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The why, when, and how of immigration amnesties


This paper deals with granting of an amnesty to illegal immigrants. We consider government behavior with respect to allocations on limiting infiltration (border control) and apprehending infiltrators (internal control) and with respect to the granting of amnesties, the timing of amnesties, and limitations on eligibility for those amnesties. We demonstrate the effects of government actions on allocations and the flow of immigrants, and how the interactions between these factors combine to yield an optimal amnesty policy. We also consider two extensions—intertemporal transfers of policing funds and “fuzziness” in declarations regarding eligibility for an amnesty aimed at apprehending and deporting undesirables.

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  1. There were instances in which immigration was not only not discouraged but was actively sought. For example, in the middle of the last century, Germany was in dire need of workers, and actively sought temporary workers from neighboring countries. Many of these “temporary” workers remained in the country after contracts expired, and became a part of the large illegal immigrant population of Germany. There are signs that this policy of actively seeking temporary workers is making a comeback due to the low birth rate and the subsequent aging of the population.

  2. Guzman et al. (2008) consider the relationship between immigration enforcement, smuggling of migrants and non-wage income. They show how technological progress in the smuggling industry affects the level of migration and capital accumulation, and the effect changes in border enforcement has on the level of migration, capital accumulation, and smuggling activity. Moreover, they investigate the optimal level of enforcement as a result of technological progress in the smuggling industry. They show that the government chooses to devote resources to border enforcement only if the deterrent effect on smugglers is large enough. Otherwise, it is not worth taxing host-country natives as the taxes paid will more than offset any income gain resulting from fewer migrants.

  3. In considering internal control, we consider deportation of apprehended illegal immigrants, while Chau (2001) considers employer sanctions.

  4. Some of these differences may be less distinctive in some European and Asian amnesties. In the recent Greek amnesty, for instance, applicants were required to identify their former place of employment, thus identifying employers willing to hire undocumented immigrants. In addition, the applicants had to pay back “social insurance” taxes, so there was a backward looking element.

  5. Although there are instances in which illegal residents are careful to pay taxes in order to avoid calling attention to them.

  6. There are numerous instances of illegal workers being taken advantage of and being the victims of crimes.

  7. Of course, the opposite effect also exists. Since illegal workers receive lower wages, local capital owners and skilled laborers tend to benefit from illegal workers more than from legal workers.

  8. In Section 3.1, we consider how the possibility of intertemporal budget transfers affects allocations between internal and border controls, and over time.

  9. Note that we do not include a tenure element in the apprehension probability functions. While it is reasonable to assume that a migrant who has been in the country longer knows how to hide better, we abstract from this consideration.

  10. Our assumption is that the percentage caught depends on expenditures and not the number of those caught. This is the same assumption made in Ethier (1986) and in most of the related literature, and it conveys the idea that the greater the stock, the easier it is to find illegals—“like shooting fish in a barrel.”

  11. If the worklife is only 2 years, a third term denoting retirement needs to be included, as in Eq. 9.

  12. A simple example can be illustrative. Assume a fixed budget of 1, and probability functions \(P^B=0.2\left( {E^B} \right)^{0.5}\) and \(P^I=0.1\left( {E^I} \right)^{0.5}\). Assume also that the flow is constant and equal to 100, and that workers retire after 5 years. In this case, in the steady state over 95% of the available budget is spent on internal control, and the stock of illegal immigrants is 330.6, with 95.8 new migrants successfully entering the country each year, 32.3 being ejected, and 63.5 retiring.

  13. Note that we do not include network effects. It is quite plausible that the flow desiring to migrate depends on the stock of similar migrants in the host country (see Bauer et al. 2009). If this is so, a model aiming to analyze the incentives to migrate would have to define the stock of migrants as all those from the same country, whether legal or not. Such a definition would differ from the stock we use in our model in two respects: we consider the total number of illegal migrants without concerning ourselves with the origin of these migrants, and we do not include legal migrants or those who received amnesties in the past.

  14. This Proposition depends on the assumption that there are no costs of migrating or of being caught at the border. If this assumption is relaxed, the flow of migrants may fall or increase, and a more exact specification of the functions is necessary to arrive at clear conclusions.

  15. The length of time between amnesties in our model will be constant in equilibrium because the problem always looks identical after each amnesty, as developed below. However, it must be noted that reality rarely behaves precisely as predicted by a deterministic model, and a glance at Table 1 shows that amnesties are not generally granted in fixed intervals. We discuss this issue in the conclusions.

  16. Note we have assumed that the migrant’s wage does not change after becoming legal. There is good reason to believe, however, that this wage would increase, as the employment options facing the legal migrant are far vaster than those facing an illegal immigrant. This increased wage would have the effect of further increasing the flow of immigrants as the amnesty date approaches.

  17. Note that this stated goal implies specific weights (α) in Eq. 3. Changing the government’s objective function to include, for instance, political considerations would alter the values of α.

  18. In the case where A is a continuous variable and the amnesty can occur at any point in time Eq. 14 becomes: (14’) \(C\left( A \right)=\int\limits_{i=1}^{N-1} {\delta ^iC_L \left( {M_i \left( A \right)} \right)d} i+\int\limits_{i=1}^{A-1} {\delta ^iC_I \left( {M_i \left( A \right)} \right)di} +\delta ^AC\left( A \right)\), and (14’) is a continuous function defined on a closed and compact set. Thus, there exists a level A that minimizes C (A). In the case that A can only take on an integer value, we can find the value of A that minimizes (14’) and then test which of the integers closest to it minimizes (14).

  19. We changed the notation for time preference from that used in Eq. 3 (α) to denote that while above we placed no restrictions on the relative values over time (see Lemma 1), here the deterioration from period to period is constant, for simplicity.

  20. Any such plan must lend for the contingency that the worker will decide to overstay his permit, and will disappear into the economy and once again become an illegal immigrant. Thus, the granting of such a permit must include a mechanism that will allow the authorities the ability to enforce the departure of these illegal aliens. One such mechanism is the posting of a bond by the worker or his employer that is forfeited if the worker does not leave the country on time. For the effects of such bonds on illegal immigrants and their employers, see Epstein et al. (1999).

  21. See Trends in International Migration, 1999.

  22. Korea, for instance, took a slightly different route. In their 1997–1998 and 1999 amnesties, they did not grant work permits, but rather allowed the illegal residents to leave the country without risking sanctions. This can be incorporated in our model by setting C D  = 0 if you accept the amnesty.

  23. If N < T nothing.

  24. It will not, though, affect the gross flow in the last year before the amnesty since internal control will not be effective for them.


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We would like to thank participants at seminars in Bar-Ilan University, IZA, Northern Illinois University, the University of Calabria, the University of Illinois at Chicago, and the European Public Choice Society meetings for helpful comments. Financial support from the Adar Foundation of the Economics Department of Bar-Ilan University is gratefully acknowledged.

We are grateful to the anonymous referees for their insightful and productive comments.

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Correspondence to Avi Weiss.

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Epstein, G.S., Weiss, A. The why, when, and how of immigration amnesties. J Popul Econ 24, 285–316 (2011).

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  • Amnesty
  • Illegal immigration
  • Border and internal controls

JEL Classification

  • J61
  • J68
  • H59