Abstract
This chapter deals with applications of the GMD and the Gini coefficient in statistics. It presents an application which replicates the ANalysis Of VAriance (ANOVA) and is referred to as ANalysis Of GIni (ANOGI).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
An alternative methodology for analyzing the melting pot policy is to compare the earnings of second generation of immigrants with the earnings of first generation (or the earnings of the natives) while controlling for other effects (Borjas (2006) and the references therein). However, this methodology requires longitudinal data and other characteristics of the population, while the methodology presented here can be applied to cross-sections. The price paid for the use of our methodology is that we end up with descriptive statistics, while regression-based methodologies offer a detailed analysis and the possibility to find causal relationship. For a regression-type analysis of discrimination and second generation analysis of the Israeli labor market see, among others, Semyonov and Cohen (1990) and Cohen and Haberfeld (1998).
- 2.
By poor (rich) it is meant that the income is below (above) a certain level.
- 3.
An additional concept that is used extensively in the literature is polarization (see, e.g., Duclos, Esteban and Ray (2003) and the references there). However, further research is needed to establish the relationship between stratification and polarization.
- 4.
Glazer (1993) considers the decline in the positive attitude toward assimilation as an ideal for migrants in the USA.
- 5.
Among the other aspects of assimilation that are not dealt within this chapter it is worth mentioning the acquisition of native language skills. See among others Chisweek (1978, 1998, 1999); Beenstock (1996) and the literature therein. Easterly and Levine (1997) relate ethnic diversity as impediment to growth.
- 6.
The classification of the ethnic group by the origin of the father is dictated by the available data.
- 7.
The equivalence scale used for comparison of economic well-being of households of different sizes is one-person: 1.25, two: 2.0, three: 2.65, four: 3.2, five: 3.75, six: 4.25, seven: 4.75, eight: 5.2 and 0.4 for each additional person. For additional explanations see Statistical Abstract of Israel, 2004, No. 55, p. 46.
- 8.
Data limitations do not allow us to refer to the place of birth of the mother.
- 9.
Note, however, the difference between “others” and “immigrants.” Immigrants in an early survey may be defined as foreign born in a later period.
- 10.
The disclaimer that the coverage of this population has changed over time, which may bias the results should be added.
- 11.
We do not have a good explanation to this result. It may be caused by the members of the Christian-Arab population who were with relatively high income and emigrated from the country.
References
Borjas, G. J. (2006). Making it in America: Social mobility in the immigrant population. NBER WP No. 12088 (March).
Cohen, Y., & Haberfeld, Y. (1998). Second-generation Jewish IMMIGRANTS in Israel: Have the Ethnic gaps in schooling and earnings declined? Ethnic and Racial Studies, 21(3 (May)), 507–528.
Cowell, F. A. (1980). On the structure of additive inequality measures. Review of Economic Studies, 47, 521–531.
Easterly, W., & Levine, R. (1997). Africa growth tragedy: Policies and ethnic divisions. Quarterly Journal of Economics, 112, 1203–1250.
Frick, R. J., Goebel, J., Schechtman, E., Wagner, G. G., & Yitzhaki, S. (2006). Using analysis of Gini (ANOGI) for detecting whether two sub-samples represent the same universe: The German Socio-Economic Panel study (SOEP) experience. Sociological Methods and Research, 34(4 (May)), 427–468.
Glazer, N. (1993). Is assimilation dead? Annals of the American Academy of Political Science, 530, 122–136.
Heller, J., & Yitzhaki, S. (2006). Assigning fossil specimens to a given recent classification when the distribution of character variation is not normal. Systematics and Biodiversity, 4(2), 161–172.
Hirschman, C. (1983). America’s melting pot policy reconsidered. Annual Review of Sociology, 9, 397–423.
Lambert, P. J., & Aronson, J. R. (1993). Inequality decomposition analysis and the Gini coefficient revisited. Economic Journal, 103, 1221–1227.
Lambert, P. J., & Decoster, A. (2005). The Gini coefficient reveals more. Metron, LXIII(3), 373–400.
Lissak, M. (1999). The mass immigration in the fifties: The failure of the melting pot policy. The Bialik Institute: Jerusalem (Hebrew).
