Putnam s Social Capital Index is flawed by the Population Size Effect: Evidence for cultural embeddedness in social capital. Shinichi KUSAKABE Graduat

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1 Putnam s Social Capital Index is flawed by the Population Size Effect: Evidence for cultural embeddedness in social capital. Shinichi KUSAKABE Graduate School of Integrated Arts and Sciences, Hiroshima University Abstract A previous report (Kusakabe, 2011, in Japanese) warned about an interpretation of a scatter diagram, with coordinates expressed in percentages or per capita data. Since most of the social indicators obey the Law of Power Function (Kusakabe, 2011), the scatter diagram of such indicaters in terms of ratio (percentage or per capita) inevitably shows positive or negative spurious correlations in cross-section data analysis, irrespective of the causation. These spurious correlations are induced by the population size effect. Here, I will critically examine Putnam's Social Capital Index (SCI) in Bowling Alone, Part 4. Putnam's SCI is highly correlated with the population size (Fig.12; R=-0.487**). Path analysis shows a clear effect of population size on Putnam s SCI (Fig. 15(2)). Thus, Putnam s SCI inevitably induces both spurious correlations with most of the various social indicators and strong bias in his estimates for Social Capital Index. However, if we exclude the population size effect from Putnam's SCI using a regression method, the resulting regression residuals (adjusted SCI or the Regression-based score, R-score, defined by Kusakabe 2002a,b,c in Japanese) almost coincide with a Regression-based score of the number of nonprofit organizations in the United States (Fig.16(1),(2), R=0.663**). Both of the Regression-based scores of Putnam s SCI(adjusted SCI) and those of NPOs significantly correlate with the Regression-based scores of murders (Fig.21(1),22(1); R= **and **, respectively). Path analyses on both Putnam s adjusted SCI and R-score for NPOs clearly show the strong effect on the R-score for murders (Fig.21(2),22(2); pass coefficient, ** and **, respectively). Additionally, R-score for NPOs show the strong effect on the R-score for suicides (Fig.24(2); pass coefficient **). These results disclose firm evidence for the cultural embeddedness of social capital in the United States. Thus, social capital, indeed, can be measurable with these R-scores for the number of nonprofit

2 organizations and Putnam s adjusted SCI (Regression-based SCI score). The revised version of Putnam s barometric map of America s Social Capital (Figure 30) is successfully presented in this study in terms of R-score for nonprofit organizations in the United States of America. Keywords: Social Capital, Social Capital Index(SCI), Cultural embeddedness, Non-profit organization, regression analysis, Regression-based score(r-score) (CSI) Putnam Social Capital Index(SCI) (Regression-based score) Putnam SCI what we can measure we should measure; what we cannot measure at present, we should endeavor to make measurable Motoo Kimura, 1983 Social Capital Loury(1977) Coleman(1988,1990) Bourdieu(1980), Putnam(1993,2000) PutnamMaking Democracy Work (1993) 2003 Coleman, Bourdieu Putnam Kawata(2010) (2003) Social Overhead Capital SOC Physical Capital Infrastructural Capital Social Capital

3 Social Capital Index Woolcock(2010) (2009) 90 NPO 2 Putnam 2Making Democracy Work Bowling Alone Putnam (2003) (2010) (2011) Durlauf(2002) Halpern(2005) Field(2008) Putnam Social Capital Index (SCI ) Putnam 2004, 2007, 2011, 2009, Nishide 2009, 2011Putnam SCI (2003) Civil Society Index(CSI ) ( 2003, 2005, Nishide and Yamauchi 2005) PutnamBowling Alone, Part 4 SCI (Wright 1921, 1968, Li 1975, Duncan 1975) 23

