot project of pro-active labor market policy. 2 The largely export-led growth period thereafter was mainly concentrated in medium and hi-tech industries, thus benefiting mainly the high skilled labor force. As is well captured in the official poverty reports of the National Insurance institute these forces had a detrimental effect on poverty incidence and particularly on poverty severity. 3 The effect of these developments on polarization and social stability is part of the present analysis. We show that the values of the new measure proposed as well as those of Zhang and Kanbur (2001) are consistent with the micro-economic multinomial logit analysis of income class association. Distinctly from polarization measures, such as Foster and Wolfson (1992, 2009), Silber et al. (2007), which use the Gini coefficient, the polarization indicator suggested here avoids social weighting by concentrating on positive rather than normative aspects of 2 According to an OECD report on the Israeli labor market and social policy, (2010), Israeli budgets on active labor market policies (ALP) was only about 0.1% of GDP compared to an average corresponding figure for OECD countries for 2006 of 0.6%. 3 See official poverty reports at www.btl.gov.il. 4 polarization, such as the variance. Consequently, the alienation-identification component of the PG polarization index, rather than reflecting a welfare measure, should be understood as a mirror of class society, giving an equal relative weight to each class, notwithstanding the ranking of the income of its members. This approach views polarization as a neutral phenomenon, differentiating it from the concept of social weighting which is an important feature of social welfare functions such as the poverty indices of Sen, Foster, Greer and Thorbecke or the Gini-inequality index. To stress this conceptual difference, imagine a society in which poverty has been eradicated. The issue of polarization will still be relevant, focusing for example on the extremely rich and the resulting concentration of political power and threat to democracy. 4 In this case the social weighting such as the squared income gap as in the FGT measures or the rank in the Gini index would give a lower weight to the richest in the society despite the considerable potential harm of social stability implied in their influence on policy makers. While being a crucial ingredient in poverty and inequality measures the Pigou- Dalton transfer axiom does not constitute a necessity in the context of polarization. After the introduction, the methodology for measuring polarization is presented in the second section. Empirical results are presented in the third section. After a description of the data and of relevant stylized facts about the Israeli economy we compare the various approaches to polarization by use of Israeli data on net equivalised income. In the third section we analyze the allocation of households to each estimated class, as produced by the algorithms, for each of the years 1998, 2004 and 2008 by a multinomial logit analysis. The explanatory variables are personal and demographic characteristics, as well as variables reflecting socioeconomic policies of the period 2002-2004. We chose the years that best reflected the three periods: (1) before the restrictive policy of 4 See for example Rubinstein, 2009, p. 186-189. In that section there is also a reference to a newspaper article on the problem of economic abundance by the same author in 2003. 5 cuts in social benefits, (2) immediately after the policy and (3) after three consecutive years of economic growth. Conclusions are drawn in the last section. 2. STATISTICAL APPROACH The aim of using a specific statistical model in a polarization exercise is to allocate each household in the sample to its appropriate income class, such that the emerging classes will be more homogeneous in the households’ net incomes than in the overall distribution. The most frequently used statistical approach is to estimate a mixture of gamma, normal and log-normal distributions, referred to here as the traditional approach. Such an approach may be found in the work of Paap and van Dijk 1998, Pittau and Zelli, 2006, Flaichare and Nuñez, 2007, Chotikapanich and Griffiths 2008, Pittau et al. 2010, among others. Maximum homogeneity is achieved by having a maximum of unique allocations of households into income groups. Unfortunately, in such exercises statistical models typically provide overlapping results, in which one household has a positive probability to be allocated to more than one group. As is well accepted in the literature (see for instance Esteban and Ray, 1994 and Zhang and Kanbur, 2001), one of the most important characteristics of polarization is the alienation-identification property. Homogeneity-heterogeneity is the statistical interpretation of this property. One of our purposes in this paper is therefore to keep overlapping results to a minimum by choosing a statistical model that enables us to reduce overlapping results to a minimum, in order to provide subpopulations that are as homogeneous as possible and less disputable. In this section we compare two estimations of unknown probability density functions of a given population. The first is a mixture of a log-normal distribution and the second is a mixture of densities based on multi-resolution analysis. 