Milanovic, B., & Yitzhaki, S. (2002). Decomposing world income distribution: Does the world have a middle class? Review of Income and Wealth, 48(2 (June)), 155–178.
Pyatt, G. (1976). On the interpretation and disaggregation of Gini coefficient. The Economic Journal, 86(342), 243–255.
Semyonov, M., & Cohen, Y. (1990). Ethnic discrimination and the income of majority-group workers. American Sociological Review, 55(1 (February)), 107–114.
Shorrocks, A. F. (1984). Inequality decomposition by population subgroups. Econometrica, 52(6), 1369–1385.
Yitzhaki, S. (1994a). Economic distance and overlapping of distributions. Journal of Econometrics, 61, 147–159.
Yitzhaki, S. (1994b). On the progressivity of commodity taxation. In W. Eichhorn (Ed.), Models and measurement of welfare and inequality (pp. 448–465). Heidelberg: Springer-Verlag.
Yitzhaki, S., & Lerman, R. I. (1991). Income stratification and income inequality. Review of Income and Wealth, 37(3 (September)), 313–329.
Yitzhaki, S., & Schechtman, E. (2009). The “Melting Pot”: A success story? Journal of Economic Inequality, 7, 137–151.
Zangwill, I. (1914). The melting pot: Drama in four acts. New York: Macmillan.
Author information
Authors and Affiliations
Appendices
Appendix 22.1
Tables 22.4 (N) and 22.5 (W) present the ranking of each group in terms of the other for the 3 years, for the two alternative definitions of the Israeli group.
Each entry in the tables presents the average rank of the members of the group indicated in the row, had they been ranked according to the ranking of the group indicated in the column. Looking at Table 22.4 (N) we see that the average rank of Jews born in Asia/Africa, had they been ranked according to Jews from Europe/America is 0.26 in 1979, 0.31 in 1992, and 0.37 in 2002. This is an indication that over time the relative status of Jews from Asia/Africa has improved. Looking at the column of Israeli born, the ranking in terms of Europe/America has slightly declined from 0.43 in 1979 to 0.42 in 1992, but has increased to 0.47 in 2002. On the other hand, the average ranking of the Arab population in terms of European/American born has increased from 0.12 in 1979 to 0.15 in 1992 but declined later (in 2002) to 0.13.Footnote 10
Tables 22.6 (N) and 22.7 (W) present the overlapping index (and standard error) of each group in terms of the other for the 3 years, for the two alternative definitions of the Israeli group. Each column represents the reference group (represented by the index j in the decomposition of Oji), while the row represents i. Multiplying the elements of each row by the share in the population of the group and summing up yields the overlapping of the group with the entire population. That is, each row represents the overlapping of the group with other groups (and with itself. The overlapping of a group with itself is 1). The first line says that Europe/America is a stratified group with respect to Asia/Africa (0.79), but it is less of a group when the reference group is Israeli born. It is definitely a group with respect to the “Others” group. In 1979 the group “Others” included several rich people so that it became a non-group with respect to all other groups.Footnote 11 However, in 1992 the “Others” became a distinct group relative to all others except immigrants, while in 2002 they were left behind by almost all other groups. Over time the groups Asia/Africa and Europe/America became less distinct from each other with the overlapping indices increasing from (0.79; 0.85) in 1979 to (0.92; 0.94) in 2002.
Appendix 22.2: ANOVA
In addition to the decomposition of Gini, a decomposition of the variance was obtained by ANOVA. Note that there are only two components: between (intra) and within (inter). The results are given in Table 22.8. We note that the question asked by ANOVA is different—it is meant to compare the means of the subpopulations. As can be seen from the last column (the F ratio), the between MS is (relatively) larger for definition N for the 3 years under study, strengthening our conclusion that definition N is a better stratifier.
Rights and permissions
Copyright information
© 2013 Springer Science+Business Media New York
About this chapter
Cite this chapter
Yitzhaki, S., Schechtman, E. (2013). An Application in Statistics: ANOGI. In: The Gini Methodology. Springer Series in Statistics, vol 272. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4720-7_22
Download citation
DOI: https://doi.org/10.1007/978-1-4614-4720-7_22
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-4719-1
Online ISBN: 978-1-4614-4720-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)