1. Household Members’ Time Allocation to Daily Activities and Decision to Hire Domestic Helpers Donggen WANG and Jiukun LI Department of Geography Hong Kong Baptist University Kowloon Tong, Kowloon Hong Kong

2. Outline  Research background and objectives  A model of household time allocation taking into consideration of hiring domestic helpers  Model estimation  An empirical study: Hiring domestic helpers and household time allocation in Hong Kong  Model prediction and impact analysis  Conclusions

3. Research Background  Modelling activity and travel interactions between household members (Bhat and Pendyala, 2005)  Structural equations models  Interactions in activity participation and travel between household heads (Golob and McNally 1997)  Time allocation models  Time allocation models of adult household members’ participation in and time allocation to independent and joint activities (Gliebe and Koppelman 2002; Scott and Kanaroglou 2002)  Group decision-based models for time allocation to independent, shared and allocated activities (Zhang et al. 2002; 2004)

4. Research Background  Discrete choice models  The allocation of maintenance activities to household members in terms of who and how (jointly or independently) the maintenance activities are conducted (Vovsha, et al. 2004; Srinivasan and associates 2005; 2006)  Tour-based discrete choice models accounting for interactions between household heads (Gliebe and Koppelman, 2005)

5. Research Background  Existing studies share an underlying assumption: no external help for household maintenance tasks  In reality, households may get helps from members of the extended family, or hire domestic helpers  External helps may change activity-travel patterns of household members  Consideration of external helps is important for understanding activity-travel behaviors of household members  Hardly any study of this kind is reported in the literature

6. Research Objectives  Develop a model to analyze time allocation of household members taking into consideration of hiring domestic helpers.  Calibrate the model by empirical data  Apply the model for analyzing the impacts of wage rate changes on time allocation

7. Notations  is the total time available for member i ;  is the time spent for activity j by member i.  is the amount of time that a domestic helper is hired.  is the baseline utility for time invested in activity j by household member i.  is the baseline utility for hiring domestic helpers  is the wage rate of household member i, is the wage rate of domestic helpers.

8. Utility Functions of Household Members and Domestic Helpers  We define the utility function of a household member as follows:  And the utility function of hiring a domestic helper is:

9. A Model of Time Allocation  Households are assumed to maximize the household utility: (1) Subject to : (a) (b)  Where and are respectively weights of household members and domestic helpers, representing their relative contributions to household utility.

10. A Model of Time Allocation  Lagrangian function  where are respectively the Lagrangian multipliers associated with the time constraint for member and that associated with the time constraint of maintenance.

11. A Model of Time Allocation  The first-order conditions of the Lagrangian function

12.  From the first-order conditions, we may derive the following interrelations among time allocation to activities and time of hiring domestic helper: (2) (3) With constraints (a) and (b) A Model of Time Allocation

13. Specification of the baseline utility function  In general the utility function can be expressed as follows: (4)  Where are error terms, is the systematic component of utility and assume that it is continuously differentiable  We assume that  The utility contribution of time allocation is dependant on socio-economic characteristics of individuals, the systematic component of utility is to capture these effects

14. Model Estimation  Substituting equation (4) into (2)and into (3), we got the following equation

15. Model Estimation  Where

16. Model Estimation  Assume that error term are independently and identically standard normal distributed  we add the following auxiliary random variable:  based on the property of normally distributed variables, Then the density function of the random vector may be derived as follows:

17. Model Estimation Where

18. Model Estimation Therefore the density function of the random vector can be derived as follows: Where

19. Model Estimation  The maximum likelihood method may be applied to estimate the parameters. Introducing the index for household, we can write the likelihood function as follows:  Where  The sequential number theoretic optimization (SNTO) algorithm can be used to solve the likelihood function to find the maximum likelihood estimation of parameters. SNTO searches for the global optimum among points uniformly scattered in the search space (Fang and Wang, 1994).