6 The empirical application of the two mixtures is carried out using Israeli income data for the year 2005 5 . The estimated parameters and coefficients of the mixtures of log-normal distributions and of the MRA are given in figure 1 and tables 1.a and 1.b. Figure 1. Components of the LNA (left panel) and MRA mixtures (right panel) Table 1.a: Parameters of the mixture of log-normal pdf Expected Values Expected Standard Deviation Parameters of the Log Normal Mixture  ˆ  ˆ p ˆ Component 1 1658.11253 757.130889 7.31874368 0.43518162 0.27936849 Component 2 4579.03612 2546.53659 8.29450515 0.51911203 0.67728094 Component 3 5203.50434 17689.0709 7.29197697 1.59066692 0.04335057 5 We use this year for the analysis because this is the first year in which the full effect of the harsh social policy carried out in the years 2002 to 2004 is fully reflected in the data, thus providing sufficient variance in the microeconomic information on homogeneity-heterogeneity and making it a good test case. 0 0.00002 0.00004 0.00006 0.00008 0.0001 0.00012 0.00014 0.00016 0.00018 0.0002 0.00022 0.00024 0.00026 0.00028 02000 4000 6000 8000 10000 12000 14000 16000 18000 20000 LN Sub population 1 LN Sub population 2 LN Sub population 3 0 0.00002 0.00004 0.00006 0.00008 0.0001 0.00012 0.00014 0.00016 0.00018 0.0002 0.00022 0.00024 0.00026 0.00028 02000 4000 6000 8000 10000 12000 14000 16000 18000 20000 MRA Sub population 1 MRA Sub population 2 MRA Sub population 3 7 Table 1.b: Estimation of the mixture of MRA pdf Expected Values Expected Standard Deviation p ˆ Component 1 1728.6713 2398.93129 0.41010639 Component 2 4599.11435 2553.50559 0.55083056 Component 3 13414.2513 10597.3815 0.03906305 Figure 1 shows that in this sample the MRA mixture produces less overlap for each of the subgroups than the log-normal mixture. This has an important economic interpretation, since as mentioned earlier one of the major purposes of a polarization exercise is to allocate each household to a unique income-subgroup. However, in the zones of overlap such uniqueness is impossible. 6 In such cases it is only possible to assign to these households probabilities of belonging to each of the groups. This is a result to be expected, since we show in sections 2.1 and 2.2 that the components of the MRA mixture are found by a process which optimizes homogeneity whereas the components of the log-normal mixture are a result of maximizing the likelihood function, without including any consideration about the homogeneity of the components. As is easily seen from figure 1 the overlap of the log-normal mixture is particularly high in the third group of high incomes. As a matter of fact it is easy to see that in the LNA there is quite a large overlap between the poor and the rich, a result that is strongly counterintuitive and the overlap of the rich and the middle class in the LNA model is almost complete. In contrast there is no overlap at all between the poor and the rich in the MRA and the overlap between the rich and the middle class is confined to a 6 In fact this is the case for all households when the model is a mixture of normal, log-normal or gamma pdfs. Although based on an intuitive reasoning, in this paper we have truncated the tails of these distributions for the analysis of overlap and the creation of table 2. 8 relatively limited range of incomes. The considerable overlap between the poor and the middle class at the lower end of the middle class distribution may well reflect the phenomenon of blurred identification and alienation at the high end of the poor class and the lower tail of the middle class. These results have an important economic implication: at the overlapping tails people find it hard to identify with one or the other group and as for the top-income group (the “tycoons”), certain members of this group often have direct access to economic policy decision making, especially concerning those decisions that directly affect rich people’s economic welfare. Since the number of households tends to decline strongly, the richer the households become, their group will typically be very small and hard to identify uniquely in a polarization exercise, while at the same time their economic importance increases. Therefore the homogeneity optimization, characteristic of the MRA procedure, has an inherent advantage, since the relative efficiency of identification by the MRA seems to increase with the reduction in the size of groups. Focusing on this problem of overlapping by giving the share out of total observations in the various groups we can see from table 2 that the share of households allocated uniquely to the lowest class is about twice as big in MRA compared to the same group in LNA. The households uniquely allocated to the middle and high classes is smaller in the MRA. In LNA 73.7% of the households are uniquely allocated to anyone class whereas in the MRA the share is 92.6%. Accordingly the share of overlapping allocations is 26.3% in the LNA and only 7.4% in the MRA, thus resulting in an overlap that is 3.6 times higher in LNA than in MRA. 15 6.11 1 1 1       jij n i n jiyyppER In which ji yy  