Life Cycles and Gender in Residential Mobility Decisions

Abstract

Using household survey data from the recent economically depressed period, we attempt to identify typical household characteristics by residential type and study whether households change their residence at different stages of life. We find that the general trend in residential choice is influenced by socioeconomic background. The results of a multinomial probit estimation highlight that the probability of homeownership is higher in rural areas and increases with age of household heads, financial wealth, and family size. In contrast, the probability of renting a house is higher in urban areas and among female households. Moreover, it is observed that people adjust residential size despite market imperfections. The dwelling size increases with age of household heads and declines once they reach retirement age; however, the residential mobility is low at older ages. Furthermore, there are gender differences in terms of attitudes toward downsizing residences; female households are more willing to accept downsizing than are male households.

Appendices

Appendix: A

Using the notations used in the main text, the probability of i choosing j can be expressed in the MNP framework as

$$ \begin{array}{@{}rcl@{}} Prob(v_{i1}\leq 0, \dots, v_{i J-1}\leq 0) &=& \frac{1}{(2\pi)^{\frac{(J-1)}{2}} \arrowvert {\Sigma} \arrowvert^{\frac{1}{2}} } {\int}_{-\infty}^{-\lambda_{i1}} \dots {\int}_{-\infty}^{-\lambda_{iJ-1}}\\ &&\times \exp \left( - \frac{1}{2} z^{\prime} {\Sigma}^{-1}z\right) dz \end{array} $$

We have used STATA to compute the MNP statistics, which use the Gaussian quadrature approximation for the integral in the above equation.

Appendix: B

Closely following Lee (2016, p. 167) and maintaining the same notations used in the main text, we can state an identification condition for the DIDID by rewriting Eq. (8). In order to distinguish between treated and untreated responses of households, we define y¹ as a potential response of treated households and y⁰ as that of untreated households. Then, the aggregate response can be expressed as y = (1 − k)y⁰ + ky¹, where k = 1 for the treated group and 0 otherwise. Assuming that the treatment occurs in the second period, it follows that y = y⁰ for the first period (Time = 0) and y = (1 − k)y⁰ + ky¹ for the second period (Time = 1). This is because only when all dummy indicators (Time, Gender and AG_s) are equal to 1, the composite term (Time ×Gender ×AG_s) becomes unity, and k = 0 when one (or two or all) of the dummies is 0. Therefore, y = y⁰ is always established for the first period.

Then, by ignoring covariate x in Eq. (8) for simplicity and by subtracting and adding E(y⁰|AG_s = 1,Gender = 1,Time = 1) after the first of Eq. (8), we can obtain the net effect that is equal to:

$$ \begin{array}{@{}rcl@{}} &&E(y^{1}| \mathrm{AG_{\textit{s}}} = 1,\text{Gender} = 1,\text{Time} = 1) - E(y^{0}| \mathrm{AG_{\textit{s}}} = 1, \text{Gender} = 1,\text{Time} = 1 )\\ &&+E(y^{0}| \mathrm{AG_{\textit{s}}} = 1,\text{Gender} = 1, \text{Time} = 1) - E(y^{0}| \mathrm{AG_{\textit{s}}} = 1, \text{Gender} = 1, \text{Time} = 0)\\ &&-[E(y^{0}| \mathrm{AG_{\textit{s}}} = 0, \text{Gender} = 1,\text{Time} = 1) - E(y^{0}| \mathrm{AG_{\textit{s}}} = 0, \text{Gender} = 1, \text{Time} = 0)]\\ &&-\{[E(y^{0}| \mathrm{AG_{\textit{s}}} = 1, \text{Gender} = 0, \text{Time} = 1) - E(y^{0}| \mathrm{AG_{\textit{s}}} = 1, \text{Gender} = 0), \text{Time} = 0]\\ &&-[E(y^{0}| \mathrm{AG_{\textit{s}}} = 0, \text{Gender} = 0, \text{Time} = 1) - E(y^{0}| \mathrm{AG_{\textit{s}}} = 0, \text{Gender} = 0, \text{Time} = 0)]\} \end{array} $$

Note that E(y⁰|AG_s = 1,Gender = 1,Time = 1) is counterfactual due to y⁰ despite AG_s = 1,Gender = 1 during the second period. Households in this group are expected to change residence. The last eight items are involved in the identification condition; that is,

$$ \begin{array}{@{}rcl@{}} &&E(y^{0}| \mathrm{AG_{\textit{s}}} = 1,\text{Gender} = 1, \text{Time} = 1) - E(y^{0}| \mathrm{AG_{\textit{s}}} = 1, \text{Gender} = 1, \text{Time} = 0)\\ &&-[E(y^{0}| \mathrm{AG_{\textit{s}}} = 0, \text{Gender} = 1,\text{Time} = 1) - E(y^{0}| \mathrm{AG_{\textit{s}}} = 0, \text{Gender} = 1, \text{Time} = 0)]\\ &=& E(y^{0}| \mathrm{AG_{\textit{s}}} = 1, \text{Gender} = 0, \text{Time} = 1) - E(y^{0}| \mathrm{AG_{\textit{s}}} = 1, \text{Gender} = 0), \text{Time} = 0\\ &&-[E(y^{0}| \mathrm{AG_{\textit{s}}} = 0, \text{Gender} = 0, \text{Time} = 1) - E(y^{0}| \mathrm{AG_{\textit{s}}} = 0, \text{Gender} = 0, \text{Time} = 0)] \end{array} $$

This abovementioned equation implies that an identification condition for the DIDID for repeated cross-sectional data requires differences between untreated response changes for the (AGs= 1,Gender= 1) group and the (AGs= 0, Gender= 1) group being equal to those between untreated response changes for the (AGs= 1,Gender= 0) group and the (AGs= 0, Gender= 0) group. For example, untreated responses of the (AGs= 1, Gender= 1) group correspond to responses of elderly females who did not move residence. As Lee (2016, pp. 168-175) stated, the identification condition for repeated cross-sectional data is difficult to understand since eight terms are involved; this condition for panel data is much simpler.

When this identification condition holds, we can obtain an expression for the net effect that identifies the effect on the treated (AG_s = 1,Gender = 1) in the second period:

$$ \begin{array}{@{}rcl@{}} &E(y^{1}-y^{0}| \mathrm{AG_{\textit{s}}}=1,\text{Gender}=1,\text{Time}=1) \end{array} $$

Thus, the net effect is equal to the expected value of differences between identified and counterfactual effects, and this is equivalent to ID_8D in Lee (2016).