Skip to main content


Log in

Spatial clustering patterns of children in single-mother households in Japan

  • Original Paper
  • Published:
Journal of Spatial Econometrics


We examine spatial clustering patterns of children living in single-mother households in Japan, where poverty risk among these children is extremely high. Our analysis employs spatial panel data at the municipal level in 2000, 2005, and 2010. The Global and Local Moran’s I statistics reveal significant spatial clustering of children in single-mother households. The spatial clusters of these children are located mostly in Hokkaido and western Japan. The spatial clustering patterns of younger children (under the age of 6) and older children (aged 6–18) are similar, but the older children are more spatially clustered. Moreover, from 2000 to 2010, the number of significant spatial clusters of high proportions of children in single-mother households (high-high clusters) increased for the older children but decreased for the younger children. These results suggest that the older children in single-mother households are more residentially clustered, and this trend intensified over the 10-year period. The results of the spatial fixed-effects models indicate that the proportions of children in single-mother households are high in areas with low income and a high out-migration rate. The spatial fixed-effects models exhibit the presence of significant indirect effects (spillover effects), suggesting the importance of addressing spatial dependency. The results of this study can help identify areas that need policy attention.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others


  1. The figures are from the Census of Japan (SBJ 2017). These numbers include households in which the mother and children reside with other household members such as grandparents.

  2. In the rest of the article, we use the term “younger children” for those younger than 6 years-old, and “older children” for those aged 6–18.

  3. The number of single-mother households decreased from 2010 to 2015, but this decrease is at the same rate as the number of households with children during the same period.

  4. Those single-parent households exclude members other than a parent and children. The figure is 85% if the other members (e.g., grandparents) are included.

  5. Relative disposable income is mean disposable (after tax and transfer) equalized income as a proportion of disposable equalized income for individuals in households with two or more adults, a working age head, no children and one worker (OECD 2018a).

  6. In the published municipal-level census data of Japan, the numbers of single-mother households that include members other than mothers and children are available only from 2010.

  7. In 2006, Kamikuishiki-mura (a municipality in Yamanashi prefecture) was divided into two already existing different municipalities, a rare style of division. For this particular division, we calculated population-weighted data for each divided portion of the municipality, using the population at the level of blocks (kihontaiku), a spatial unit smaller than municipalities, and then merged the population-weighted data with the data in the existing municipalities.

  8. We also experimented with the crude divorce rate (the number of divorces per 1000 population) and divorce-to-marriage ratio (the number of divorces to the number of marriages). We decided to use the refined divorce rate, which is considered most appropriate among the three measures.

  9. The remote-area childcare centers are non-licensed centers located at sparsely populated area. They are run under less strict standards than the licensed childcare centers.

  10. Wooldridge (2016 p. 437, Example 14.2) uses a similar approach, including interactions of education with year dummies to examine whether the returns to education change over time.

  11. We also calculated differential Moran’s I statistics (Anselin 2019), or Global Moran’s I statistics for the changes in the proportions of children under ages 6 and 18 in single-mother households from 2000 to 2010. The resultant statistics are significant at the 1% level.


  • Abe A (2018) Long-term trends in the relative poverty rates: 1985 to 2015. [Soutaitekihinkonritsu no Choukiteki Doukou: 1985–2015]. In a Report on the research to build the frontier of “poverty studies”, JSPS Grants-in-Aid for Scientific Research (B). (in Japanese)

  • Allard SW (2017) Places in need: the changing geography of poverty. Russell Sage Foundation, New York

    Google Scholar 

  • Altonji JG, Mansfield RK (2018) Estimating group effects using averages of observables to control for sorting on unobservables: school and neighborhood effects. Am Econ Rev 108(10):2902–2946

    Article  Google Scholar 

  • Anselin L (1995) Local indicator of spatial association-LISA. Geogr Anal 27(2):93–115