represents the alienation (distance) felt by individuals of incomes i y and j y . The share of population is given by i p , and  i p represents the sense of group identification of each of the i p members of group i within their own group. The sense of identification increases with the number of people in the group which have the same income level. The parameter falls into the interval   6.1,1 to be consistent with the set of axioms proposed by Esteban and Ray (1994). Zhang and Kanbur (2001, henceforth ZK) provided an alternative approach to polarization based on the idea that polarization is generated by two tendencies: for exogenously given groups, as income differences within the group decrease, that is as the groups are more homogeneous internally, differences across groups are, magnified and polarization is higher. In a similar way, for given within group differences, the further apart are the means of the groups the higher is polarization. These authors quantified these tendencies by the ratio of the between groups inequality to the within group inequality, that is For the Theil index the above expression can be written as follows ∑ ( ) ∑ 16 where ∑ ( ) k is the number of groups; is the total population; is the population of the jth group; is the total sample mean; is the mean of the jth group and is the jth income. Our polarization measure has the following advantages with respect to those provided by of ER and ZK. In contrast to ER and ZK, the PG is a normalized measure, taking values between 0 and 1. It can thus be interpreted as a percentage portraying the degree of polarization. The expressions of Zhang and Kanbur (2001) and Esteban and Ray 12 (1994) are not normalized and consequently the results cannot be interpreted in terms of percentages. Indeed the results of both measures are difficult to interpret since there is no established standard of measurement. For example it can be shown that the Zhang and Kanbur polarization measure increases systematically with the number of groups. The introduction of the index in the PG measure compensates the effect that the increasing of the number of groups has on the intra-group variance and hence on polarization, thus correcting this drawback of the ZK measure. Furthermore it is easy to see, that the Zhang and Kanbur measure tends to infinity when the within-group inequality tends to zero. However, this drawback of the index can be corrected by normalizing their measure, using the decomposition property of the Theil index 13 , as follows 12 Although Esteban and Ray (1994) made an attempt of normalizing their measure, using log income and replacing the population weights by the population frequencies, it is easy to show that this measure can take values higher than one. 13 The index of Theil can be broken down in a similar way as the variance. That is, the overall inequality is equal to the inter-groups inequality plus the intra-group inequality. This property is also verified by the Gini index if the groups do not overlap. 17 where . Observe that such a normalized Zhang and Kanbur measure resembles the alienationidentification index ( ) in PG. The main modification introduced by , concerns the way in which we compute identification and alienation. According to the concept of polarization, if there is a high degree of homogeneity within each group and a high degree of heterogeneity across groups, society is polarized. In other words polarization focuses on dispersion and for this reason we prefer the use of the intra-group and the inter-groups variance to that of the intra-group and inter-group inequality to quantify the contribution of identification and alienation to polarization. 14 Indeed, from a statistical point of view, the intra-group variance and the inter-groups variance are the most appropriate approaches to evaluate the homogeneity within a group and the heterogeneity across groups respectively, when the representative magnitude of each group is the mean of the variable of interest, in our case the mean income (see among others Fisher, 1958). Moreover the concept of polarization, on the contrary to the inequality indices, is not linked directly to welfare. For this reason we think that positive measures, such as the variance, are more appropriate for the computation of alienation and identification and consequently for polarization. 3. EMPIRICAL RESULTS Israel’s society is highly heterogeneous both culturally and also with respect to the standards of living of the various population groups. Heterogeneity is driven mainly by 14 As mentioned above, the negative effects of polarization may occur both at the bottom and the top of the distribution. Therefore the higher ranking of lower incomes, as for example in the Gini measure, may diminish the indicator’s measurement of the damage caused by the concentration of excessive economic power at top incomes. 