1. 1 An Empirical Analysis of Divorce or Separation among Cross-Border Marriages in Taiwan By Wen-Shai Hung Department of Business Administration Providence University Shu-Hsi Ho Department of International Business Ling Tung University 靜宜大學財務與計算數學系 學術研討會

2. 2 Outline 1. Introduction 2. Some Basic Facts about Cross-Border Marriages in Taiwan 3. Estimation Method: Weibull Model 4. Data Description 5. Empirical Results 6. Conclusion

3. 3 1. Introduction  Previous studies of cross-border marriages in Taiwan have analysed children’s health (Hung, 2006), spatial pattern (Chi, Jhou, & Hsieh, 2009), low fertility (Chen, 2008; Liaw, Lin, & Liu, 2009), marital transition (Chen, 2009), and low- income families (Wang, 2005).  Few papers analysed the issues of divorce or separation among cross-border marriages, except analysis of marital stability by Chen (2007). However, she did not estimate the accurate hazard rate of divorce or separation.  The purposes of this paper include to describe the factors influencing divorce or separation, to estimate the hazard rates of divorce or separation, and to investigate the effect of unobserved heterogeneity of divorce or separation among cross-border marriages in Taiwan.

4. 4 2. Some Basic Facts on Cross-Border Marriages in Taiwan According to the government 2010 report, the proportion of cross-border marriages gradually increased from 15.69% in 1998 to 31.86% in 2003, after that it decreased to 18.71% in 2009 as shown in Figure 1. However, the proportions of cross-border divorce or separation also gradually increased from 6.06% in 1998 to 16.91% in 2003, and 22.99% in 2009 as shown in Figure 2.

5. 5 Figure 1 the trends in the proportion of Taiwanese spouses from different nationalities, 1998-2009.

6. 6 Figure 2 the trends in the nationality of spouses who’s marriages end in divorce or separation in Taiwan, 1998-2009.

7. 7 3. Estimation Method: Weibull Model 3.1 The Model without Unobserved Heterogeneity The hazard function of marriage duration without unobserved heterogeneity is specified as (1) where is the hazard rate, is a marriage duration, is the explanatory variables. The parameters and by maximum likelihood. in the Weibull distribution can be estimated

8. 8 For observed duration data, can be formulated and maximized to include censored and uncensored observations. Combining these duration models into a general parametric likelihood yields:, the log-likelihood function (2) where, and represents uncensored observations, represents right-censored observations.

9. 9 To obtain the maximum likelihood with respect to the parameters of interest,, then maximise the log-likelihood function: (3) The procedure to obtain the values of maximum likelihood estimation requires taking derivatives of with respect to, the unknown parameters, setting these equations equal to zero, and solving for

10. 10 3.2 The Model with Unobserved Heterogeneity After considering unobserved heterogeneity on estimated individual marriage behaviour, the hazard function can be defined as (4) Where can represent unobserved heterogeneity, the differences between observations are introduced via a multiplicative scaling factor.

11. 11 4.1 Data Source: The 2003 Survey of Foreign and Mainland Chinese Spouses’ Living Conditions in Taiwan (SFMLCT). 4.2 Variables Specification 4.2.1 Dependent Variable: Marriage duration includes the period from when an individual first married to the end of the marriage for the “uncensored” duration spells, and they continue married for the “right-censored” duration spells. 4.2.2 Explanatory Variables: 4. Data Description

12. 12 Table 1 Descriptive Statistics of Variables VariableDescriptionMeanStd. Dev. DurationDuration of marriage between 1 and 70 years.4.4624.473 Censor1 = Uncensored, 0 = Otherwise.0.0140.121 Age17-89 years old of respondent.30.6978.860 Gender1 = Female, 0 = Male.0.9540.207 Native11 = Spouse come from Southern Asia, 0 = Otherwise.0.4840.499 Native21 = Spouse come from Mainland China, 0 = Otherwise.0.5150.499 Edu11 = Informal schooling, 0 = Otherwise.0.0240.154 Edu21 = Primary school, 0 = Otherwise.0.2450.430 Edu31 = Junior high school, 0 = Otherwise.0.3730.483 Edu41 = Senior high school, 0 = Otherwise.0.2490.432 Edu51 = College, 0 = Otherwise.0.0470.212 Edu61 = University, 0 = Otherwise.0.0540.227 Edu71 = Degree of master or PhD, 0 = Otherwise.0.0050.073 Health11 = Good health, 0 = Otherwise.0.9290.256 Health21 = Sick, 0 = Otherwise.0.0580.235 Health31 = Need help, 0 = Otherwise.0.0110.102 Health41 = Disabled, 0 = Otherwise.0.0010.033 R-employed1 = Respondent’s employment, 0 = Otherwise.0.3150.464 P-employed1 = Partner’s employment, 0 = Otherwise.0.8500.356 ChildrenThe number of children1.0060.865

