Mobility decisions within couples

Abstract

We analyze couples mode choice, focusing on the interdependence of spouses’ decisions. We set up a discrete collective (cooperative) model in which spouses with competing objectives reach a Pareto optimal decision, and we apply it to Paris region. We estimate the determinants of the bargaining power (spouses’ age, nationality, type of job contract, tenure status and number of children) using this collective model. To control for the endogeneity of car ownership, we finally model the joint choice of car ownership and mode. Econometric estimations show that spouses’ values of time driving alone and together are significantly different.

Appendix: Estimates of alternatives to the nested collective model

In the model with independent decision, each spouse G is assumed to prefer mode j with probability: $P_{iG} (j)=\frac{\exp \left( {V_{iG}^j } \right) }{\sum \nolimits _{k\in \left\{ {B, C} \right\} } {\exp \left( {V_{iG}^k } \right) } }, j\in \left\{ {B, C} \right\}$ and to prefer one car to zero car with probability:

$P_{iG}^{\text {Car}} =\frac{\exp \left( {V_{iG}^{\text {Car}} +\mu ^{\text {Car}}I_{iG}^{\text {Car}} } \right) }{\exp \left( {\mu ^{\text {noCar}}I_{iG}^{\text {noCar}} } \right) +\exp \left( {V_{iG}^{\text {Car}} +\mu ^{\text {Car}}I_{iG}^{\text {Car}} } \right) }$

where $V_{iG}^{\text {Car}}$ designs the deterministic utility of owning at least one car (the deterministic utility of owning no car is normalized at zero) for spouse G and the inclusive value $I_{iG}^{\text {Car}} (I_i^{\text {noCar}} )$ corresponds to the maximum utility that spouse G can obtain from mode choice when owning at least one car (no car) (Tables 8, 9):

$$\begin{aligned} I_i^{\text {Car}}= & {} \log \left[ {\exp \left( {V_{iG}^B } \right) +\exp \left( {V_{iG}^C } \right) } \right] ,\\ I_i^{\text {noCar}}= & {} \log \left[ {\exp \left( {V_{iG}^B } \right) } \right] =V_{iG}^B . \end{aligned}$$

When both spouses wants a car, two car are bought with probability $\alpha$. So the probability that the household i has 2 cars is given by the product $\alpha \times P_{iF}^{\text {Car}} \times P_{iM}^{\text {Car}}$. Consequently, the probability of choosing mode ($j,j')$ and having 2 cars is:

$$\begin{aligned} {P}_i \left( {j,j^{\prime },2 \text {car}} \right) =\alpha \times P_i^{\text {Car}} \times P_{iM}^{\text {Car}} \times P_{iF} (j)\times P_{iM} (j^{\prime }) , j,j^{\prime }\in \left\{ {B,C} \right\} \end{aligned}$$

Only one car is bought when both spouses wants one and buy a common one (with probability $\left( {1-\alpha } \right) \times P_{iF}^{\text {Car}} \times P_{iM}^{\text {Car}} )$ or when only one spouse wants a car (with probability $P_{iF}^{\text {Car}} \times \left( {1-P_{iM}^{\text {Car}} } \right) +\left( {1-P_{iF}^{\text {Car}} } \right) \times P_{iM}^{\text {Car}} )$. In this latter case, the spouse who chooses to have a car has the choice between both travel modes, while the other spouse is assumed to take public transport. Therefore, the probability of choosing mode $(j,j')$ and having 1 car is given by the following equations:

$$\begin{aligned} P_i \left( {B,B,1 \text {car}} \right)&=P_{iF}^{\text {Car}} \times \left( {1-P_{iM}^{\text {Car}} } \right) \times P_{iF} (B)+\left( {1-P_{iF}^{\text {Car}} } \right) \times P_{iM}^{\text {Car}} \\&\quad \times P_{iM} (B)+\left( {1-\alpha } \right) \times P_{iF}^{\text {Car}} \times P_{iM}^{\text {Car}} \times {P}_{iF} (B)\times P_{iM} (B), \\ P_i \left( {C,C,1 \text {car}} \right)&=P_{iF}^{\text {Car}} \times \left( {1-P_{iM}^{\text {Car}} } \right) \times P_{iF} (C)+\left( {1-P_{iF}^{\text {Car}} } \right) \times P_{iM}^{\text {Car}} \\&\quad \times P_{iM} (C)+\left( {1-\alpha } \right) \times P_{iF}^{\text {Car}} \times P_{iM}^{\text {Car}} \times P_{iF} (C)\times P_{iM} (C), \\ P_i \left( {B,C,1 \text {car}} \right)&=\left( {1-P_{iF}^{\text {Car}} } \right) \times P_{iM}^{\text {Car}} \times P_{iM} (C)+\left( {1-\alpha } \right) \\&\quad \times P_{iF}^{\text {Car}} \times P_{iM}^{\text {Car}} \times P_{iF} (B)\times P_{iM} (C) \\ P_i \left( {C,B,1 \text {car}} \right)&=P_{iF}^{\text {Car}} \times \left( {1-P_{iM}^{\text {Car}} } \right) \times P_{iF} (C)+\left( {1-\alpha } \right) \\&\quad \times P_{iF}^{\text {Car}} \times P_{iM}^{\text {Car}} \times P_{iF} (C)\times P_{iM} (B) \end{aligned}$$

When neither spouses want a car, the couple has no car and the couple mode choice is given by: $P_i \left( {B,B,0 \text {car}} \right) =\left( {1-P_{iF}^{\text {Car}} } \right) \times \left( {1-P_{iM}^{\text {Car}} } \right)$.