18 cultural differences based on nationality and religiosity: four fifth of the population being Jewish and one fifth Arab and within the Jewish population there is a significant cultural divide concerning religiosity between orthodox (henceforth Haredi) Jews, who account for about 10% of Israeli Jewish population, and the rest. Heterogeneity is emphasized by Haredi preference to let the men concentrate on theological studies, rather than earning a living, leaving this task to the wives. This tendency is underlined by the de facto exemption of the young Haredi from army service. Marriage at an early age, large family size and low labor market participation are typical in the Haredi society and create large (equivalised) income differences in favor of the non-orthodox Jewish majority. Important cultural differences as well as differences in opportunities for the Arabs create a further possible source for polarization between Jews and Arabs. However, in contrast to the Haredi society the Arab society is in a process of rapid reduction in family size, thus reducing heterogeneity over time. A further source of polarization stems from government policy and the economic environment. The Israeli economy being small and open has been subject to significant shocks during the observation period. These shocks may affect various population groups differently, for example, depending on their involvement in the labor market. During the second half of the 1990's the Israeli economy had become increasingly open, not only due to its high and rising share of imports and - largely hi-tech oriented - exports, but also due to the increasingly liberal regime of flows of international capital and of migrant workers. 15 Economic vulnerability and polarization have been enhanced by the Israeli-Arab conflict which brought about repeated outbursts of violence, thus exposing the Israeli economy to politico-economic shocks. Such a shock occurred from the last quarter of 2001 to early 2003. Another cause of sharp changes in the income 15 See Gottlieb and Blejer (2001). 19 distribution was the harsh mix of macroeconomic and socio-economic policies implemented during the years 2002 to 2004 and a previously started de facto liberal policy towards the influx of migrant workers 16 , coupled with a policy of lax compliance and enforcement of labor laws among their employers. 17 This policy caused a significant influx of migrant workers 18 since 1993, affecting negatively the employment prospects and salaries of low skilled Israeli workers and thus possibly exacerbating polarization. A fiscal policy, led by a tax reform (from 2006 onward) which reduced income tax rates mainly for the well-to-do, coupled with severe cuts in social benefits (2002 to 2004) - particularly in child benefits, income support of families whose head of household was in working age, and in the eligibility criteria for unemployment – further emphasized the tendency of economic hardship for the low-skilled. The main goal of these cuts in welfare budgets which occurred mainly between 2002 and 2004, was aimed at raising labor market participation of income support receivers and at reducing the budget deficit through a reduction in social expenditure, which in the past was characterized by a higher degree of solidarity. 19 The worldwide economic crisis of 2008/9 was not significantly felt in the Israeli economy until the last two months of the year of 2008, such that it is hardly reflected in our observation period. 20 The above mentioned intense economic history of Israel thus presents a unique opportunity for studying polarization during the period of 1997 to 2008. 16 The migrant workers which started to flow into Israel from 1993 onward in reaction to the gradual closure of the borders for Palestinian workers, due to cycles of political violence, are not to be confounded with Jewish immigrant workers who have been entering Israel for many decades and particularly since 1990. 17 The government has undertaken several attempts over recent years to regulate migrant workers' influx but until now without much success (see various Bank of Israel Annual Reports and Gottlieb, 2002). 18 Migrant workers, whose sole aim is to come to work in Israel are not to be confused with new immigrants, who immigrate to Israel by the law of return. 19 See National Insurance Institute, Annual Surveys, 2004 to 2008. 20 See Annual Survey, 2008, National Insurance Institute, p. 15-18. 20 3.1 Description of the survey The data is from the annual income surveys for the years 1997 to 2008, carried out by the Israeli Central Bureau of Statistics (CBS). 21 The number of households surveyed each year varies between 12,815 and 15,000. The cash income data used in the analysis throughout the observation period are in constant 2006 prices. The mean net equivalised income varied between 2,577 NIS and 4,222 NIS per month, implying a real growth rate of that income by about 2.3% p.a. 22 Table 3: Basic data 23 21 The CBS began to top-code the highest incomes since 2006. At first we analysed the non-top-coded data in the present framework, but eventually concluded that the top-coding had no significant effect on the results derived from income surveys. 