20. An Empirical Study  Hong Kong: A special Administrative region of China  Area size: 1100 square kilometers  High population density (more than 6,000 per square kilometers)  In 2004, about 218,430 foreign domestic helpers working in Hong Kong

21. An Empirical Study  Hong Kong Travel Characteristics Survey conducted in 2002; only households that have married couples and at least one of the couple is employed are selected;  About the sample:  size: 10,381 households;  About 9.9% have live-in maids;  About 15.9% have car available for private use;  About 17.0% have child aged 1 to 5 and 45.4% have child aged 6-17;  About 48.2% of the households live in private apartment or house  About 76.1% of male heads are employed and 49.2% of female heads are employed.

22. An Empirical Study  Variable definitions  Time duration of the following activities: subsistence, maintenance and recreation  Wage rate: calculated from monthly household income (divided by duration of subsistence activity)  If both household heads are working: Male : female (1.35 :1)  If only one head is working, all household income is allocated to the person  Domestic helper:  Monthly costs of a domestic helper: around 6000 HK dollars  Working time: 10 hour/day,  Wage rate: 20 HKD/hour

23. An Empirical Study  Socio-Economic variables  household size,  type of housing (‘1’ for private housing and ‘0’ for public housing),  the presence of child aged 5 or younger and of child aged 6 to 17,  age of household head (1: 20 years old or younger, 2: 21 – 40, 3: 41 – 60, 4: older than 60)  car ownership.  Assume the baseline utility is defined as follows:

24. Parameter Estimation Estimation of parameters for subsistence activity Male headFemale head VariablesCoefficientst t Constant -0.8847-7.3371-0.8580 -4.9138 Type of housing-0.6497-6.78520.15022.9280 Household size-0.3326-6.9505-0.0942-3.2963 Age of household head-0.5415-6.74530.08882.5447 Presence of child aged 5 or lower -0.6595-6.5558-0.3638-3.5682 Presence of child aged 6 to 170.02333.4570-0.5304-4.1895 Car ownership-0.2778-5.6680-0.3441-3.4894

25. Parameter Estimation Estimation of parameters for maintenance activity Male headFemale head VariablesCoefficientst t Constant2.92255.8414-2.4992-4.7717 Type of housing-0.7391-4.22350.90473.6105 Household size-0.6348-4.9063-0.6739-3.3160 Age of household head -0.2128-3.12070.0710 1.0656 Presence of child aged 5 or lower 0.36543.2747-0.2371 -2.2714 Presence of child aged 6 to 17 0.78214.27990.1066 1.4720 Car ownership-0.0394-1.0243-0.3398-2.6312

26. Parameter Estimation Estimation of parameters for recreation activity Male headFemale head VariablesCoefficientst t Constant-2.7043-8.4545-0.6257-6.9907 Type of housing-0.4099-6.3246-0.6213-4.3478 Household size0.46747.29080.02181.8328 Age of household head -0.7797 -7.1099 -0.1273-2.9048 Presence of child aged 5 or lower 0.5436 6.3625 -0.1447-2.6463 Presence of child aged 6 to 17 -0.4085 -6.3211 0.21073.2663 Car ownership-0.8141-6.74320.73424.2472 1.801159.03890.86064.6398 Number of observations=10381

27. Model Prediction  The model can be used to predict the time use of household members and time of hiring domestic helpers for household. Subject to:

28. Model Prediction  Based on the parameters estimation, we can forecast the time allocation to activities for household members and the time of hiring domestic helper  Assume that the socio-economic variables: (type of housing, household size, Age of household head, Presence of child aged 5 or lower, Presence of child aged 6 to 17, Car ownership)=(1, 4, 2, 1, 1,1)

29. Model Prediction Optimal time allocation to activities for household members and time of hiring domestic helper MemberActivitiesTotal SubsistenceMaintenanceRecreation Male head 6.34163.89735.7612 16 Female head 5.90193.21996.8782 16 Helper 2.8828

30. Impact Analysis

33. Conclusions  A model of time allocation considering hiring domestic helpers is developed and successfully applied calibrated by a large empirical data set.  The model is tested by analyzing the impacts of wage rate change on time allocation to various activities and the time of hiring domestic helper.  Future extension of the model should consider other types of external helps, such as that from members of the extended family.