13. 13 Table 1 (Continued) Note: The effective samples have 145,261 observations, including 2,176 observations that do not remain married, including divorced or separated, and 143,085 people who remain married. Variable Description MeanStd. Dev. Living-E 1 = Family expenditure from respondent or partner’s earnings, 0 = Otherwise. 0.9120.282 Living-P 1 = Family expenditure from respondent or partner’s pension benefits, 0 = Otherwise. 0.0580.234 Living-C 1 = Family expenditure from respondent or partner’s children support, 0 = Otherwise. 0.0060.079 Living-S 1 = Family expenditure from respondent or partner’s savings, 0 = Otherwise. 0.0510.220 Family-P 1 = Living with partner, 0 = Otherwise. 0.9480.222 Family-C 1 = Living with children, 0 = Otherwise. 0.6010.489 Family-PP 1 = Living with partner’s parents, 0 = Otherwise. 0.4540.497 Family-BS 1 = Living with partner’s brothers or sisters, 0 = Otherwise. 0.1490.356 Periods 1-7 years living in Taiwan 3.4981.529 Resid1 1 = Living in North of Taiwan, 0 = Otherwise. 0.4380.496 Resid2 1 = Living in Central Taiwan, 0 = Otherwise. 0.2570.437 Resid3 1 = Living in South of Taiwan, 0 = Otherwise. 0.2750.446 Resid4 1 = Living in East of Taiwan, 0 = Otherwise. 0.0230.151

14. 14 5. Empirical Results 5.1 The Estimated Hazard Rates of Divorce or Separation by Weibull Model are shown in Table 2.

15. 15 Table 2 Estimation by Weibull Models VariablesCoefficientStandard ErrorHazard RatioStandard Error Age-0.076***0.0020.926***0.002 Gender-0.269***0.0980.764***0.074 Native20.235***0.0591.265***0.075 Edu20.301**0.1341.351**0.181 Edu30.0660.1351.0680.144 Edu4-0.1040.1380.9010.124 Edu5-0.459***0.1770.631***0.111 Edu6-0.597***0.1740.550***0.095 Edu7-2.191**1.0090.111**0.112 Health1-0.270***0.0640.762***0.049 R-employed-0.518***0.0630.595***0.037 P-employed-0.244***0.0570.782***0.045 Children-0.800***0.0430.449***0.019 Living-E-0.133**0.0640.875**0.056 Living-P-0.452***0.1010.636***0.064 Living-C-0.3280.2180.7200.157 Living-S-0.341***0.1090.710***0.077

16. 16 Table 2 (Continued) VariablesCoefficientStandard ErrorHazard RatioStandard Error Family-P-2.753***0.0540.063***0.003 Family-C-1.052***0.0840.349***0.029 Family-PP-0.712***0.0690.490***0.034 Family-BS-0.789***0.1180.454***0.054 Periods-0.441***0.0160.643***0.010 Resid20.345***0.0551.413***0.078 Resid30.270***0.0531.310***0.070 Resid40.691***0.1081.996***0.217 Constant0.686***0.221 0.645***0.0140.645***0.014 1.906***0.0281.906***0.028 0.524***0.0070.524***0.007 Log likelihood-6268.472 LR chi2(25)11963.23

17. 17 5.2 The Model without and with Unobserved Heterogeneity are shown in Tables 3 and 4.

18. 18 Table 3 Estimation by Weibull Models: the Case of All Samples VariablesWithout Unobserved HeterogeneityWith Gamma- Heterogeneity CoefficientStandard ErrorCoefficientStandard Error Age-0.075***0.002-0.076***0.002 Native20.227***0.0590.233***0.059 Edu20.314**0.1340.305**0.134 Edu30.0810.1350.0710.135 Edu4-0.0860.138-0.0980.138 Edu5-0.440**0.177-0.453**0.177 Edu6-0.551***0.173-0.582***0.174 Edu7-2.115**1.008-2.167**1.009 Health1-0.258***0.064-0.266***0.064 R-employed-0.493***0.062-0.510***0.063 P-employed-0.247***0.057-0.245***0.057 Children-0.794***0.043-0.798***0.043 Living-E-0.136**0.064-0.134**0.064 Living-P-0.482***0.101-0.462***0.101 Living-C-0.3120.219-0.3230.219 Living-S-0.337***0.109-0.340***0.109