22 We use the official Israeli equivalence scale which is based on the traditional food-share scale of the Engel type: The values of the scale are 1.25, 2, 2.65, 3.2, 3.75, 4.25, 4.75, 5.2 for one, two, persons etc. respectively until it reaches 6 for 10 persons, continuing with an addition of 0.4 for each additional person. Israeli families are in general much larger than those found in Western countries. This is mainly due to Jewish and Muslim religiosity. Therefore the scale is not truncated for particularly large families. The numbers for the lower sized families are quite similar to those of the OECD scale, that prevailed before the OECD switched to using the square root of family size. 22 In order to be able to analyse polarization over time we had to exclude the Jerusalem-Arabs from our data set, since they had not been surveyed in the years 2000 and 2001.This was necessary to ascertain a consistent, though incomplete measurement of polarization for Israel. Their population has been growing rapidly from somewhat more than 10% to nearly 20% of Israel’s Arab population. They mostly belong to the poorest class of the income distribution. Their omission may thus slightly bias the overall results for polarization. 23 The data are in real New Israeli Shekel (NIS in 2006 prices). Due to problems of collecting data on Jerusalem Arabs in the years 2000 and 2001 we excluded them from the sample throughout the observation period in order to analyse a consistent data set. Negative and zero incomes were excluded from the analysis. The data in table 3 are calculated from non-weighted household survey data. Total population Number of households in sample Mean net equivalized income in sample Standard deviation in sample Average number of school years Average family size Average number of earners in household 1997 12,815 3,263 2,554 12.3 3.41 1.41 1998 13,266 3,324 2,512 12.4 3.36 1.37 1999 13,273 3,406 2,876 12.6 3.35 1.24 2000 13,424 3,523 2,697 12.4 3.33 1.25 2001 13,608 3,683 3,016 12.6 3.30 1.19 2002 13,955 3,519 2,647 12.7 3.31 1.18 2003 14,112 3,505 2,618 12.7 3.31 1.18 2004 14,337 3,634 2,788 12.8 3.30 1.20 2005 14,239 3,755 3,088 12.9 3.28 1.21 2006 14,282 3,989 3,452 13.0 3.28 1.24 2007 13,879 4,112 3,265 13.1 3.26 1.26 2008 13,854 4,139 3,285 13.2 3.26 1.27 21 3.2 Analysis and results To model the equivalised net income distribution the MRA pdf given by (1) is used. The coefficients of the MRA model given by expression (1) are estimated by the maximum likelihood procedure using the EM algorithm (Hartley, 1958; Dempster et al., 1977; McLachlan and Krishman, 1997). Different approximations to the theoretical distribution, are performed by increasing the resolution level m. Attending to the parsimony principle, the model with minimum m which is non-rejected by the test of Kolmogorov-Smirnov fits well to the pdf and will be used to apply the measure of polarization. After estimating the MRA pdf, the number of groups and their location are obtained by applying the algorithm 1 described in Palacios-Gonzalez and García-Fernández (2012). The results presented in Appendix figures A.1 to A.12 reveal that according to the algorithm the number of significant income groups shrank during the observation period – from 4 groups in the first year (1997) to 3 groups in the following years. 24 Figure 2 displays the overall probability density function of net incomes and reveals that over the three years compared 25 – 1998, 2005, 2008 – the shape of the overall distribution underwent important changes: while in 1998 there were two distinctive modes to the distribution, over time the second mode became more flattened. This flattening process was accompanied by an increase in dispersion as can be observed by an outward shift of the right hand side of the distribution, suggesting a movement within the middle class to its upper part. This reminds of a similar development for UK data, as 24 Possibly the sample of 1997 was of lesser quality, compared to the following years, since this was the first year for which the income survey combined information from two sources – from the labour force survey and the expenditure survey – thus implying that the results from 1998 onwards are more qualitative. When we accidentally used original data (including Arabs from East Jerusalem) the algorithms produced only two classes, implying a vanishing middle class in 2008. 25 The years 1998, 2005 and 2008 reflect respectively the first year of qualitatively improved data, the first year after the harsh social policy and the first year after a prolonged period of growth in GDP. 22 reported in Jenkins (1995), reflecting the ‘shrinking middle class’ phenomenon of the income distribution during the 1980s. Figure 2: Changes in the overall probability density function of the equivalised net income distribution over time: 1998 – 2005 - 2008 The estimated MRA pdfs in appendix figures A.1-A.12, given for the overall population and for each group from 1997 to 2008 reflect two major forces that were at work: (1) a harsh socio-economic policy carried out from 2002 to 2004, with an emphasis on 2003- 2004; (2) a sharp fluctuation in the per capita growth environment of GDP over the observation period of 1.7%, a negative growth rate (-1.9%) during the recession of 2001 to 2003 and renewed positive growth of 3.2% per capita over the years 2005-2008. 26 In the context of polarization the average per capita growth rate differed for each income group. When splitting down the changes into net household income by group, income actually declined during the recession for the lower and middle classes while it increased for the upper class. In the period of enhanced growth of 2005 to 2008, though 26 We neglect 2004 in the calculation of sub-period p.c. growth because it reflects a year of transition. 