    Article  Google Scholar 

  • Anselin L (1996) The Moran scatterplot as an ESDA tool to assess local instability in spatial association. In: Fischer M, Scholten H, Unwin D (eds) Spatial analytical perspectives on GIS. Taylor & Francis, London, pp 121–138

    Google Scholar 

  • Anselin L (2018) Global Spatial Autocorrelation (1): Moran scatter plot and spatial correlogram. Accessed 18 Jan 2020

  • Anselin L (2019) Local spatial autocorrelation (2): advanced topics. Accessed 18 Jan 2020

  • Anselin L, Rey SJ (2014) Modern spatial econometrics in practice a guide to GeoDa. GeoDaSpace and PySAL GeoDa Press, Chikago

    Google Scholar 

  • Baltagi BH (2013) Econometric analysis of panel data, 5th edn. Wiley, Chichester

    Google Scholar 

  • Baltagi BH, Liu L (2011) Instrumental variable estimation of a spatial autoregressive panel model with random effects. Eco Lett 111:135–137

    Article  Google Scholar 

  • Bartfeld J (2000) Child support and the postdivorce economic well-being of mothers, fathers, and children. Demography 37(2):203–213

    Article  Google Scholar 

  • Brooks-Gunn J, Duncan G (1997) The effects of poverty on children. Future Child 7(2):55–71

    Article  Google Scholar 

  • Cabinet Office for the Government of Japan (CAO) (2014) General principles regarding measures against child poverty. [Kodomo no Hinkontaisaku ni Kansuru Taikou] Accessed 18 Jan 2020 (in Japanese)

  • Cabinet Office for the Government of Japan (CAO) (2019) Suggestions by the panel of experts regarding policy measures against child poverty (public announcement on august, 2019): about the ways of future anti-child poverty policy. [Kodomo no Hinkon Taisakuni Kansuru Yuusikisyakaigi niokeru Teigen (Reiwa Gannen Hachigatsu Kouhyou): Kongo no Kodomo no Hinkontaisaku no Arikata ni Tsuite] Accessed 18 Jan 2020 (in Japanese)

  • Chetty R, Hendren N, Katz LF (2016) The effects of exposure to better neighborhoods on children: new evidence from the moving to opportunity experiment. Am Econ Rev 106(4):855–902

    Article  Google Scholar 

  • Chetty R, Hendren N (2018a) The impacts of neighborhoods on intergenerational mobility I: childhood exposure effects. Quart J Econ 133(3):1107–1162

    Article  Google Scholar 

  • Chetty R, Hendren N (2018b) The impacts of neighborhoods on intergenerational mobility II: county-level estimates. Q J Econ 133(3):1163–1228

    Article  Google Scholar 

  • Chyn E (2018) Moved to opportunity: the long-run effects of public housing demolition on children. Am Econ Rev 108(10):3028–3056

    Article  Google Scholar 

  • Cliff AD, Ord JK (1973) Spatial autocorrelation. Pion, London

    Google Scholar 

  • Cliff AD, Ord JK (1981) Spatial processes: models & applications. Pion, London

    Google Scholar 

  • Cutler DM, Glaeser EL (1997) Are ghettos good or bad? Quart J Econ 112(3):827–872

    Article  Google Scholar 

  • Duncan G, Menestrel SL (eds) (2019) A roadmap to reducing child poverty. The National Academic Press, Washington

    Google Scholar 

  • Elhorst JP (2014) Spatial econometrics: from cross-sectional data to spatial panels. Springer, Heidelberg

    Book  Google Scholar 

  • England JL, Kunz PR (1975) The application of age-specific rates to divorce. J Marr Fam 37(1):40–46

    Article  Google Scholar 

  • Hausman JA (1978) Specification tests in econometrics. Econometrica 46(6):1251–1271

    Article  Google Scholar 

  • Ishii K, Yamada A (2009) Differences in poverty dynamics by age, work and household type in Japan 2005–2007 evidence from Keio household panel survey. J Soc Policy Stud 9:38–63 (In Japanese)

