Illegal immigration and the shadow economy

We restrict our analysis to economic migration, without considering refugees and asylum seekers.

The closest approach to our work is that by Dell’Aringa and Neri (1987), who study the effects of an exogenous increase in immigration on the labour market in Italy. Another related paper is Djajic and Mesnard (2015). They look at the rules of guest-workers programmes as the main determinant of illegal immigration, but are not primarily interested in the size of the shadow economy.

In online Appendix C, we work out a numerical exercise based on an extended version of the model, in which border enforcement and fiscal controls are both financed out of the government budget constraint. In this case, we show that tighter border controls might be associated with larger flows of illegal immigrants.

This is a pretty standard assumption in the literature on the shadow economy. See for instance (Amaral and Quintin 2006; Casarico, Facchini and Frattini 2016; Chong and Gradstein 2007; Dabla-Norris et al. 2008; Djajic and Mesnard 2015; Ihrig and Moe 2004; Hazari and Sgro 2003).

In online Appendix C, we explore an extension of the model where \(\lambda \) is endogenous.

See, for instance, Maroukis et al. (2011), Schneider (2011), Hillman and Weiss (1999) and papers cited therein.

This will require us to specify preferences over the two goods and derive the general equilibrium of the model, which will include a demand side. This changes the nature of the model and consequently some of its results.

Our formulation conforms to Borjas et al. (2011), who argue in favour of perfect substitutability between legal immigrants and natives. An article by Peri (2011) finds that the elasticity of substitution between equally skilled legal immigrants and natives is very high. For what concerns the degree of substitutability between illegal immigrants and natives in the informal sector, to the best of our knowledge there is no empirical evidence upon which we can rely. However, as suggested by Hazari and Sgro (2003), it is realistic to assume less-than-perfect substitutability between legal and illegal workers.

The Cobb–Douglas function in (9) is a convenient way to introduce imperfect substitutability between legal and illegal workers in the model, as it allows for the derivation of analytical results. A drawback of this formulation is that the informal sector would not exist without illegal immigration. Notice that a more general CES aggregator likewould have the same implication, provided that the elasticity of substitution is high enough, i.e. if \(\varphi \in [1,+\infty )\). However, this does not hold in the limit case: if \(\varphi \rightarrow \infty \), the two inputs are perfect substitutes and illegal workers are not needed for the informal sector to exist. If \(\varphi \in (0,1)\), the marginal productivity of illegal workers can tend to a positive constant when Z tends to zero, so that the informal sector does not need illegal aliens to exist. In such a case, it is possible to prove that there always exists an equilibrium with both Z and \(\rho \) strictly positive, and the model delivers the same qualitative result as in the Cobb–Douglas case.

The deportation penalty x is meant to capture social stigma or effective punishment (like jailing, property seizure and the like) that deported migrants can incur. Note also that \(\eta \) is exogenous in the benchmark version of the model, but this assumption will be relaxed in online Appendix C.

Although data on underground phenomena like illegal immigration and the shadow economy are quite sparse, the case of strategic complementarity seems relevant. For instance, Bracco and Onnis (2015) find a positive relationship between immigration and the shadow economy in Italy.

Thus, we obtain a sort of migration Laffer curve.

In online Appendix C, we propose an extended version of the model that gets closer to reality, by assuming that border control and detection of informal activity are police-operated and therefore financed through fiscal receipts. This introduces a trade-off between border patrolling and detection of informal activity in the context of a balanced government budget, but the extended model can only be solved numerically. Simulations, however, confirm and even reinforce our analytical findings. Indeed, a country enforcing stricter border controls might end up hosting more illegal aliens. This stems from the fact that border enforcement subtracts resources from fiscal controls, and thus decreases the likelihood of detecting informal activities. As a consequence, the returns to the informal sector increase and more potential migrants try to illegally enter the country.

Our government differs from a benevolent dictator, concerned with the implementation of the social optimum. Unlike a full-fledged social planner, the government here takes as given the structure of incentives that determine the market equilibrium, without internalizing the externality due to the presence of public expenditure G. The underlying assumption is that the government chooses its policy variables by aggregating individual preferences. Accordingly, we are in a second-best scenario, but this does not impinge on the overall validity of our analysis, since the main focus of this article is on illegal immigration and not on optimal taxation per se.

Notice that wages include profits as may be recalled from the discussion of Eqs. (12), (13) and (14).

In Sect. 3.2.2, we will explicitly reinterpret welfare maximization in a voting framework.

Therefore, our model provides a rationale for the common observation that xenophobic parties typically advocate lower taxes.

The result of the proposition is actually more general, as it applies also to the case of substitutability. See the proof in Appendix A.

In other words, lowering the tax rate below \(\tau _b\) implies a reduction in wages in both sectors, which in turn reduces illegal immigration.

The results of Proposition 5 do not rest on the assumption of strategic complementarity. They do depend, however, on the way we have introduced altruism towards illegal immigrants in Eq. (28). Alternative specifications are possible. In particular, the relevant variable for altruistic natives who consider migration as a poverty-alleviation device might not be the average wage for illegal immigrants. An altruistic social welfare function could, for instance, depend on (i) the difference between the immigrants’ wage and what they would have earned, had they never migrated, and/or (ii) the number of illegal immigrants (if illegal immigration is seen as the only chance of escaping poverty). In such cases, social welfare need not depend negatively on \(Z^*\). Furthermore, one could argue that a truly altruistic government may want to guarantee a legal status to all migrants in the first place.

To better understand why both \(\tau _{x}\) and \(\tau _{a}\) are lower than \(\tau _b\), notice that \(\Omega _x\) and \(\Omega _a\) have a similar structure: both are equal to \(\Omega _b\) minus a positive function of \(Z^*\).

See Persson and Tabellini (2000).

Considering that migrants react to real-wage or utility differentials would be more satisfactory, but would require a full-fledged model of the source economy, which is outside the scope of the paper.

We assume a logarithmic utility function with unitary elasticity of substitution for the sake of analytical tractability. This implies that consumers devote constant shares of their income to the purchase of the two goods.

Details are available upon request.

Notice that the equilibrium wages of legal workers are the same as in the benchmark model, as given in Eq. (11).

If some fraction of the public demand G, even very small, is not addressed to the domestic formal sector, the tax rate \(\tau \) retains is positive effect on \(\rho ^{*\circ }\). Results are available upon request.

It can be shown that informal production in physical terms is a non-monotonic function of the tax rate, with \(Y_I\) reaching a maximum for \(\tau =\alpha +(1-\alpha )\alpha /(1-(1-\alpha )\beta )\), while the volume \(Y_F\) of formal production is an increasing function of \(\tau \). However, an increase in \(\tau \) makes \(Y_I\) grow faster than \(Y_F\), if \(\tau <\alpha \). This goes hand in hand with point (vi) of Proposition B.2: as long as we are on the ascending part of the Laffer curve for illegal migration, an increase in taxes brings about an expansion of the shadow economy, in relative terms and as measured by physical production.