Long-distance commuting and the effect of differentiated salary expectations in the commuters’ place of living on the wage obtained in the place of working

Abstract

Despite the efficiency produced by long-distance commuting (LDC) as an adjustment mechanism between local labor markets, the impact that it has on the equilibrium of labor markets has not been studied in depth. This paper uses the case of Chile, since in the last two decades the LDC has increased its importance as a strategy of labor mobility for workers in this country. We demonstrate, both theoretically and empirically, that LDC generates wage differences in the labor markets that receive commuters, as a function of the market equilibrium of these workers’ place of origin. These differences are not only related to labor productivity and/or employment, but also to the wage expectations of commuters in their place of origin.

Appendices

Appendix 1

See Fig. 4.

Fig. 4

Source: Self-elaborated

Maps for Chile identifying the regions of the country and the 135 LMFA’s defined by Berdegué et al. (2017).

Appendix 2

When considering the following Bellman equation—already considered in Eq. (1):

$$ w_{r}^{a} = b - c^{a} \left( {s^{a} } \right) - c^{b} \left( {s^{b} } \right) + s^{a} \cdot\frac{{\lambda^{a} \left( {s^{a} } \right)}}{r}\cdot\mathop \smallint \limits_{{w_{r} }}^{\infty } \left[ {w^{a} - w_{r}^{a} } \right] \cdot {\text{d}}F\left( {w^{a} } \right) + s^{b} \cdot\frac{{\lambda^{b} \left( {s^{b} } \right)}}{r}\cdot\mathop \smallint \limits_{{w_{r} }}^{\infty } \left[ {w^{b} - w_{r}^{b} } \right] \cdot {\text{d}}F\left( {w^{b} } \right) $$

(15)

The optimal effort in the search for employment in the host region (b) is obtained as a solution to the following problem:

$$ \mathop {argmax}\limits_{{s^{b} }} w_{r}^{a} $$

Upon solving:

$$ \frac{{\partial c^{b} \left( {s^{b} } \right)}}{{\partial s^{b} }} = \frac{{\left( {\lambda^{b} \left( {s^{b} } \right) + s^{b} \cdot\frac{{\partial \lambda^{b} \left( {s^{b} } \right)}}{{\partial s^{b} }}} \right)}}{r}\cdot\mathop \smallint \limits_{{w_{r} }}^{\infty } \left[ {w^{b} - w_{r}^{b} } \right] \cdot {\text{d}}F\left( {w^{b} } \right) $$

(16)

Using this equation, we can calculate the optimal wage that would be obtained in the optimal search effort applied on the host region (b) which is:

$$ w^{*b} = \frac{{\frac{{\partial c^{b} \left( {s^{b} } \right)}}{{\partial s^{b} }} \cdot r}}{{\lambda^{b} \left( {s^{b} } \right) + s^{b} \cdot\frac{{\partial \lambda^{b} \left( {s^{b} } \right)}}{{\partial s^{b} }}}}\cdot\frac{1}{{\left( {1 - F\left( {w_{r}^{b} } \right)} \right)}} + w_{r}^{b} $$

(17)

When considering that the reservation wage in the host region ($w_{r}^{b}$) is dependent on the sum of the reservation wage in the source region ($w_{r}^{a}$) and the transport costs ($c_{t} \left( {d_{a,b} } \right)$):

$$ w_{r}^{b} = w_{r}^{a} + c_{t} \left( {d_{a,b} } \right) $$

(18)

Then, we can define Eq. (17) as:

$$ w^{b} = \frac{{\frac{{\partial c^{b} \left( {s^{b} } \right)}}{{\partial s^{b} }} \cdot r}}{{\lambda^{b} \left( {s^{b} } \right) + s^{b} \cdot\frac{{\partial \lambda^{b} \left( {s^{b} } \right)}}{{\partial s^{b} }}}}\cdot\frac{1}{{\left( {1 - F\left( {w_{r}^{b} } \right)} \right)}} + w_{r}^{a} + c_{t} \left( {d_{a,b} } \right). $$

(19)