Modeling Intra-household Activity Time Allocation ...

Modeling Intra-household Activity Time Allocation from Group Decision Making Process Kali Prasad NEPAL(1), Daisuke FUKUDA(2) and Tetsuo YAI(3) (1, 2)

Department of Civil Engineering, Tokyo Institute of Technology G3-14, 4259 Nagatsuta-cho, Midori-ku, Yokohama, Japan, 226-8502 E-mails: @plan.cv.titech.ac.jp (3)

Department of Built Environment, Tokyo Institute of Technology G3-14, 4259, Nagatsuda-cho, Midori-ku, Yokohama, Japan, 226-8502 E-mail: [email protected] Abstract: The objective of this study is to analyze group decision-making process leading to the intrahousehold activity time allocation models. Each household is characterized as a group of individuals making joint decisions about their activity participation, time allocation and consumption of goods. Household members make several decisions jointly, not by an individual member, including independent and joint activity time allocations as well as private and shared consumption of goods. Since the individualbased activity time allocation models are not realistic for multi-person households, it is beneficial to consider group decision-making process in modeling time allocation behavior of household members. We summarize various intra-household activity time allocation models, ranging from unitary models to collective models, based on different group decision-making processes. The models are presented under microeconomic principle of utility maximization to represent the economic behavior of the households. Key Words: Intra-household activity time allocation, unitary models, bargaining models, collective models 1. INTRODUCTION In the development of the activity time allocation models, or related travel demand and activity behavior analysis, a decision usually has to be made between the individual level analysis and household level analysis. The existing individual-based activity time allocation models lack several aspects of behavioral realism because each individual is more or less associated within the household with care and share. The household is more than a convenient aggregation unit to summarize the behavior of its members. Some behavioral characteristics and attributes only become observable at the household level. Utility maximization can be thought of occurring at household level. The intra-household activity time allocation decisions are affected by the characteristics of the households they belong to, the resources available to them and the constraints they have to face to satisfy household needs. The existing research attempts to incorporate the household effects in time allocation modeling are using few explanatory variables related to household characteristics. To the best of our knowledge, none of the existing models have treated explicitly the household as the unit of analysis in activity time allocation modeling except few attempts in the last few years (Gliebe and Koppleman 1999, Zhang et al. 2004). The actual unit of analysis for modeling activity time allocations is the household just like the unit of analysis in the theory of consumption and the demand for travel is not only affected by the personal behavior but also by the household decision making process. Household models are useful for understanding joint and allocated activity participation and effects of household income in its members’ activity time allocation decisions. The primary purpose of this chapter is to analyze the decision-making mechanism of a collective group leading to the allocation of different amounts of time to different activities and, to explore microeconomic models of intra-household activity time allocations. Detailed description of these models can be found in Nepal et al. (2005). Each household is characterized as a group of individuals making joint decisions about their activity participation and travel choices. Collective group, not an individual agent, makes several decisions including independent and joint activity time allocation as well as private and shared consumption of goods. The proposed models are derived within microeconomic utility maximization principle and social welfare analysis that provides insights into the behavior of the households regarding activity time allocations and travel decisions. 2. DEVELOPMENT OF THE MODELS 2.1 Notations

W un T tni

Twice continuously differentiable strongly concave household welfare function; Twice continuously differentiable strongly concave direct utility of an individual n ; Total time available to each household member per period; n n Total time allocated to an independent activity i by an individual n = ai + tti ;

1

ain

Time allocated to an independent activity i by an individual n at the destination;

ttin tj

Travel time required to access to an independent activity i for an individual n ;

aj

Activity duration of a joint activity j at the destination;

tt j

Travel time required to access to a joint activity j ;

twn

Time allocated to market labor by individual n = aw + tt w ; n

awn

w tt

Total time allocated to a joint activity j = a j + tt j ;

n

n w

zkn zs n i

n

Working time duration of an individual n per period; Wage rate of an individual n ; Travel time for work commute for individual n ; Private good k consumed by an individual n in a household; Shared good s consumed by the household;

tc

Travel cost to access to independent activity i for individual n ;

tcwn

Travel cost to access to work location for individual n ;

tc j

Total travel cost to access to joint activity j for all individuals in the household;

pk ps

Market price of the independent good k and

y

n

Market price of the shared good s ; Unearned income of an individual n ;