4 Y = a + b 1 *X 1 + b 2 *X 2 X 1 (GDP) GDP Regression-based score ( 2002a,b,c) (error) (residual) (regression deviation) ( 2002a,b,c) Weisberg 1985 β 決定係数 :R 2 相関係数 :R 郵便物数刑犯罪件数会社数県民所得警察官数献血者数 NPO NPO 検挙件数自殺数共同募金寄付金地方交付税 (Table 1. The regression analysis for the various logtransformed social indicators on population size. β is the slope of the regression line, and R, R 2 are the correlation coefficient and the coefficient of determinant, respectively.) GDP (part correlation or semi-partial correlation) (Figure 15(1),(2)) (partial correlation) Ezekiel 1930, 1941, 2002 Figure 16, 21, 22, (1),(2) 3 2 (SCI) (CSI) NPO 2 Putnam SCINPO 3Nonprofit Almanac(GDP) (2003)

5 Social Capital Index 表 2 Prefecture SCI by Cabinet Yamauchi's CSI NPO(2003) NPO(2010) SCI Rank CSI Rank number R-score Rank number R-score Rank 北海道青森岩手宮城秋田山形福島茨城栃木群馬埼玉千葉東京神奈川新潟富山石川福井山梨長野岐阜静岡愛知三重滋賀京都大阪兵庫奈良和歌山鳥取島根岡山広島山口徳島香川愛媛高知福岡佐賀長崎熊本大分宮崎鹿児島沖縄総数 (Table 2. Social Capital Index (SCI) proposed by the Cabinet Office of the Japanese government, Civil Society Index (CSI) by Yamauchi, and Regression-based score (R-score) for the number of non-profit organizations in 2003 and 2010.)

6 Kruskal and Tanur %40.1% 95% 1000 Figure 1(1) per capita The occurrence of the recognized criminals (1000 per capita) y = x R 2 = 0.228,R= The rate of volunteering (%) (1) The relationship between the occurrence of recognized criminals and the rate of volunteering. 1 per capita per capita Figure 1(1), R=-0.478** 3GDP Figure 1(2) (-0.500**) R 2 =1.000** GDP NPO GDP 2002a,b,c,2004 Figure ** (2) Path analysis for the effect of population size on the rate of volunteering. Regression-based score for GDP of the tertiary industry (GDP3) is set as a control. Figure 1. The effect of population size on volunteering rate. Figure 2. Path analysis for the effect of population size on the occurrence of recognized criminals.

7 Social Capital Index (R 2 =0.944**) 2011 (2003) , , 0.244, (2003) web 10 SCI SCI Figure 3, R=0.963** Figure 4, R=-0.366** SCI Figure 5, R=-0.614** SCI Figure 6(1), R=-0.602** SCI NPO SCI NPO Log Sample Size y = x R 2 = 0.927,R= Log Population Size Degrees of associations with neighbors(%) y = x R 2 = 0.134,R= Log Sample Size Figure 3. The relationship between the logarithm of the sample size and the logarithm of the population size. Figure 4. The relationship between Log sample size and the degrees of associations with neighbors.

8 SCI GDP R-score Figure 6(2) SCI **(R 2 =0.369**) SCI SCI Figure 7 SCI 2.0 Social Capital Index by the Cabinet Office y = x R 2 =0.363,R= Log Population Size (1) The relationship between Log population size and SCI by JCO. Social Capital Index by the Cabinet Office y = x R 2 = 0.377,R= Log Sample Size Figure 5. The relationship between Social Capital Index (SCI) by the Japanese Cabinet Office (JCO) and the Log sample size. (2) Path analysis for the effect of population size on the number of recognized criminals. Figure 6. The effect of population size on the number of recognized criminals. Figure 7. Path analysis for the effect of population size on the the number of recognized criminals.

9 Social Capital Index R 2 =0.952** SCI SCI (Civil Society Index, CSI ) CSI NPO Salamon(1999, 2004, 2012) size effect y x y = αx β β β β 1( ) β 1 β 1 β R CSI (Figure 8(1)) CSI CSI 3 GDP Regression-based score, R-score Figure 8(2) CSI ( **R 2 =0.310** CSI CSI Yamauchi's Civil Society Index y = x R 2 = 0.310,R= Log Population Size (1) The relationship between Log population size and Civil Society Index (CSI) by Yamauchi. (2) Path analysis for the effect of population size on CSI. R-score for GDP of the tertiary industry (GDP3) is set as a control. Figure 8. The effect of population size on CSI by Yamauchi.