    Google Scholar 

  • Jagowsky PA (1997) Poverty and place: ghettos, barrios, and the American city. Russell Sage Foundation, New York

    Google Scholar 

  • Katz LF, Kling JR, Liebman JB (2001) Moving to opportunity in Boston: early results of a randomized mobility experiment. Quart J Econ 116(2):607–654

    Article  Google Scholar 

  • Kelejian HH, Prucha IR (2001) On the asymptotic distribution of the Moran I test statistic with applications. J Econom 104(2):219–257

    Article  Google Scholar 

  • Kuzunishi L (2017) Residential poverty among single-mother households. [Boshisetai no Kyojuhinkon] Nihon Keizai Hyoronsya Ltd (in Japanese)

  • Lee L-F (2004) Asymptotic distributions of quasi-maximum likelihood estimators for spatial autoregressive models. Econometrica 72(6):1899–1925

    Article  Google Scholar 

  • Lee L-F, Yu J (2010a) Estimation of spatial autoregressive panel data models with fixed effects. J Econom 154(2):165–185

    Article  Google Scholar 

  • Lee L-F, Yu J (2010b) Some recent developments in spatial panel data models. Reg Sci Urban Econ 40(5):255–271

    Article  Google Scholar 

  • LeSage J, Pace RK (2009) Introduction to spatial econometrics. CRC Press, Boca Raton

    Book  Google Scholar 

  • Ludwig J, Duncan GJ, Gennetian LA, Katz LF, Kessler RC, Kling JR, Sanbonmatsu L (2013) Long-term neighborhood effects on low-income families: evidence from moving to opportunity. Am Econ Rev 103(3):226–231

    Article  Google Scholar 

  • Massey DS, Denton NA (1993) American apartheid: segregation and the making of the underclass. Harvard University Press, Cambridge

    Google Scholar 

  • Ministry of Health, Labour and Welfare of Japan (MHLW) (2012) Result report on the 2011 nationwide survey on single-mother household. [Zenkoku Boshi Setaitou Chosa Kekka Houkoku] MHLW. (in Japanese)

  • Ministry of Health, Labour and Welfare of Japan (MHLW) (2015) About present state of single-parent households. [Hitorioya Kateiou no Genjounitsuite] MHLW. Accessed 18 Jan 2020 (in Japanese)

  • Ministry of Health, Labour and Welfare of Japan (MHLW) (2017a) Result report on the 2016 nationwide survey on single parent household. [Zenkoku Hitorioya Setaitou Chosa Kekka Houkoku] MHLW. (in Japanese)

  • Ministry of Health, Labour and Welfare of Japan (MHLW) (2017b) Summary of 2016 comprehensive survey of living conditions. [Heisei 28nendo Kokumin Seikatsu Kiso Chosa no Gaikyo] MHLW. (in Japanese)

  • Ministry of Internal Affairs and Communications of Japan (MIC) (2011) Report on internal migration in Japan derived from the basic resident registration: 2010 detailed summary results (summary). [Juumin Kihon Daicho Jinko Ido Hokoku Heisei 22 Nen Syousai Syuukei Kekka (Youyaku)] MIC. Accessed 18 Jan 2020 (in Japanese)

  • Moran PAP (1950) Notes on continuous stochastic phenomena. Biometrika 37(1–2):17–23

    Article  Google Scholar 

  • Nonoyama-Tarumi Y (2017) Educational achievement of children from single-mother and single-father families: the case of Japan. J Marr Fam 79(4):915–931

    Article  Google Scholar 

  • Oishi AS (2013) Child support and the poverty of single-mother households in Japan. IPSS Discussion Paper Series, No.2013-E01.

  • Oreopoulos P (2003) The long-run consequences of living in a poor neighborhood. Quart J Econ 118(4):1533–1175

    Article  Google Scholar 

  • Organisation for Economic Co-operation and Development (OECD) (2011) Doing better for families. OECD Publishing.