2.2 Groupings of Activities and Consumption Bundles An individual in a household allocates his available time to a vector of independent activities I ( 1,..., i,..., I ) and to the vector of joint activities J ( 1,..., j ,..., J ). Similarly, the household consumption can be either private consumption bundle K ( 1,..., k ,..., K ) or the shared consumption bundle S ( 1,..., s,..., S ). I is the universal set of independent activities and K is the universal set of private consumption bundle for all household members. It is possible that some elements of set I and K are null for a specific household member when he or she may not participate all activities in a given day. 2.3 THE MODELS Three different models of intra-household activity time allocation are discussed in this section. 2.3.1 Unitary Models: The standard theory of consumer behavior is an example of the economic problem: households are needs and desires that they want to satisfy. But they have to make choices because they are limited in their possibilities. A fundamental assumption made in the unitary intra-household model is that the households needs and desires are fully captured by the rational preference ordering over alternative activities and goods so that they are well-behaved units. Unitary models, which are based on the traditional intra-household decision making process, treat each household as a black box, the models do not address how decision are made but only what the outcome is. Such models are either ‘common preferences’ models or ‘dictator model’ in which household maximizes single household utility function with pooling of family incomes. The household preferences are usually represented by a unique well-behaved household welfare function and explicit choices are deduced from the maximization of household utility function under resource constraints. Let us assume that the utility of an individual is derived from all activity participation and good consumption within the fixed period (DeSerpa, 1971) and the household welfare function is the constant function of individuals’ utilities. Then the household chooses to maximize:

W = W {(tin , t j , zkn , zs ), ∀n, i ≠ w, j , k , s} Subject to:

T − twn − ∑ tin − ∑ t j = 0 i

(1)

∀n

(2)

j

2

∑y

n

n

+ ∑ wn (twn − ttwn ) − ∑ pk ∑ zkn − ∑ ps zs − ∑ tcwn − ∑∑ tcin − ∑ tc j ≥ 0 n

k

n

s

n

n

i

(3)

j

2.3.2 Non-Unitary Models. The unitary models do not explicitly takes into account the notion that the household is a group of individuals, with different preferences, and among whom an intra-household decision making process takes place. In fact, a household can be seen as a micro-society that consists of several individuals with their own rational preferences. Observed household time allocations and good consumption patterns can in this sense be considered as a social state chosen by the household members. Non-unitary intra-household models explicitly take into account the fact that multi-person households consist of several members, which may have different preferences. For all non-unitary intra-household models, the preferences of the household members regarding the optimal allocation of resources (time and money) need not be the same and they are assumed to be independent. Each person has the separate utility function of the form

u n = u n {(tin , t j , zkn , zs ), ∀i ≠ w, j , k , s}

∀n

(4)

(i) Cooperative Bargaining Models. In the presence of joint activity participation and shared goods within the household and companionship, loving and caring etc, the intra-household bargaining problem is a cooperative game approach and now widely used in economics. The cooperation understood in the sense of game theory. The intra-household cooperative bargaining models explicitly address the question of how individual preferences lead to a solution of bargaining problem. A bargaining problem requires specifying a set of feasible payoff combinations and a payoff combination that obtains in the case of a breakdown of a negotiation (Manser and Brown, 1980 and McElroy and Horney, 1981). If the bargaining process ends without a solution, each individual obtains a disagreement payoff, which is also called the threat point payoff. The Nash-bargained solution to the resource allocation problem dictates that all members jointly choose the arguments in the utility function to maximize the gains from living together. The household decision process is assumed to lead to a Pareto efficient allocation, and household members jointly maximize the following household utility function:

W = ∏ [u n − φ n ]

(5)

n

Subject to:

T − twn − ∑ tin − ∑ t j = 0 i

∑y n

n

∀n

(6)

j

+ ∑ wn (twn − ttwn ) − ∑ pk ∑ zkn − ∑ ps zs − ∑ tcwn − ∑∑ tcin − ∑ tc j ≥ 0 n

k

n

s

n

n

i

(7)

j

The value of u is given by (4) and φ is the threat point (maximized indirect utility which member n would achieve outside of the household). Bargaining models differ from the unitary models in that the decision making process within the household is explicitly specified. n

n

(ii) Collective Models. Chiappori (1988) pioneered another approach to non-unitary household models that does not require an explicit bargaining framework. As emphasized by Chiappori (1988) and Browning and Chiappori (1998), the intra-household decision-making process cannot be represented by a unique household utility function. Each household is a political place, characterized by conflicts of interests, but also companionship and share. Each member in the household is an economic agent, endowed with the preferences. In sharing rule approach, each household decision is the outcome of the collective understanding and sharing between its members. Collective household models are more general and based on the assumption that the household wastes nothing- that is its allocation is Pareto efficient. That is, chosen consumption bundles are such that an individual’s welfare cannot be increased without decreasing the welfare of other household member. Then, the collective household model can be formulated using the standard instruments of welfare economics. Household chooses consumption to maximize:

u n = u n {(tin , t j , zkn , zs ), ∀i ≠ w, j , k , s}

(8)