10 Figure 9 ( 0.935**)CSI R 2 =0.946**SCI CSI SCICSI Figure ** SCI CSI 2003; 2003,2005; Nishide and Yamauchi 2005 SCICSI 2002a,b,cSalamon Global Civil Society Index Sakamoto's Happiness index 8 y = x R 2 = 0.281,R= Log Population Size Figure 9. Path analysis for the effect of population size on the number of recognized criminals. (1) The relationship between Log population size and Sakamoto s HI. Yamauchi's Civil Society Index y = x R 2 = 0.270, R= Social Capital Index by Cabinet Office Figure 10. The relationship between SCI by JCO and CSI by Yamauchi. (2) Path analysis for the effect of population size on Sakamoto s HI. R-score for GDP of the tertiary industry (GDP3) is set as a control. Figure 11. The effect of population size on Sakamoto s Happiness Index (HI).

11 Social Capital Index per capita Putnam SCI 47 Figure 11(1) (R=-0.530**) 3 GDP GDP3 Figure 11(2) GDP PutnamBowling Alone 20 Social Capital Putnam's Social Capital Index y = x R 2 =0.237,R= Log Population size Figure 12. The relationship between Log population size and Putnam s Social Capital Index (SCI) in the United States. Index(SCI ) (http//bowlingalone. com/?page_id=13) Putnam SCI 14 SCI per capita NPO 14 (2010) Putnam (per capita) Putnam SCIFigure 12 (R=-0.487**) Putnam Bowling Alone1411 Putnam SCI Putnam Putnam SCI 1

12 , Regression-based score 2002a,b,c (error) (outlier) 2002a,b,c 20 per capita Gould(1980) (Weisberg 1985; Myers 1990; Cook and Weisberg 1994,1999) NPO Nonprofit Almanac NPO 50NPO3 per capita per capita NPO 2002a,b,cMontana Wyoming New York, Pennsylvania California Putnam SCI NPO Putnam SCI p.293 in Bowling Alone NPO Figure 13(R=0.953**) NPO NPO 3 10 Figure ** 0.968** NPO Putnam SCI Putnam SCI

13 Social Capital Index 表 3 Putnam's SCI NPO(1992) NPO(2005) State SCI Rank adj SCI Rank Number R-score Rank Number R-score Rank Connecticut Maine Massachusetts New Hampshire Rhode Island Vermont New Jersey New York Pennsylvania Illinois Indiana Michigan Ohio Wisconsin Iowa Kansas Minnesota Missouri Nebraska North Dakota South Dakota Delaware Florida Georgia Maryland North Carolina South Carolina Virginia West Virginia Alabama Kentucky Mississippi Tennessee Arkansas Louisiana Oklahoma Texas Arizona Colorado Idaho Montana Nevada New Mexico Utah Wyoming Alaska California Hawaii Oregon Washington Total ( ) Putnam SCIAlaska Hawaii. Table 3. Putnam's SCI data and the Regression-based score (R-score or adj SCI). The R-score of the size of nonprofit organizations are shown both for 1992 and The adj SCI is calculated for the population size in 1992.)

14 NPO 1992 Putnam SCI 3 SCI SCI(adjusted SCI or Regression-based score) adj SCI Putnam SCI 15(1) 0.866** Putnam SCI, adj SCI Log Number of nonprofit Organizations Regression-based Score for NPOs in y = x R 2 =0.909,R= Log Population Size Figure 13. The relationship between Log population size and Log number of nonprofit organizations(npos) in the United States y = x R 2 =0.943,R= Regression-based Score for NPOs in 1992 Figure 14. The relationship of the R-score for the number of nonprofit organizations (NPOs) between 1992 and Figure 15(2)Putnam SCI **; R 2 =1.000** SCI 2 (0.25) adj SCI SCI 2 (0.75) R 2 =1Putnam SCI25% adj SCISCI (0.866) Figure 15(2) adj SCI NPOFigure 16(1) 0.663** adj SCI NPO adj SCI NPO Figure 16(2) Putnam's SCI y = x R 2 =0.750,R= adjusted Putnam's Social Capital Index (1) The relationship between Putnam s SCI and the adjusted SCI. (2) Path analysis for the effect of population size on Putnam s SCI. Figure 15. The effect of population size on Putnam s SCI.