0 0.00005 0.0001 0.00015 0.0002 0.00025 0.0003 0.00035 0 5000 10000 15000 20000 f(x) 1998 f(x) 2005 f(x)2008 23 while all three classes benefitted, the increase in the lower class was almost nil and in the middle class significantly smaller than in the upper class. 27 The polarization indicator as defined in equation (2) is presented in figure 3 and in Appendix table A.3. Over the period 1998 to 2006 this indicator fluctuated around a negative trend. This trend was sharply reversed in the years 2007 and 2008. Figure 3: The Polarization Index, its trend and the confidence intervals (95%) Table A.2 shows that during the tri-polar period (1998 to 2008) the size of the middle class was not stable and in 2007 and 2008 there was a tendency towards a ‘shrinking middle class’. As shown below, the harsh (permanent) change in social policy which occurred in 2003 and 2004, following the recession of 2001/3, raised the probability for economically disadvantaged households to remain in (or fall into) the lower class. This policy included sharp cuts in various social security benefits, especially in child benefits, income support to heads of households in working age and unemployment benefits as well as a tightening of their eligibility criteria. This is shown in the Multinomial Logit equations below. 27 These results can be calculated from table A.1. The p. c. GDP calculations are based on data from the Central Bureau of Statistics. 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 Upper confidence level P-2006 to 2008 PG P-1998 to 2006 Lower confidence level Poly. (P-2006 to 2008) Linear (P-1998 to 2006) 24 The polarization index given by expression (2) is presented in Figure 3 and in appendix tables A.3 and A.4. The figure of the components of the polarization index is given in Appendix figure A.13. : At the heart of the polarization measure is the measure of identification and alienation. After some fluctuation it increased during 2001 to 2004, a period of harsh socio-economic policy (2002 -2004), which coincided with a severe recession (late 2001 – late 2003). This cut in social expenditure, during an economic downturn not only worsened the economic situation of the low and middle class but probably deepened the downturn by neutralizing the expected built-in-stabilizer. This effect was somewhat dampened during the period of enhanced growth 28 , only to deteriorate again towards the end of the period. : As explained above this indicator reflects the number of groups, raising polarization, when the number of groups is falling. As mentioned above, this happened from 1997 to 1998, and possibly from 2007 to 2008. The factor compensates for the “squeezing effect” on the intra-group variance of the subgroup probability density functions, when introducing an additional class. We give great importance to this factor even if the empirical observation of a reduction in the number of classes from 1997 to 1998 and again from 2007 to 2008 (when Arabs living in East Jerusalem are included – see also footnote 24) is not a robust econometric result at this stage. 29 : While the size of the middle class increased (except during the period of harsh socio-econoic policy) during the years 1998 to 2006, this tendency was reversed towards the end of the period. The present analysis suggests that when the 28 An econometric test of this hypothesis exceeds the scope of the present paper and will be taken up in future research. 29 The possibility of a polarization model to accommodate endogenously for a change in the number of classes can be useful with the availability of qualitative data for longer observation periods. 31 5. REFERENCES Abu Bader S. and D. Gottlieb, 2009, "Poverty in the Bedouin Society", forthcoming in Monetary Poverty and Social Exclusion around the Mediterranean Sea, eds. V. Berenger and F. Bresson; in the series :Economic Studies in Inequality, Social Exclusion and Well-Being, Springer. Atkinson A.B. and A. Brandolini, 2011, "On the identification of the “middle class”, Working Papers 217, ECINEQ, Society for the Study of Economic Inequality. Bank of Israel, Annual Reports, http://www.bankisrael.gov.il/publeng/publeslf.php?misg_id=12 Burtless G., 2007, “Globalization and Income Polarization in Rich Countries”, Issues in Economic Policy, Brookings Institution, April, 1-36. Chotikapanich, D. and W.E. Griffiths, 2008, Estimating Income Distributions Using a Mixture of Gamma Densities,Department of Economics - Working Papers Series 1034, The University of Melbourne D’Ambrosio C. 2001, “Household characteristics and the distribution of income in Italy: an application of social distance measures”, Review of Income and Wealth, 47(1), pp. 43-63. Dempster, A., Laird, N., and Rubin, D. ,1977, “Maximum likelihood for incomplete data via the EM algorithm”, Journal of the Royal Statistical Society, Series B, 39(1):1-38. Duclos, J. Y., Esteban J.M., and Ray D. ,2004, “Polarization: Concepts, Measurement, Estimation” , Econometrica, 74 pp1337-1772. Duncan G., T. Smeeding and W. Rogers, 1993, “W(h)ither the Middle Class? A Dynamic View.” 240-71, in Poverty and Prosperity in the USA in the Late Twentieth Century, eds. D. B. Papadimitriou and E. N. Wolff, New York: St. Martin’s Press. Duro J. A., 2005, “Another look to income polarization across countries”, Journal of Policy Modeling 27, 1001–1007. Esteban J. M., 2002, Economic Polarization in the Mediterranean Basin.CREI, (10), UniversitatPompeuFabra. Esteban J.M., and Ray D. ,1994, “On the Measurement of Polarization”, Econometrica, 62 (4), pp. 819-851. Esteban J.M., Gradín C. and Ray D., 1999, Extensions of a Measure of Polarization OCDE Countries, Luxembourg income Study, Working Paper, 218, New York. Fisher W. D. ,1958, “ On Grouping for Maximum Homogeneity”, Journal of the American Statistical Association, 53 (284), pp. 789-798. 