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Household Members’ Time Allocation to Daily Activities and Decision to Hire Domestic Helpers

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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

- 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

- 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)

- Structural equations models

- 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)

- 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

- 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

- 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.

- We define the utility function of a household member as follows:
- And the utility function of hiring a domestic helper is:

- 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.

- Lagrangian function
- where are respectively the Lagrangian multipliers associated with the time constraint for member and that associated with the time constraint of maintenance.

- The first-order conditions of the Lagrangian function

A Model of Time Allocation

- 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)

- 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

- Substituting equation (4) into (2)and into (3), we got the following equation

- Where

- 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:

- Where

- Therefore the density function of the random vector can be derived as follows:
- Where

- 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).

- 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

- 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.

- 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

- 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.

Estimation of parameters for subsistence activity

Estimation of parameters for maintenance activity

Estimation of parameters for recreation activity

Number of observations=10381

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

- 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)

Optimal time allocation to activities for household members and time of hiring domestic helper

- 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.