15 Social Capital Index 0.663** Figure 16(1) adj SCI NPO Putnam SCI 14 adj SCI 1NPO Putnam SCI, R-score for NPOs y = x R 2 =0.439,R= adjusted Putnam's SCI (1) The relationship between adjusted Putnam s SCI and R-score for nonprofit organizations (NPOs). (2) Path analysis for the effect between R-score for NPOs and adjusted Putnam s SCI. Figure 16. The relationship between R-score for NPOs and adjusted Putnam s SCI. NPO NPO Putnam SCI Putnam Putnam SCI Alaska Hawaii 48 Figure 17(per capita) SCI (R=-0.804) 2005 Putnam Figure 84(p.309 in Bowling Alone ) Figure 18 β=1.328 per capita Putnam SCI (Figure 12) (Figure17) Putnam SCI Figure19(1) ** Putnam SCI Figure 19(2) 0.797**

16 Putnam SCI ** Putnam SCI adjsci (Figure 20(1),(2)) adj SCI adj SCI 95%(R 2 =0.951= ) Murder Rate y = x R 2 =0.646,R= Putnam's Social Capital Index Figure 17. The relationship between Putnam s SCI and the murder rate (per capita). This correlation is spurious due to the popultion size effect. ( =0.878)SCIadj SCI ( =0.073) Putnam SCI adj SCI 4 NPO 2005 adj SCI Putnam SCIFigure 21(1) ** Log Number of Murders y = x R 2 =0.470,R= Putnam's SCI (1) The relationship between Putnam s SCI and Log number of murders. 8 Log Number of Murders y = x R 2 =0.887,R= Log Population Size Figure 18. The relationship between Log number of murders and Log population size. (2) Path analysis for the effect of Putnam s SCI on the number of murders. Figure 19. The effect of Putnam s SCI on the number of murders.

17 Social Capital Index **(Figure 21(2)) Figure21(1) adjsci **, Figure22(1),(2) NPO ** 40% (R 2 =0.367) NPO SCI NPO PutnamDurkheim(1897) Durkheim(1888) per capita Figure 23 adj SCI NPO adj SCI NPO 8 Log Number of Murders y = x R 2 =0.497,R= adjusted Putnam's SCI (1) The relationship between adjusted SCI and Log number of murders. R-score for murders y = x R 2 =0.602,R= Putnam's adjusted SCI (1) The relationship between adjusted Putnam s SCI and R-score for murders. (2) Path analysis for both the effect of adjusted SCI and population size on the number of murders. Figure 20. The effect of population size and adjusted Putnam s SCI on the number of murders. (2) Path analysis for the effect of adjusted Putnam s SCI on R-score for murders. Figure 21. The effect of adjusted Putnam s SCI on R-score for murders.

18 表 4 Putnam's SCI Murders(2005) Suicides(2005) GDP(2005) NPO(2005) R-score Rank Number R-score Rank Number R-score Rank GDP R-score Rank R-score Rank Connecticut Maine Massachusetts New Hampshire Rhode Island Vermont New Jersey New York Pennsylvania Illinois Indiana Michigan Ohio Wisconsin Iowa Kansas Minnesota Missouri Nebraska North Dakota South Dakota Delaware Florida Georgia Maryland North Carolina South Carolina Virginia West Virginia Alabama Kentucky Mississippi Tennessee Arkansas Louisiana Oklahoma Texas Arizona Colorado Idaho Montana Nevada New Mexico Utah Wyoming California Oregon Washington (Table 4. The R-score for Putnam'sSCI, murders, suicides, GDP and NPOs, respectively, after excluding Hawaii and Alaska. The ranks in murders and suicides are in ascending order, and the others are descending. All of the R-scores are calculated for the population size in 2005.)