32 Flaichare E., and Nuñez, O., 2007, “Estimation of the income distribution and detection of subpopulations: An explanatory model”. Computational Statistic and Data Analysis, 51, 3368-3380. Foster J.E. and M.C. Wolfson, 1992, "Polarization and the decline of the middle class: Canada and the U.S.", mimeo, Vanderbilt University. Foster J.E. and M.C. Wolfson, 2009, "Polarization and the decline of the middle class: Canada and the U.S.". This paper appeared first in 1992, mimeo, Vanderbilt University. Gottlieb D. and L.Kushnir, 2009, "Social Policy Targeting and Binary Information Transfer between Surveys”, Economics, The Open-Access, Open Assessment E- journal; http://www.economics-ejournal.org/economics/journalarticles/2009-28 Gottlieb D. and M.Blejer, 2001, “Liberalization in the Capital Account of the Balance of Payments,” in “From Government Intervention to a Market Economy: The Israeli Economy 1985-1998”, in Memory of Michael Bruno” ed: Avi Ben-Bassat, English, MIT Press, 291 - 340. Gottlieb D., 2002, “The Effect of Migrant Workers on Employment, Real Wages and Inequality”, The Case of Israel - 1995 to 2000”, http://ideas.repec.org/p/pra/mprapa/3148.html. Gottlieb D., 2007, "Poverty and Labor Market Behavior in the Ultra-Orthodox Population in Israel" (Hebrew), July, 1-56, www.vanleer.org.il/econsoc/pdf/1_research_mdiniut4.pdf Gottlieb, D. ,2000, Globalization and World financial Turmoil - A Test for Israel's Economic Policy; in: Small Economies Adjustment to Global Tendencies (2000): pp. 213-244; or http://mpra.ub.uni-muenchen.de/3150/. Gradín C., 2000, “Polarization by sub-populations in Spain, 1973-91” , Review of Income and Wealth, 46 (4), pp. 457-474. Hartley, H.,1958, “Maximumlikelihood estimation form incomplete data”, Biometrics, 14, pp.174-194. Horrigan M.W. and S.E. Haugen, 1988, “The Declining Middle-Class Thesis: A Sensitivity Analysis, Monthly Labor Review 103, April, 51-53. Jenkins, S., 1995, “Did the middle class shrink during the 1980s? UK evidence from Kernel density estimates, Economics letters, Volume 49, Issue 4, October, 407-413. Kosters, M. H. and M. N. Ross, 1988, "A Shrinking Middle Class?" The Public Interest, no. 90 (Winter): 3-27 Mallat, S., 1999, A Wavelet Tour of Signal Processing. Academic Press Cambridge. McLachlan G and D. Peel, 2000, Finite Mixture Models, New York, Wiley. McLachlan, G. and T. Krishnan, 1997, The EM algorithms and extensions.Wiley series in probability and statistics.Jonh Wiley &Sons. National Insurance Institute, 2004-2008, Annual Surveys, Jerusalem, Israel. 33 National Insurance Institute, 2008, Poverty and Social Gaps, Annual Report, November, Jerusalem, Israel, 1-54. OECD, 2010, OECD Reviews of Labour Market and Social Policies, Israel,1-288. Paap R., and H.K. van Dijk (1998). Distribution and mobility of wealth of nations. European Economic Review 42, pp. 1269-1293 Palacios-González, F, and García-Fernández R., 2008, Polarization in a mixture of density functions. Paper presented in the Research Workshop of the Israel Science Foundation on Income Polarization: Measurement, Determinant, Implications. Palacios-González, F, and García-Fernández R., 2009, “A multiresolution analysis of income polarization”, European Journal of Economic and Social Systems, 119-142. Palacios-González, F, and García-Fernández R., 2010, An intra-group variance based polarization measure. Available at http://econopapers.repec.org/paper/inqinqwps. Palacios-Gonzalez F., and R. García-Fernández, 2012, Mixtures of Mixtures base don Multiresolution analysis, Communications in Statistics- Simulation and Computation, forthcoming. Pittau M.G. and R. Zelli, 2006, “Trends in income distribution in Italy: A non parametric and a semi-parametric analysis”, Journal of Income Distribution, 15, 90- 118. Pittau M.G., Zelli, R and P.A. Johnson, 2010, “Mixture models and convergence clubs”, Review of Income and Wealth 56(1), 102-122. Rubinstein, Ariel, 2009, Economic Fables, (in Hebrew), Kinneret, Zmora-Bitan, Dvir. Also available in English (2012) under the same title at www.openbook.publishers.com. Shubhasree S. and S. Decornez, 2003, "Income polarization and inequality across countries: an empirical study", Journal of Policy Modeling, January, 25, 335-358. Silber, J., J. Deutsch, and M. Hanoka, (2007) .On the Link between the Concepts of Kurtosis and Bi-polarization.Economics Bulletin, Vol. 4, No. 36 pp. 1-5. Tsui, K and Wang, Y. ,2000, Ordering and New Classes of Polarisation Indices, Journal of Public Economic Theory, 2 (3), pp. 349-363. Wolfson, M. C., 1994, When Inequalities Diverge?, American Economic Review, 84, pp. 353-58. Zhang X., and Kanbur R. , 2001, “What Difference Do Polarization Measures Make? An Application to China”, The Journal of Development Studies, 3/37, 85-98. 