  • Organisation for Economic Co-operation and Development (OECD) (2016) OECD Family Database: LMF1.3: Maternal employment by partnership status (updated: 26–09–16).

  • Organisation for Economic Co-operation and Development (OECD) (2018a) OECD Family Database: CO2.1: Income inequality and the income position of different household types (updated: 03–01–18).

  • Organisation for Economic Co-operation and Development (OECD) (2018b) OECD Family Database: CO2.2: Child poverty (updated: 13–07–18).

  • Raymo JM, Park H, Iwasawa M, Zhou Y (2014) Single motherhood, living arrangements, and time with children in Japan. J Marr Fam 76(4):843–861

    Article  Google Scholar 

  • Rowlingson K, McKay S (2002) Lone parent families: gender, class and state. Pearson Education, Harlow

    Google Scholar 

  • Sampson RJ (2012) Great American city: Chicago and the enduring neighborhood effect. University of Chicago Press, Chicago

    Book  Google Scholar 

  • Shirahase S, Raymo JM (2014) Single mothers and poverty in Japan: the role of intergenerational coresidence. Soc Forces 93(2):545–569

    Article  Google Scholar 

  • Skinner C, Bradshaw J, Davidson J (2007) Child support policy: an international perspective. Research Report No 405, Department for Work and Pensions, University of York

  • Statistical Bureau of Japan (SBJ) (2017) 2015 Census: results of basic complete tabulation on households and families, summary of results. [Heisei 27 Nen Kokusei Chosa: Setai Kouzoutou Kihon Shukei Kekka, Kekka no Gaiyou] (in Japanese).

  • Tamiya Y (2019) An analysis of poverty and policy effects towards low wages of single-mother households. S Policy, Japan Assoc Soc Policy Stud 10(3):26–38 (in Japanese)

    Google Scholar 

  • Tamiya Y, Shikata M (2007) Work and childcare in single mother families: a comparative analysis of mother’s time allocation. Quart Soc Secur Res 43(3):219–231 (in Japanese)

    Google Scholar 

  • Thevenon O (2018) Policy brief on child well-being: poor children in rich countries: why we need policy action. OECD

  • Watanabe K, Shikata M (2018) Estimating poverty rates in Japan. [Nihon ni Okeru Hinkonritsu no Suikei] In Komamura, K. (Ed.) Poverty (pp. 51–62). Minerva Shobo. (in Japanese)

  • Wilson WJ (1987) The truly disadvantaged: the inner city, the underclass, and public policy. The University of Chicago Press, Chicago

    Google Scholar 

  • Winchester HPM (1990) Women and children last: the poverty and marginalization of one-parent families. Tran Inst Br Geogr 15(1):70–86

    Article  Google Scholar 

  • Wooldridge JM (2016) Introductory econometrics: a modern approach, 6th edn. Cengage, Boston

    Google Scholar 

  • Zhou Y (2014) Work and life and economic independence of single mothers. [Boshisetai no Work Life to Keizaitekijiritsu] The Japan Institute for Labour Policy and Training. (in Japanese)

Download references


We are grateful to the editors and referees for valuable comments and suggestions. We would also like to thank Shinichiro Iwata, Tohru Naito, Akiko Oishi, Chigusa Okamoto, and seminar participants at various conferences for their constructive comments. This research was supported by JSPS KAKENHI Grant Numbers JP16K13363, JP17K18550, JP19K01691, and 20K01617 and Keio Gijuku Academic Development Funds (Individual Research A).

Author information

Authors and Affiliations


Corresponding author

Correspondence to Mizuki Kawabata.



See Table 7

Table 7 Average marginal effects for children under ages 6 and age 6–18 in single-mother households: spatial fixed-effects models(W: inverse-distance matrix)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Abe, Y., Kawabata, M. & Shibatsuji, Y. Spatial clustering patterns of children in single-mother households in Japan. J Spat Econometrics 2, 1 (2021).

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI:


JEL classification