19 Social Capital Index NPO Figure 24 NPO Figure 25 Putnam14 NPO R-score for murders y = x R 2 =0.367,R= R-score for NPOs (1) The relationship between R-score for nonprofit organizations (NPOs) and R-score for murders. Putnam SCI NPO GDP 2003b (POP) GDP(Murder)(Suicide) Putnam SCI NPO 5 AMOS Figure 26 Log Number of suicides (1) Japan y = x R 2 = 0.947,R= Log Population Size Log Number of Suicides y = x R 2 = 0.934,R=0.966 (2) Path analysis for the effect of R-score for NPOs on R-score for murders. Figure 22. The effect of R-score for NPOs on R-score for murders (2) United States of America Log Population Size Figure 23. The relationship between Log number of suicides and Log population size.

20 10%5% Putnam SCI NPO NPO 10%5% FBI 9Figure 26 5NPO R-score for suicides y = x R 2 = 0.154,R= R-score for nonprofit organizations (1) The relationship between R-score for nonprofit organizations (NPOs) and R-score for suicides. Putnam SCI NPO Granovetter(1985) embeddedness() (Cultural embeddedness) R-score for murders y = x R 2 = 0.060,R= R-score for suicides (1) The relationship between R-score for suicides and R-score for murders. (2) Path analysis for the effect of R-scre for NPOs on R-score for suicides. Figure 24. The effect of R-score for NPOs on R-score for suicides. (2) Path analysis for R-scre for suicides and R-score for suicides. Figure 25. The effect between R-score for suicides and R-score for murders.

21 Social Capital Index 2 = df = 3 Prob= GFI = AIC = (1) Putnam's Social Capital Index 2 = df=1 Prob = GFI = AIC = (2) Non-profit Organizations Figure 26. Summary of path analyses among the social indicators. (The effect of number of nonprofit organizations on the crimes listed on FBI report (2009) on line. The analyses were carried out based on the similar structural equation recursive model in Fig. 26. All of the path coefficients are statistically highly significant.)

22 Putnam Bowling Alone SCI11 SCI (civic engagement) (p.295, Putnam 2000) 3 NPO Tocqueville 1832 Putnam Bowling Alone Putnam 2 (2005) (2009) Salamon (1999, 2004) NPO OECDWorld Value Survey(WVS) 2 % per capita per capita Drucker The Age of Discontinuity1992

23 Social Capital Index 1988 web 2001 NPO Kawachi1997, 1999 Figure 27(1) Kawachi (1997)Figure 1 (R=0.712) Figure 27(2) 0.442**Kawachi (1999) Percent Responding: "Most people would try to take advantage of you if they got the chance." Percent Responding: "Most people would try to take advantage of you if they got the chance." y = x R 2 = 0.507,R= Robin Hood Index (1) The reproduced Figure 1 by Kawachi et al. (1997). 0 y = x R 2 =0.195,R= Log Population Size (2) The relationship between population size and the percentage of positive responses. Figure 27. The population size effect in Kawachi et al. (1997).

24 per capita (2) NPO NPO Figure ** Figure NPO0.971** NPO NPO 22010NPO9 5 Figure 29 NPO NPO NPO2003a Figure 29 NPO Putnam Bowling Alone Making Democracy Work R-score for the number of NPOs(2010) y = x R 2 =0.555,R= R-score for the number of NPOs(2003) Figure 28. The relationship of the R-score for the number of the Japanese nonprofit organizations (NPOs) between 2003 and 2010.

25 Social Capital Index Putnam (p in Putnam 1993) Putnam Bowling Alone 293 Putnam SCI 2005NPO 10 5 Figure Social Capital in Japan in terms of R-score for nonprofit organizations Rank 1~9 10~18 19~27 28~36 37~47 Figure 29. Social Capital in Japan in terms of R-score for the number of nonprofit organizations (2010) in Table 2.