34 APPENDIX Figure A.1. Global pdf and group pdfs - 1997 Figure A.2. Global pdf and group pdfs - 1998 Figure A.3. Global pdf and group pdfs – 1999 Figure A.4. Global pdf and group pdfs - 2000 Figure A.5. Global pdf and group pdfs – 2001 Figure A.6. Global pdf and group pdfs - 2002 Figure A.7. Global pdf and group pdfs – 2003 Figure A.8. Global pdf and group pdfs - 2004 0 0,00005 0,0001 0,00015 0,0002 0,00025 0,0003 0,00035 05000 10000 15000 20000 0 0.00005 0.0001 0.00015 0.0002 0.00025 0.0003 0.00035 0 5000 10000 15000 20000 0 0.00005 0.0001 0.00015 0.0002 0.00025 0.0003 0.00035 0 5000 10000 15000 20000 0 0.00005 0.0001 0.00015 0.0002 0.00025 0.0003 0.00035 0 5000 10000 15000 20000 0 0.00005 0.0001 0.00015 0.0002 0.00025 0.0003 0.00035 0 5000 10000 15000 20000 0 0.00005 0.0001 0.00015 0.0002 0.00025 0.0003 0.00035 0 5000 10000 15000 20000 0 0.00005 0.0001 0.00015 0.0002 0.00025 0.0003 0.00035 0 5000 10000 15000 20000 0 0.00005 0.0001 0.00015 0.0002 0.00025 0.0003 0.00035 0 5000 10000 15000 20000 35 Figure A.9. Global pdf and group pdfs - 2005 Figure A.10. Global pdf and group pdfs - 2006 Figure A.11. Global pdf and group pdfs - 2007 Figure A.12. Global pdf and group pdfs – 2008 (three groups) Figure A.13. The components of the polarization index 0 0.00005 0.0001 0.00015 0.0002 0.00025 0.0003 0.00035 0 5000 10000 15000 20000 0 0.00005 0.0001 0.00015 0.0002 0.00025 0.0003 0.00035 0 5000 10000 15000 20000 0 0.00005 0.0001 0.00015 0.0002 0.00025 0.0003 0.00035 0 5000 10000 15000 20000 0 0,00005 0,0001 0,00015 0,0002 0,00025 05000 10000 15000 20000 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 Iia Ig Im 36 Table A.1: Net equivalised mean income by income groups, 2006 prices Table A.2: The weights of the classes in the tri-polar period Lower class Middle Class Top class Overall average Relative income: Upper versus lower class Relative income: Middle versus lower class 1997 1,181 3,084 9,266 3,263 7.8 2.6 1998 1,535 4,007 10,300 3,324 6.7 2.6 1999 1,571 3,981 9,925 3,406 6.3 2.5 2000 1,540 4,149 10,940 3,523 7.1 2.7 2001 1,635 4,243 10,565 3,683 6.5 2.6 2002 1,455 4,021 10,536 3,519 7.2 2.8 2003 1,463 4,245 11,850 3,505 8.1 2.9 2004 1,482 4,256 10,850 3,634 7.3 2.9 2005 1,590 4,686 13,496 3,755 8.5 2.9 2006 1,605 4,785 14,170 3,989 8.8 3.0 2007 1,650 4,560 11,744 4,112 7.1 2.8 2008 1,728 4,725 11,853 4,139 6.9 2.7 Average of yearly ratios of the means 7.4 2.8 lower class middle class upper class sum of weights 1998 0.410 0.538 0.052 1.000 1999 0.431 0.491 0.078 1.000 2000 0.383 0.562 0.055 1.000 2001 0.401 0.522 0.077 1.000 2002 0.353 0.585 0.062 1.000 2003 0.376 0.584 0.040 1.000 2004 0.378 0.557 0.065 1.000 2005 0.409 0.553 0.038 1.000 2006 0.374 0.584 0.042 1.000 2007 0.366 0.549 0.086 1.000 2008 0.393 0.525 0.083 1.000 37 Table A.3: The Polarization measure and its components Table A.4 The Polarization measure and other tri-polar measures P Interval of Conf. 95% ZK Interval of Conf. 95% 1998 0.194 0.144 0.250 3.107 2.331 4.104 1999 0.200 0.143 0.246 3.199 2.297 4.027 2000 0.185 0.142 0.243 2.983 2.260 3.954 2001 0.190 0.140 0.240 3.149 2.218 3.885 2002 0.181 0.139 0.237 2.834 2.173 3.820 2003 0.180 0.137 0.234 2.789 2.124 3.758 2004 0.199 0.134 0.232 3.203 2.071 3.701 2005 0.178 0.132 0.230 2.773 2.014 3.648 2006 0.152 0.129 0.228 2.604 1.952 3.598 2007 0.206 0.126 0.226 3.427 1.887 3.553 2008 0.217 0.123 0.225 3.163 1.817 3.512 ZKN Interval of Conf. 95% ER Interval of Conf. 95% 1998 0.757 0.703 0.830 0.213 0.198 0.235 1999 0.762 0.700 0.824 0.218 0.198 0.234 2000 0.749 0.697 0.818 0.212 0.198 0.234 2001 0.759 0.694 0.813 0.214 0.199 0.233 2002 0.739 0.690 0.808 0.208 0.199 0.233 2003 0.736 0.686 0.803 0.218 0.199 0.233 2004 0.762 0.682 0.798 0.219 0.199 0.233 2005 0.735 0.677 0.794 0.231 0.199 0.233 2006 0.723 0.672 0.790 0.224 0.199 0.233 2007 0.774 0.667 0.786 0.217 0.198 0.233 2008 0.760 0.662 0.783 0.214 0.198 0.233 Iia Ig Im P 1998 0.652 0.667 0.446 0.194 1999 0.596 0.667 0.504 0.2 2000 0.655 0.667 0.425 0.185 2001 0.603 0.667 0.473 0.19 2002 0.671 0.667 0.405 0.181 2003 0.683 0.667 0.396 0.18 2004 0.688 0.667 0.434 0.199 2005 0.63 0.667 0.424 0.178 2006 0.575 0.667 0.397 0.152 2007 0.686 0.667 0.451 0.206 2008 0.685 0.667 0.474 0.217 38 Table A.5. An Index (1998=1) of the measures in table A.3 during the Tri-polar period P ZK ZKN ER 1998 1 1 1 1 1999 1.032 1.029 1.007 1.024 2000 0.956 0.960 0.990 0.996 2001 0.981 1.013 1.003 1.004 2002 0.934 0.912 0.977 0.977 2003 0.931 0.898 0.973 1.021 2004 1.028 1.031 1.007 1.029 2005 0.920 0.893 0.972 1.083 2006 0.786 0.838 0.955 1.049 2007 1.064 1.103 1.023 1.017 2008 1.118 1.018 1.004 1.006 Please note: You are most sincerely encouraged to participate in the open assessment of this discussion paper. You can do so by either recommending the paper or by posting your comments. Please go to: http://www.economics-ejournal.org/economics/discussionpapers/2012-55 The Editor © Author(s) 2012. Licensed under a Creative Commons License - Attribution-NonCommercial 2.0 Germany