Subject to:

u n '{(tin ' , t j , zkn ' , zs ), ∀i ≠ w, j , k , s} = u n ' , ∀n ' ≠ n

3

(9)

T − twn − ∑ tin − ∑ t j = 0 i

n

n

(10)

+ ∑ wn (twn − ttwn ) − ∑ pk ∑ zkn − ∑ ps zs − ∑ tcwn − ∑∑ tcin − ∑ tc j ≥ 0 n

k

n

s

n

Where,

u n ' is

value of

u n ' , n ' ≠ n and household full income constraint. By u n ' , n ' ≠ n , all Pareto efficient allocations can be

some required level of welfare for individual n ' ≠ n . Thus the maximization of this problem seeks an allocation that maximizes welfare of individual n at the given varying

n

i

(11)

j

Utility Possibility Frontier Member n’’s utility

∑y

∀n

j

k J J’

k’

I traced out. This set of Pareto efficient allocations forms the J’’ k’’ boundary of utility possibility Frontier that captures all attainable vectors of utility levels for the household. For the case Member n’s utility of only 2 members household, this utility possibility frontiers Fig1. Utility Possibility Frontier can be shown in plan as shown in Figure 1. This is an important result because it allows characterizing all Pareto efficient allocations as stationary points of the Linear Household Welfare Function for some positive welfare weights for both individuals. That is, the household allocation problem can be defined as the unique solution to maximize:

W = ∑θ nu n ,

∑θ

n

n

n

= 1, u n = u n {(tin , t j , zkn , zs ), ∀i ≠ w, j , k , s}

∀n

(12)

Subject to:

T − twn − ∑ tin − ∑ t j = 0 i

∑y n

n

∀n

(13)

j

+ ∑ wn (twn − ttwn ) − ∑ pk ∑ zkn − ∑ ps zs − ∑ tcwn − ∑∑ tcin − ∑ tc j ≥ 0 n

k

n

s

n

n

i

(14)

j

where θ is the Pareto weight or welfare weight or bargaining power assigned to individual i . The welfare function in (12) may be interpreted as being a sort of weighted average of individual preferences. i

3.

SYNTHESIS AND DISCUSSION

This research proposes general microeconomic models of intra-household activity time allocation, explicitly considering household as the unit of analysis. This is an important shift in activity time allocation paradigms from individual-based to household-based. We have summarized microeconomic models of intra-household activity time allocation based on different decision-making strategies. The proposed models underscore the realistic behavioral contexts for parameter estimation and econometric forecasting. If found acceptable from practical point of view, these models will be the keys in analyzing activity time allocation behavior. There are more research works still to be done. First, the proposed microeconomic models have to be specified into estimable econometric models so that the model parameters could be estimated from the statistical data collected from the households. Second, development of an effective way of collecting information or data from the households are very important. Third, the detail empirical analysis is required in order to analyze the practical efficiency of the models. REFERENCES 1. 2. 3. 4. 5. 6.

Browning, M. and Chiappori, P.A. (1998) Efficient intra-household allocations: A general characterization and empirical test, Econometrica, 66, 1241-1278. Chiappori, P.A. (1988) Rational household labor supply, Econometrica, 56, 63-89. DeSerpa, A. (1971) A Theory of the economics of the time, The Economic Journal, 81, 828-845. Gliebe, J. P. and Koppleman, F.S. (2002) A model of joint activity participation between household members, Transportation, 29, 49-72. Nepal, K.P., Fukuda, D. and Yai, T. (2005). Microeconomic models of intra-household activity time allocations. Journal of Eastern Society for Transportation Studies, CD-ROM, Bangkok (Accepted) Zhang, J., Fujiwara, A., Timmermans, H. and Borgers, A. (2004) Methodology for modeling household time allocation behavior, Presented in EIRASS Conference, Maastricht, The Netherlands.

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