26 Putnam p in Bowling Alone Putnam Putnam Social Capital map Figure 30 Putnam SCI a,b,c per capita per capita 1 1 Duncan 1975 Excel GDPNPO 5 Figure 26 NPO Maddala 2001 Social Capital in the United States in terms of R-score for nonprofit organizations Rank 1~10 11~20 21~30 31~40 41~50 Figure 30. Social Capital in the United States in terms of R-score for the number of nonprofit organizations (2005) in Table 3.

27 Social Capital Index per capita And still the knowledge society with a social mobility that threatens to become rootless, with its other half, with its dissolution of ties of farm and small town and their narrow horizons needs community, freely chosen and yet a bond. Peter F. Drucker, (2) Putnam Putnam SCI Putnam SCI NPO Granovetter(1985) embeddedness cultural embeddedness NPO Putnam Social Capital Index Joseph Lauer (2007) (2011) (2011) 1994, R.G. 2005, R.G (2002a) IV, (2002b) NPO NPO II, (2002c) NPO NPO NPO, The Nonprofit Review, 2: (2003a) NPO : (2003b) II, (2004) (3), 552, (2011)

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29 Social Capital Index Capital and Self-Rated Health: A Contextual Analysis. Am. J. of Public Health, 89: Kawata, J. (2010) Social Capital, Trust, and Democracy: Asia in Comparative Perspective. In No. 150, Social Capital and Citizen Participation. Kansai University Research Publications. Kimura, M. (1983) The Neutral Theory of Molecular Evolution. Cambridge University Press. Kruskal, W. and Tanur, J, M. (1978) International Encyclopedia in Statistics. Collier Macmillan. Li, C. C. (1975) Path Analysis a primer. The Boxwood Press, Pacific Grove, CA. Loury, G. (1977) A dynamic theory of income differences. Chapter 8 of Women, minorities, and employment discrimination, ed. P. A. Wallace and A Le Mund. Lexington, Mass. Lexington Books. Maddala, G. S. (2001) Introduction to Econometrics 3 rd ed. John Wiley. McLean, S. L., Schultz, D. A., Steger, M. B. ed. (2002) Social Capital: Critical Perspectives on Community and "Bowling Alone. New York University Press. Myers, R. H. (1990) Classical and Modern Regression with Applications, 2nd edition, Boston: PWS-KENT Publishing Company. Nishide Yuko (2009) Social Capital and Civil Society in Japan. Tohoku University Press, Sendai, Japan. Nishide Yuko and Yamauchi Naoto (2005) Social Capital and Civic Activities in Japan. The Nonprofit Review, Vol. 5, No. 1, Putnam, R. D. (1993) Making Democracy Work: Civic Traditions in Modern Italy. Princeton University Press, Princeton, NJ. Putnam, R. D. (2000) Bowling Alone: The Collapse and Revival of American Community. Simon and Schuster Paperbacks,NY. (http//bowlingalone.com /?page_id =13) Putnam, R. D. and Feldstein, L. M. (2003) Better Together. Simon and Schuster, NY. Salamon, L. M. (1999) Global Civil Society. The Johns Hopkins University Press. Salamon, L. M. (2004) Global Civil Society. Kumarian Press. Salamon, L. M. (2012) The State of Nonprofit America. Brookings Inst. Steel, R. G. D. and Torrie, J. H. (1980) Principles and Procedures of Statistics, A Biometrical Approach. 2nd.ed. McGraw-Hill. Suicide statistics. http// html#2005. Tocqueville, A. de. (1835) Democracy in America. U. S. Energy Information Administration. Real Gross Domestic Product by State. (http// Weisberg, S. (1985) Applied Linear Regression, 2nd edition, John Wiley & Sons, Inc. Wing, K. T., Pollak, T. H. and Blackwood, A. (2008) The Nonprofit almanac The Urban Institute Press, W,D. C. Woolcook, M. (2010) The Rise and Routinization of Social Capital, Ann. Rev. Polit. Sci. 13: Wright, S. (1921) Correlation and causation. J. Agric. Res., 20, Wright, S. (1968) Evolution and the genetics of population, Vol. 1. Genetic and biometric foundations. Chicago: Univ. of Chicago Press, Zar, J. H. (1974) Biostatistical Analysis. Prentice-Hall.

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