Spatial Variations in Covariates on Marriage and Marital Fertility: Geographically Weighted Regression Analyses in Japan

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1 Spatal Varatons n Covarates on Marrage and Martal Fertlty: Geographcally Weghted Regresson Analyses n Japan Kenj Kamata (Natonal Insttute of Populaton and Socal Securty Research) Abstract (134) To understand the determnants of rasng fertlty rates after 2005 n Japan, ths study nvestgates the spatal varatons of the relatonshp between changes n marrage and martal fertlty, and the relatonshps wth covarates usng geographcally weghted regresson models. Our sample s 1,853 towns and vllages based on 2010 admnstratve boundares. The ndexes of marrage and martal fertlty are made by the standardzed method. The dependent varables are the standardzed martal populaton rato () and the martal fertlty rato (MFR). As for the explanatory factors, we focus on female labor force partcpaton, the sex rato, and chldcare avalablty. All coeffcents for covarates on have statstcally sgnfcant geographcal varatons. But for MFR some coeffcents ddn t have sgnfcant. The female labor force partcpaton and chldcare avalablty show a postve relatonshp wth MFR n the urban areas. Introducton Regonal patterns n Japanese fertlty are characterzed as "Low n the metropoltan areas, hgher n the non-metropoltan areas" trends came to be observed from 1950 to Snce the 1970s TFR showed a downward trend throughout the country, but regonal dfferences were mantaned. After 2005, TFR went from 1.26 n 2005 to 1.39 n Our goal s to analyze the determnants of rasng fertlty rates after 2005 n Japan and explore the spatal varatons n marrage and martal fertlty how covarates relate wth regons. Investgatng the cause of such varatons by regon may provde an mportant perspectve to explan marrage and martal fertlty. In general, socal behavor s not spatally homogeneous, whch ndcates that ndvduals are nfluenced by a spatal effect. Prevous research usng regresson analyss wthout takng spatal correlaton and non-statonarty across regons nto account may have led to an naccurate nference. Our study frst examnes the spatal autocorrelatons for varables relevant to marrage and martal fertlty, and then apples geographcally weghted regresson methods to assess heterogenety of the relatonshp between regonal marrage and martal fertlty and ther covarates. Data and Methods The sample s 1,853 towns and vllages based on 2010 admnstratve boundares. The dependent varables are the standardzed martal populaton rato () and the martal fertlty rato (MFR) (Fgure 1 and 2). The explanatory varables nclude female labor partcpaton, the sex rato for model, chldcare for MFR model and so on. Descrptve statstcs of varables are shown n Table 1.

2 M m P, SFR b B P, SFR MFR where : age, M: Martal Populaton, m : age-specfc martal rates n standard populaton, B: number of brths, b : age-specfc brth rate, P : age-specfc standard populaton To assess heterogenety of the relatonshp between regonal fertlty rates and ther covarates, we appled geographcally weghted regresson (GWR). GWR extends to the tradtonal regresson model by allowng the estmaton of local rather than global parameters (Brunsdon et al. 1996; Fotherngham et al. 2002). Basc model: y 0 ( ) 1( ) x1 2( ) x2 n ( ) x Parameter: ˆ T T ( ) ( X ( X W ( ) X ) 1 X W ( ) Y where W(): n by n spatal weghtng matrx n GWR model s assumng that observed data near to pont have more of an nfluence n the estmaton of the values located farther from. The equaton measures the relatonshps n the model around each pont. The weghts are defned as contnuous functons (kernel functons) of dstance that the closer a data pont s to the calbraton pont, the greater s ts weght n the estmaton of the parameters for that calbraton pont. We have selected an adapted b-square functon model. Results and Dscusson Table 2 shows the descrptve statstcs of the GWR results. From the results of Leung et al.' s F-test (Table 3), all coeffcents for covarates on have statstcally sgnfcant geographcal varatons. But for MFR some coeffcents ddn t have sgnfcant. The female labor force partcpaton and chldcare avalablty show a postve relatonshp wth MFR n the urban areas (Fgure 3). For model, the sex rato s a postve relatonshp n the urban areas where are low sex ratos. These results ndcate that marrage and martal fertlty responses to external forces may vary across regons nfluenced by ther hstorcal and geographcal settngs, and results of the global model may not be approprate to unformly apply for each regon. In addton, the result from our study suggests that there should be some unque crcumstances that ease, reverse or accelerate the usual relatonshps n the area where coeffcents show a dfference from the area surroundng them. Reference Brunsdon, C., Fotherngham, A.S., and Charlton, M., 1996, Geographcally Weghted Regresson: A Method for Explorng Spatal Nonstatonarty, Geographcal Analyss, No.28, pp Fotherngham, A. S., Brunsdon, C., and Charlton, M., 2002, Geographcally Weghted Regresson: The Analyss of Spatally Varyng Relatonshps, New York, John Wley & Sons. Leung, Y., Me, C.-L., and Zhang, W.-X., 2000, Statstcal Tests for Spatal Nonstatonarty based on the Geographcally Weghted Regresson Model, Envronment and Plannng A, 32, pp

3 Table 1 Varable Lst and Descrptve Statstcs Varables Year Source Drecton Mn 25% Mean Medan 75% Max Dependent Varable Standardzed Marrage Rato 2010 Census Martal Fertlty Rato 2010 Census Independent Varable Proporton of Nuclear Famly Household (%) 2010 Census Excess Inbound Mgrant Rate (%) 2010 Census, Prefecture Report Census Male Unemployment rate (%) 2010 Census Propoton of Foregn Populaton (%) 2010 Census Sex Rato aged Census per populaton of 100,000 aged 0 to 5 years old 2010 Socal Welfare Faclty Survey Table 2 The descrptve statstcs of the GWR results: summary Kernel functon: B-square Adaptve quantle Summary of GWR coeffcent estmates: MFR (about 75 of 1853) (about 158 of 1853) Independent Varable Model Mn. 25% Medan 75% Max. Global Intercept MFR Proporton of Nuclear Famly Household (%) MFR Excess Inbound Mgrant Rate (%) MFR MFR Male Unemployment rate (%) MFR Propoton of Foregn Populaton (%) MFR Sex Rato aged per populaton of 100,000 aged 0 to 5 years old MFR Effectve number of parameters: (), (MFR) Effectve degree of freedom: (), (MFR) AIC: (), (MFR), AICc: (), (MFR) Quas-global R 2 : (), (MFR), Resdual sum of squares: (), (MFR) Table 3 The results of Leung et al.' s F-test Leung et al. (2000) year F d.f.1 d.f.2 F(1) test F(2) test F(3) test SS GWR resduals SS GWR mprovement *** MFR *** *** MFR *** F () Numerator d.f. () Domnator d.f. () Numerator d.f. (MFR) Domnator d.f. (MFR) Intercept *** Proporton of Nuclear Famly Household (%) *** *** Excess Inbound Mgrant Rate (%) *** ** *** *** Male Unemployment rate (%) *** *** Propoton of Foregn Populaton (%) *** Sex Rato aged *** per populaton of 100,000 aged 0 to 5 years old Sgnfcance Level: 0 *** ** 0.01 * SS OLS resduals F (MFR) ***

4 Fgure 1 Dstrbuton of 2010 (Rght Fgure s Cartogram by Female Populaton aged 15-49) The Cartogram s created by Gastner-Newman method usng ArcGIS Fgure 2 Dstrbuton of MFR 2010 (Rght Fgure s Cartogram by Female Populaton aged 15-49) The Cartogram s created by Gastner-Newman method usng ArcGIS

5 Fgure 3 Dstrbutons of Local Coeffcents estmated by GWR