Temporary Migration and Foreign Direct Investment

Abstract

The question of complementarity or substitutability of FDI and international labour mobility has not yet been answered. The substitutability assumption does not take into consideration the technological spillover of FDI in the host countries. Moreover, migration flows reveal cultural characteristics and labour force properties of their native country which may stimulate bilateral business networks, strengthening the complementarity assumption between capital and labour flows. In this paper we build a continuous time dynamic model where these offsetting forces are at work. We analyze whether, and to what extent, the increase in labour mobility might affect FDI outflows. A numerical simulation is performed showing that a higher income growth rate corresponds to a higher labour mobility. Some policy implications and further research direction are suggested.

Appendices

Appendix A

Given the simultaneous differential equation system in the text (Eqs. 14–16), the characteristic polynomial is the following

$$\lambda ^{3}+A\lambda ^{2}+B\lambda +C=0,$$

(19)

where

$$\begin{array}{rll}A &=&(\eta _{1}+\eta _{2}+\eta _{3}) \\ B &=&\eta _{1}\eta _{3}\left[ 1+\left( 1-\beta \right) \alpha _{3}\alpha _{4}\alpha _{7}\right] +\eta _{1}\eta _{2}\left( 1-\alpha _{2}\alpha _{6}\right) +\eta _{3}\eta _{2}\left[ 1-\alpha _{5}\alpha _{7}\left( 1-\beta \right) \right] \\ C &=&\eta _{1}\eta _{2}\eta _{3}\left\{ \alpha _{7}\left( 1-\beta \right) [\alpha _{3}\alpha _{4}\left( 1-\alpha _{6}\right) -\alpha _{5}(1-\alpha _{2})]+1-\alpha _{2}\alpha _{6}\right\} . \end{array}$$

For a dynamic system to be convergent to a local stable equilibrium, the roots of the characteristic polynomial must have negative real part. A set of necessary and sufficient conditions for all the roots of Eq. 19 to have negative real parts is

$$\begin{array}{ccc} A & > & 0 \\ B & > & 0 \\ C & > & 0 \\ AB-C & > &\kern2pt 0. \end{array}$$

It is possible to observe that the first two conditions are immediately satisfied. For the last two conditions to be verified, it is necessary that the following two conditions are satisfied:

$$1-\alpha _{2}\alpha _{6}>\left( 1-\beta \right) \alpha _{7}\left( \alpha _{5}+\alpha _{3}\alpha _{4}\alpha _{6}-\alpha _{2}\alpha _{5}-\alpha _{3}\alpha _{4}\right)$$

and

$$\begin{array}{l} \eta _{1}\eta _{2}\eta _{3}\left( 1-\alpha _{2}\alpha _{6}\right) +(\eta _{1}+\eta _{2}+\eta _{3})\left[ \eta _{1}\eta _{2}\left( 1-\alpha _{2}\alpha _{6}\right) \right] \\ {\kern1pc}+\,\eta _{3}\left( 1-\beta \right) \alpha _{7}\left[ \eta _{1}\eta _{2}\alpha _{5}\left( \alpha _{2}-2\right) +\eta _{2}+\eta _{3}\right] \\ {\kern1pc}+\,\eta _{1}\alpha _{3}\alpha _{4}\left[ \eta _{1}+\eta _{3}+\eta _{2}\left( 2-\alpha _{6}\right) \right] >0. \end{array}$$

Let us analyze the four elements of the last condition separately.

The first one is certainly greater than zero given the economic assumptions discussed in the text. So are the second and the fourth element. Their sum thus will be positive. Let indicate that sum with Z

$$\begin{array}{rll} Z&=&\eta _{1}\eta _{2}\eta _{3}\left( 1-\alpha _{2}\alpha _{6}\right) +(\eta _{1}+\eta _{2}+\eta _{3})\left[ \eta _{1}\eta _{2}\left( 1-\alpha _{2}\alpha _{6}\right) \right] \\ &&+\,\eta _{1}\alpha _{3}\alpha _{4}\left[ \eta _{1}+\eta _{3}+\eta _{2}\left( 2-\alpha _{6}\right) \right] >0. \end{array}$$

Hence, for the second condition to be verified it is sufficient that

$$\eta _{3}\left( 1-\beta \right) \alpha _{7}\left[ \eta _{1}\eta _{2}\alpha _{5}\left( \alpha _{2}-2\right) +\eta _{2}+\eta _{3}\right] <Z. $$

Appendix B

In order to find the particular solution of the model (Eqs. 14–16), we apply the rule of undetermined coefficients.¹⁴

Given

$$ \overset{\cdot }{\mathbf{y}}+\mathbf{y}B=\mathbf{g}(t)\text{ \quad with \quad }\mathbf{g}(t)=\mathbf{C}_{0}+\mathbf{C}_{1}t $$

where

$$ \begin{array}{rll} \overset{\cdot }{\mathbf{y}} &=& \begin{vmatrix} \overset{\cdot }{k} \\ \overset{\cdot }{\psi } \\ \overset{\cdot }{\gamma } \end{vmatrix} ,\text{ }\mathbf{y=} \begin{vmatrix} k \\ \psi \\ \gamma \end{vmatrix} ,\quad \mathbf{B}= \begin{vmatrix} -\eta _{1} & \eta _{1}\alpha _{2} & \eta _{1}\alpha _{3}\alpha _{4} \\ \eta _{2}\alpha _{6} & -\eta _{2} & \eta _{2}\alpha _{5} \\ -\eta _{3}\left( 1-\beta \right) \alpha _{7} & \eta _{3}\left( 1-\beta \right) \alpha _{7} & -\eta _{3} \end{vmatrix} , \\\\ \mathbf{C}_{0} &=& \begin{vmatrix} \eta _{1}\left( b+\alpha _{3}h\right) \\ \eta _{2}c \\ \eta _{3}\left[ \omega -\alpha _{7}\left( a+\log \beta +w^{\ast }\right) \right] \end{vmatrix} ,\quad \mathbf{C}_{1}= \begin{vmatrix} 0 \\ 0 \\ \eta _{3}\alpha _{7}\left( \beta n+\theta \right) \end{vmatrix} , \end{array}$$

we try as a particular solution of the system

$$ \overline{\mathbf{y}}=\mathbf{\mu +\sigma }t, $$

where μ and σ are vectors of coefficients to be determined. We thus obtain

$$ \mathbf{\sigma }+\mathbf{B}\left( \mathbf{\mu +\sigma }t\right) =\mathbf{C} _{0}+\mathbf{C}_{1}t $$

from which

$$ \left( \mathbf{B\sigma -C}_{1}\right) t+\left( \mathbf{B\mu +\sigma -C} _{0}\right) =\mathbf{0.} $$

This equation will hold for each value of t if, and only if, the following relations are simultaneously verified

$$ \begin{array}{rll} \left( \mathbf{B\sigma -C}_{1}\right) &=&\mathbf{0} \\ \left( \mathbf{B\mu +\sigma -C}_{0}\right) &=&\mathbf{0.} \end{array}$$

By solving the system, we find the values of μ _i and σ _i shown in the text.