The role of capital mobility in illegal immigration policy

Abstract

This paper analyzes the effectiveness of enforcement in controlling illegal immigration in two scenarios, capital mobility and capital immobility in the host nation (for illegal immigrants). The source nation is assumed throughout to have immobility of capital. We show that the net enforcement expenditure is higher (lower) in the presence of capital mobility if the host nation is an importer (exporter) of capital at the target immigration level. Furthermore, we show that if the host nation is an exporter of capital at the point of zero enforcement (unrestricted immigration), it must have lower enforcement expenditure (compared to capital immobility) for any illegal immigration target. If it is an importer of capital at zero enforcement, there is some ambiguity. National income must be higher (lower) under capital mobility (compared to immobility) if the host nation is an importer (exporter) of capital at the target immigration level. The analysis is extended to consider endogenous determination of optimal immigration level. Under capital mobility, for a capital exporting nation, the optimal enforcement and the national income levels are higher, while the optimal immigration level is lower.

Key words:

• Illegal immigration
• capital mobility
• optimal enforcement

Acknowledgments

We would like to thank the editor Professor Giles and an anonymous referee for their very helpful comments. The usual disclaimer applies.

Notes

¹ Throughout this paper the host nation and the source nation refer to the host and source nations for illegal labor, respectively.

² More recent contributions include Bandyopadhyay & Bandyopadhyay (1998), Hanson and Spilimbergo (1999 2001), Gaytan-Fregoso and Lahiri (2000 2004), among others.

³ For simplicity, let us denote the host nation and the source nation for illegal labor as the home nation and the foreign nation, respectively.

⁴ The assumption of capital immobility for the source nation is necessary for obtaining a sensible equilibrium in the market for illegal immigrants when the host country faces capital mobility. With capital mobility in both the source and host nations the demand and supply curves for illegal immigrants are perfectly elastic and no well-defined equilibrium exists. A possible (and arguably reasonable) way of handling this issue is to assume that the host nation has market power in the international capital market. In that case, one can assume perfect capital mobility in the source nation and yet have a sensible solution. For the sake of simplicity and clarity of exposition, we maintain the assumption of capital immobility for the source nation. Given that many source nations have (at best) imperfect access to global capital markets, our assumption of complete immobility may not be very unreasonable.

⁵ Note that p _i I _t z are total fine collections by the government at the target immigration level. Thus, the expenditure net of these fine collections is: e _i  + e _b  − p _i I _t z.

⁶ Notice from equation (14) that K ^m is not independent of I under capital mobility. When I = I_b , .

⁷ Note that while the NE functions look the same in the two cases, they may assume different values (in general) because as Proposition 1 shows, the optimal enforcement may differ between the regimes.

⁸ For clarity of exposition, we can refer to Figure 4. Given the factor price frontier, if r (under immobility) happens to equal [rtilde], then w must equal [wtilde] and we have Case 1. Similarly, r (under immobility) < [rtilde], requires that w > [wtilde] and this is analyzed in Case 2.

⁹ There is no lack of continuity between the second and third sections of this paper, because in the second section, the analysis focuses on a given (target) I and hence will lead to the same B(I) in the two regimes. Given that B(I) will appear symmetrically in the two regimes, the national income comparisons in that section are unchanged.

¹⁰ The joint optimality of enforcement policy and second best trade policies in a preferential trading model have recently been addressed in Bandyopadhyay (2006).

¹¹ Note that the functional forms of and are different in general, because they are the optimal enforcement levels for two different cost minimization problems – the former uses the function η(R) for I, while the latter uses the function μ(R). Similarly, and are distinct functions.

¹² From inequality (16) we know that for the same I, η′(.) > μ′(.). However, note that for the same I, the corresponding Rs are different between the two regimes. Therefore, (16) does not necessarily imply that: . For a capital exporting nation, Figures 1 –  3 tell us that for the same R, I is lower under mobility. Relations (11′) and (15′) suggest that if the third partial derivative (with respect to labor) of the foreign production function is not too large then we must have: .