Immigration amnesties

Abstract

Barriers and border patrols complement amnesty in a coherent policy that creates incentives for illegal immigrants to self-select on the basis of ability in a way that benefits a rich host country. We consider the roles of barriers to migration and immigration amnesties in greater depth and, in particular, we examine the rich country's optimal policies. Encouraging self-selection is optimal under some, but not all, circumstances, because there are mixes of potential immigrants for which the cost of welfare migration is more than offset by the gains from productive workers enticed by a more lenient immigration policy. Furthermore, under plausible assumptions, the rich country's optimum may require a probabilistic rather than a certain amnesty to fine-tune the mix of migrants. Numerical examples illustrate that probabilistic or certain amnesties, addressed to different partitions of the migrant population, are each optimal as the mix of potential migrants changes.

Acknowledgements

We thank Ardeshir Dalal, Young Kim, Robert E. Martin, Jacob Rosenberg and the referee for comments and suggestions on earlier drafts of this article. We also thank seminar participants at Loyola University of Chicago, Northern Illinois University and the University of Illinois at Chicago. An earlier version of this article was presented at the 2002 Chicago meetings of the Midwest Economics Association.

Notes

¹ The research continues to model the heterogeneity of illegal immigrants introduced by Karlson and Katz (2003). The research thus differs from Chau's (2001) model of amnesty in which all illegal migrants offer the same skills to the rich country's labour market.

² The evidence on whether rich countries selectively ignore illegal immigration is mixed. Borjas (1999a, p. 204) suggests that illegal immigrants indeed do work that legal residents of the United States will not do, a perspective that receives anecdotal support in Schlosser (2001, pp. 161–162), although Chiswick (1988, p. 126) finds no evidence of a distinct ‘illegal’ sector in Chicago. United States government policies are consistent with acceptance of some illegal immigration. For example, the US Immigration and Naturalization Service is not allowed to carry out surprise searches for illegal immigrants in the agricultural sector. Some banks and police departments, primarily in the Southwest, accept identity articles, known as matriculas, issued by Latin American governments, for transactions at inter alia banks and libraries (Walker, 2003).

³ Given the absence of effective capital markets in many poor countries, some individuals who do not obtain certificates of ability, such as university degrees, will, nonetheless have high ability. The proportion of such individuals among potential illegal immigrants is, however, likely to be significantly smaller than in the population as a whole.

⁴ We do not propose that all residents of B will be enticed to migrate to A under some policies. A large proportion of B's population comprises individuals whose valuation of income earned abroad is so low that they will not migrate to A. Because these individuals do not affect our analysis, we make no further consideration of them.

⁵ Borjas (1999b, p. 610) uses a similar specification of welfare benefits. His research focuses on the evolution of welfare-magnet states for (presumably) legal migrants rather than on the illegal entry of migrants seeking post-amnesty welfare benefits that we model in this article.

⁶ Because all potential migrants earn the same income x in B, a constant entry cost of b is equivalent to a constant proportion of source-country income as in Borjas's (1999b, p. 612) model.

⁷ The treatment of illegal immigrants as taxpayers or as welfare recipients after the amnesty provides a convenient framework for thinking about the general phenomenon, which is that all illegal immigrants provide the rich country with gains from trade by working in the underground economy. As legal workers, asking whether they pay taxes or become public charges is equivalent to asking whether they provide gains as legal residents.

⁸ Without loss of generality.

⁹ Note that workers who are given public assistance are assumed to be working to the extent of their ability, producing a _ℓ. Relaxing this assumption complicates but does not alter our results.

¹⁰ Any combination of μ and b for which V_hh > 0, and , also allows A to achieve Policy 2. However, as shown by Equations 8 and 9, A achieves maximum welfare under Policy 2 with μ = 1.

¹¹ Note that t(a_h − a ₀) > 0 and , implying that 1 > α₄ > 0.

¹² With probabilistic amnesty, b = 0 is A's optimal choice. If b > 0, migrants expect a larger value of μ, which, in this case, reduces A's benefits.

¹³ Although we are seeking conditions that yield and , the conditions on k* differ from the conditions we used to derive k _sep, because A's problem is different. Proposition 1 provides a separation condition that assures V _ℓh  = 0 with μ = 1 and b > 0. Equation 16 ensures nonnegativity of V _ℓh and with μ = μ₄ < 1 and b = 0.

¹⁴ Because 0 ≤ β ≤ 1, 0 ≤ α₄ < 1.

¹⁵ See Hillman and Weiss (1999, pp. 585–586) and the references cited therein, which they interpret as support for perceived ‘permissible illegal immigration’. The current regularization policies under debate in the United States, despite protestations by government officials to the contrary, have features consistent with the probabilistic amnesties we consider as policies 4 and 5.

¹⁶ Note that t(a_h − a ₀) > 0 and , implying that 1 > α₅ > 0.

¹⁷ We show below that both the denominator and numerator of Equation 28 are positive, and that the numerator is smaller than the denominator.

¹⁸ Note that the coefficient of α in (29) is α[(1 − β)[y − w + t(a_h − a ₀)] − β[y − w + (a_ℓ − a ₀)]]. The first term of this positive, as is the second term, because by Equation 5. The coefficient can be rewritten as (1 − 2β)(y − w) + (1 − β)t(a _h  − a ₀) − β(a _ℓ − a ₀) as in (28). The denominator of (28) is also positive, by Equation 5.

¹⁹ Proofs of these results will be made available to readers upon request.

²⁰ If α = 1, there are no welfare migrants. Because μ₅ = 1 at k = k _min to induce ℓℓ migrants, a probabilistic Policy 5 will never be optimal for valuation parameters in a neighbourhood of k _min.

²¹ Because y > w and a ₀ a _ℓ, both the denominator and numerator of Equation 34 are positive.

²² Our numerical examples provide no such occurrences, but we cannot rule out a priori k < k _sep such that Equation 36 holds at all k* > k _sep.

²³ Derivations of these results are available from us on request.

²⁴ Differentiating α₄₃ yields

which is positive at all values of . That condition holds in our numerical examples, such that an increase in β shifts α₄₃ upward.

²⁵ Differentiation of α₅₃ with respect to a ₀ and to t yields

such that a decrease in a ₀ would shift α₅₃ up, but

is negative provided, as is the case in our numerical examples,

Thus, an increase in the tax rate t shifts α₅₃ down. The effect of a change in a ₀ on α₄₃ is ambiguous, with

however

is negative provided .

²⁶ Borjas (1999b, p. 610, note 6) argues, ‘A state's welfare policy is probably very sensitive to the in-migration of potential welfare recipients either from other states or from abroad’. That sensitivity does not always imply a reduction of public benefits. For example, the Health Policy Tracking Service (http://www.stateserv.hpts.org) of the National Conference of State Legislatures reports that nearly half the States of the United States have introduced legislation under which the children of illegal immigrants – not necessarily born in the United States – may qualify for tuition at in-state rates.

²⁷ Some of these possibilities may be viewed as socially unacceptable, and be subjected to various legal challenges.