How to partly bounce back the struggle against illegal immigration to the source countries

Abstract

Recent models on the dynamics of immigration control claim that tightening internal borders may trigger the formation of networks supporting clandestine foreign workers. This may, in turn, increase the overall stock of illegal immigrants in the economy. One possible solution to this threatening situation might be to partly bounce back the struggle against illegal immigration to the source countries. This paper suggests that under certain conditions, the receiving country should direct some of the resources earmarked for coping with the problem of the illegal flow of workers to financially supporting the source countries, allowing them to compete among themselves for such aid. This support would be allocated according to the relative effort made by each source country in curbing illegal immigration, thereby motivating them to moderate the phenomenon. The model is also applicable to other fields of negative externalities, such as the smuggling of drugs and weapons, terrorism, and pollution.

Appendix 1

The reaction curve of country S _i , which is derived from the first-order condition for maximum (Eq. 3) and its slope are given by Eqs. (A1) and (A2), respectively:

$$N_{j} + N_{i} - \frac{{2N_{i} }} {{1 \pm {\sqrt {1 - \frac{{4N_{i} }} {F}{\left( {B_{e} - \frac{1} {{\partial N_{i} /\partial C_{i} }}} \right)}} }}} = 0$$

(A1)

and

$$\frac{{\partial C_{i} }}{{\partial C_{j} }} = - \frac{{\frac{{\partial ^{2} R_{i} }}{{\partial C_{j} \partial C_{i} }}}}{{\frac{{\partial ^{2} R_{i} }}{{\partial C_{i} ^{2} }}}} = - \frac{{\frac{{f^{\prime }_{i} f^{\prime }_{j} (N_{j} - N_{i} )F}}{{N^{3} }}}}{{\frac{{A_{i} }}{{N^{3} f^{\prime }_{i} }}}} = \frac{{f^{\prime }_{j} {\left( {f^{\prime }_{i} } \right)}^{2} (N_{i} - N_{j} )F}}{{A_{i} }}.$$

(A2)

Alternatively, the reaction curve of country S _i can be formulated as N _i (N _j ) with a slope as follows:

$$\frac{{\partial N_{i} }}{{\partial N_{j} }} = f^{\prime }_{i} \frac{{\partial C_{i} }}{{\partial C_{j} }}{\left( {f^{\prime }_{j} } \right)}^{{ - 1}} = \frac{{{\left( {f^{\prime }_{i} } \right)}^{3} (N_{i} - N_{j} )F}}{{A_{i} }} = \left\{ {\begin{array}{*{20}c} {{{\text{negative}}}} & {{{\text{if}}}} & {{N_{i} > N_{j} }} \\ {{\text{0}}} & {{{\text{if}}}} & {{N_{i} = N_{j} }} \\ {{{\text{positive}}}} & {{{\text{if}}}} & {{N_{i} < N_{j} }} \\ \end{array} .} \right.$$

(A3)

As shown in Eq. A3, the sign of the slope of the reaction curve of country S _i depends on its share of the foreign aid. Thus, if s _i >0.5 (i.e., N _i <N _j ), the costs to country S _i are positively related to the costs to country S _j and vice versa if s _i <0.5. Note that country S _i 's net expected financial receipts reflect two components: its share of the foreign aid and the expected benefits as a result of uncaught illegal immigrants in the receiving country. It may therefore be concluded that for s _i >0.5, if country S _j increases its costs in curbing illegal immigration and thereby its share of the foreign aid, it is optimal for country S _i to “fight” for a larger share of the funds by raising its costs. However, if s _i <0.5, the optimal strategy is the opposite: to increase the expected benefits from uncaught illegal immigrants in the receiving country by decreasing the costs of the preventative measures.