19. 19 Table 3 (Continued) VariablesWithout Unobserved HeterogeneityWith Gamma- Heterogeneity CoefficientStandard ErrorCoefficientStandard Error Family-P-2.751***0.054-2.752***0.053 Family-C-1.061***0.083-1.055***0.084 Family-PP-0.720***0.069-0.715***0.069 Family-BS-0.788***0.118-0.788***0.118 Periods-0.442***0.017-0.441***0.016 Resid20.338***0.0550.343***0.055 Resid30.266***0.0530.268***0.053 Resid40.684***0.1080.688***0.108 Constant0.391**0.1930.506**0.224 0.643***0.0140.644***0.011 -4.476***1.512 1.903***0.0281.904***0.021 0.525***0.0070.524***0.006 0.011***0.017 Log likelihood-6271.998-6271.614 LR chi2(24)11956.1811927.48

20. 20 Table 4 Estimation by Weibull Models: the Case of Spouses from Mainland China VariablesWithout Unobserved HeterogeneityWith Gamma- Heterogeneity CoefficientStandard ErrorCoefficientStandard Error Age-0.068***0.003-0.068***0.002 Native20.354***0.0630.360***0.063 Edu20.444***0.1630.432***0.163 Edu30.2340.1650.2230.165 Edu40.0250.1680.0140.168 Edu5-0.361*0.206-0.371*0.206 Edu6-0.349*0.206-0.375*0.206 Edu7-1.6310.926-1.0340.457 Health1-0.226***0.071-0.236***0.071 R-employed-0.439***0.075-0.462***0.076 P-employed-0.175***0.064-0.175***0.064 Children-1.044***0.063-1.053***0.063 Living-E-0.163**0.070-0.161**0.070 Living-P-0.470***0.105-0.448***0.106 Living-C-0.2410.234-0.2630.234 Living-S-0.370***0.122-0.370***0.122

21. 21 Table 4 (Continued) VariablesWithout Unobserved HeterogeneityWith Gamma- Heterogeneity CoefficientStandard ErrorCoefficientStandard Error Family-P-2.444***0.060-2.445***0.059 Family-C-0.960***0.107-0.953***0.107 Family-PP-0.496***0.083-0.490***0.083 Family-BS-0.477***0.130-0.479***0.130 Periods-0.504***0.020-0.502***0.020 Resid20.354***0.0630.360***0.063 Resid30.350***0.0600.352***0.059 Resid40.771***0.1190.774***0.119 Constant0.418*0.2270.576**0.265 0.568***0.0160.569***0.013 -3.900***1.349 1.765***0.0291.767***0.023 0.566***0.0090.565***0.007 0.020***0.027 Log likelihood-4750.524-4749.644 LR chi2(23)8823.038817.08

22. 22 6. Conclusion  First, for the demographic characteristics, the empirical results show that older people, females, people with high educational attainments, and people with good health have lower hazard rates and they are less likely to divorce or separate, ceteris paribus. In contrast, people with primary educational attainment and spouses from Mainland China have higher hazard rates and they are more likely to divorce or separate.  Second, for the employment status, respondents and their partners with jobs all have lower hazard rates and they are less likely to divorce or separate.  Third, for the family structure and economic status, people with more children, family expenditure from earnings, pension benefits, and savings, respondents living with partner, children, partner’s parents, and partner’s brothers/sisters, and living in Taiwan longer have lower hazard rates and they are less likely to divorce or separate. In contrast, respondents living in central, south, and east regions have higher hazard rates and they are more likely to divorce or separate, ceteris paribus.

23. 23  After considering unobserved heterogeneity, the estimated theta of spouses from Mainland China is larger than the case of all samples. This is possibly the reason that spouses from Mainland China have higher hazard rates and are more likely to divorce or separate. Therefore, unobserved heterogeneity is an important factor in marriage duration, particularly for spouses from Mainland China.  Future work: Using the 2008 Survey of Foreign and Mainland Chinese Spouses’ Living Conditions in Taiwan (SFMLCT), it can be found further changes of this issue. Using the 2004 Survey of Family and Fertility (SFF) in Taiwan, it can be found some different results between domestic and foreign wives.

24. 24 Your suggestions are warmly welcome ！