Spatiotemporal Analysis of Marriage and Marital Fertility in Japan: Using Geographically Weighted Regression

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1 Spatotemporal Analyss of Marrage and Martal ertlty n Japan: Usng Geographcally Weghted Regresson Kenj Kamata (Natonal Insttute of Populaton and Socal Securty Research) Abstract (125) 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, each decade from 1980 to The analytcal 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 (SMR) and the martal fertlty rato (MR). As for the explanatory factors, we focus on female labor force partcpaton. The result shows almost coeffcents for covarates have statstcally sgnfcant geographcal varatons. The coeffcents by spatal areas are relatvely stable at each perod. The female labor force partcpaton has a postve relatonshp wth martal fertlty n the urban areas. Introducton Regonal patterns n Japanese fertlty are characterzed as "Low n the metropoltan areas, hgher n non-metropoltan areas" trends came to be observed from 1950 to Snce the 1970s TR showed a downward trend throughout the country, but regonal dfferences were mantaned. After 2005, TR went from 1.26 n 2005 to 1.43 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 (SMR) and the martal fertlty rato (MR) (gure 1). Descrptve statstcs of varables are shown n Table 1. SMR M m P, SR b B P, SR MR SMR 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

2 To assess heterogenety of the relatonshp between regonal fertlty rates and ther covarates, we appled geographcally weghted regresson (GWR), each decade from 1980 to GWR extends to the tradtonal regresson model by allowng the estmaton of local rather than global parameters (Brunsdon et al. 1996; otherngham 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. rom the results of Leung et al.' s -test (Table 3), almost coeffcents for covarates have statstcally sgnfcant geographcal varatons. The coeffcents by spatal areas are relatvely stable at each perod. The female labor force partcpaton and excess nbound rate have a postve relatonshp wth martal fertlty n the urban areas (gure 2-3). These results ndcate that the 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., otherngham, A.S., and Charlton, M., 1996, Geographcally Weghted Regresson: A Method for Explorng Spatal Nonstatonarty, Geographcal Analyss, No.28, pp otherngham, 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 Dependent Varable Independent Varable Varable Lst and Descrptve Statstcs Varables Standardzed Marrage Rato (SMR) 1 Martal ertlty Rato (MRb) 1 2 Proporton of Never-marred Populaton [30-39 years old, emale] (%) Proporton of Nuclear amly Household (%) [15-49 years old, emale] (%) Proporton of oregn Populaton (%) Sex Rato for Never-marred Populaton Source Drecton Year Mn 25% Mean Medan 75% Max, Vtal statstcs, Vtal statstcs, Prefecture Report Socal Welfare aclty Survey Indrect standardzed estmaton method (Koke 2010) 2 Number of brth s estmated by bayes methods usng second medcal areas Table 2 The descrptve statstcs of the GWR results: summary [SMR model] [MR model] Kernel functon: B-square (about 64 of 1901) Adaptve quantle (about 71 of 1901) (about 75 of 1901) (about 86 of 1901) Summary of GWR coeffcent estmates: Independent Varable Model Mn. 25% Medan 75% Max. Global Intercept Proporton of Nuclear amly Household (%) [15-49 years old, emale] (%) Proporton of oregn Populaton (%) Sex Rato for Never-marred Populaton Effectve number of parameters: (1980), (1990), (2000), (2010) Effectve degree of freedom: (1980), (1990), (2000), (2010) AIC: (1980), (1990), (2000), (2010), AICc: (1980), (1990), Quas-global R 2 : (1980), (1990), (2000), (2010) Kernel functon: B-square (about 74 of 1901) Adaptve quantle (about 116 of 1901) (about 137 of 1901) (about 158 of 1853) Summary of GWR coeffcent estmates: Independent Varable Model Mn. 25% Medan 75% Max. Global Intercept Proporton of Never-marred Populaton [30-39 years old, emale] (%) Proporton of Nuclear amly Household (%) [15-49 years old, emale] (%) Proporton of oregn Populaton (%) Effectve number of parameters: (1980), (1990), (2000), (2010) Effectve degree of freedom: (1980), (1990), (2000), (2010) AIC: (1980), (1990), (2000), (2010), AICc: (1980), (19 Quas-global R 2 : (1980), (1990), (2000), (2010)

4 Table 3 The results of Leung et al.' s -test [SMR model] Leung et al. (2000) year d.f.1 d.f.2 (1) test (2) test (3) test resduals mprovement *** *** *** *** *** *** *** *** d.f.(1980) d.f. (1980) Intercept *** *** Proporton of Nuclear amly Household (%) [15-49 years old, emale] (%) Proporton of oregn Populaton (%) Sex Rato for Never-marred Populaton (3) test (1980) *** *** *** *** *** *** *** *** *** *** *** *** SS OLS resduals (1990) Intercept *** *** Proporton of Nuclear amly Household (%) [15-49 years old, emale] (%) Proporton of oregn Populaton (%) Sex Rato for Never-marred Populaton (2000) Sgnfcance Level: 0 *** ** 0.01 * (2010) *** *** *** *** *** *** *** *** *** *** *** *** [MR model] Leung et al. (2000) year d.f.1 d.f.2 (1) test (2) test (3) test [15-49 years old, emale] (%) Proporton of oregn Populaton (%) (3) test resduals mprovement *** *** *** *** *** *** *** *** (1980) Proporton of oregn Populaton (%) Sgnfcance Level: 0 *** ** 0.01 * d.f.(1980) d.f. (1980) *** *** *** *** *** *** *** *** ** SS OLS resduals (1990) Intercept *** *** Proporton of Never-marred Populaton [30-39 years old, emale] (%) *** *** Proporton of Nuclear amly Household (%) (2000) (2010) Intercept *** *** Proporton of Never-marred Populaton [30-39 years old, emale] (%) *** *** Proporton of Nuclear amly Household (%) [15-49 years old, emale] (%) *** *** *** *** *** *** *** *** *** *** SR B b P 1980 SMR m M P 1980 MR SR SMR gure 1 Dstrbuton of SR, SMR and MR: The Cartogram s created by Gastner-Newman method usng ArcGIS

5 Proporton of Never-marred Populaton [30-39 years old, emale] (%) Proporton of Nuclear amly Household (%) km 0 15 km Excess Inbound Mgrant Rate (%) [15-49 years old, emale] (%) km 0 15 km Proporton of oregn Populaton (%) km 0 15 km gure 3 Dstrbuton of average GWR coeffcents [SMR model]: The Cartogram s created by Gastner-Newman method usng ArcGIS

6 Proporton of Nuclear amly Household (%) Excess Inbound Mgrant Rate (%) km 0 15km [15-49 years old, emale] (%) Male Unemployment rate (%) km 0 15km Proporton of oregn Populaton (%) Sex Rato for Never-marred Populaton km 0 15km gure 3 Dstrbuton of average GWR coeffcents [MR model]: The Cartogram s created by Gastner-Newman method usng ArcGIS