Temporary Foreign Work Permits: honing the tools to defeat human smuggling

We study how temporary visa schemes can be designed to drive smugglers out of business while meeting labor market demand in host countries. The policy trade-off between migration control and ending human smuggling can be overcome by combining internal and external controls with a regulated market for temporary visas. In this market, visa duration and price are set at “eviction” levels that throttle smuggling activity. We use information on irregular migration from Senegal to Spain and the Democratic Republic of Congo to South Africa to calibrate the eviction prices of visas for these two routes. Our results highlight important constraints for governments seeking to prevent temporary workers from overstaying, especially on South-North routes such as Senegal to Spain. They suggest combining a regulated market for visas with tighter sanctions against employers of undocumented workers as a way forward. JEL Classifications : F22,I18,L51,O15.

The smuggling market: the demand home irregular mig. Temporary visas scheme (IR) migrate legally rather than stay home → to price out smugglers, eviction price lower than p L , s.t.
Temporary visas scheme: self-enforceable visas (SE) workers return home after visa expires: Detail • retain share of income earned abroad, s, • increase risk of deportation, δ.
Proposition 1 : self-enforceability • Always possible, as long as δ is "high enough". The eviction price p L (τ ) of temporary visas of duration τ below which smugglers exit the market is implicitly defined by Policies to regulate migration A government may want to maintain at least the same skill diversity of foreign workers following the sale of visa (τ ,p L (τ )) .
Proposition 4: increasing skill diversity → Set the visa duration below a thresholdτ (q, c, d) ∈ [0, 1] solution to τ decreases with q, c and increases with d.

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Policies to regulate migration A government may want to maintain at least the same skill diversity of foreign workers following the sale of visa (τ ,p L (τ )) .
Proposition 4: increasing skill diversity τ decreases with q, c and increases with d.

Proposition 5: cost-effective visas
A government may seek to minimise its budget, combining optimally enforcement of internal and external controls (d(I * 1 ), c(I * 2 ), q(I * 3 )) with sale of visa (τ ,p L (τ )) to reach its migration target.

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Numerical applications Numerical applications  To everyone asking about the way and the price. Travelling straight to Europe by plane costs between 4,000 and 8,000 euros. If you only want a passport and pay for the plane ticket yourself, and you take the consequences, then the price is 4,000 euro for a 100% genuine passport belonging to someone who looks like you. But if you want to pay after arriving in Europe, the price is 8,000 euro and we will pay for everything and take all the risk. Just send your picture and your number via Facebook message so we can find a passport belonging to someone who looks like you, and then we will call you." Value function u(.) is S-shaped, with an inflection point in zero, and shows a kink at the origin. Remarks: • Looks like CRRA for x > 0; • α, risk-aversion parameter for gains: individuals are risk-averse for gains; • β, risk-aversion parameter for losses: individuals are risk-seeking for losses; • In practice, α = β. Weighting functions are concave near 0 and convex near 1.
• Individuals overestimate the probabilities related to rare salient events (e.g. successful irregular migration to Europe).
• They underestimate the probability of frequent but non salient events (e.g. failed irregular migration).
• γ captures this distorted perception of reality.
• γ = 1 means no distortion.  • face the following lottery if they overstay to work illegally • which they compare to a payoff τ w f + (1 − τ )∆ h (θ)w h − p L if they comply with visa rules.
• Self Enforcement condition is: increasing skill diversity A government may want to maintain at least the same skill diversity of foreign workers following the scheme.

Proposition 4: increasing skill diversity
If the visa is short enough, below a threshold τ (q, c, d) ∈ [0, 1] solution to the scheme increases the skill diversity of migrants. This threshold decreases with q, c and increases with d.

Calibrating the distribution
To distribution To benchmark values • We follow Grogger and Hanson (2011).
• Relationship between Gini coefficient Γ, average income and distribution parameters, when income is log-normal.
• For ln R ∼ N (µ, σ 2 ), Calibrating the distribution  • Log-revenue is linear in θ and follows a normal distribution.
where G denotes the cumulative density function of the distribution N (µ h , σ h ), while R L h = ∆ h (θ L )w h and R I h = ∆ h (θ I )w h are the incomes of individuals θ L and θ I in the home country.
• Using the Tversky and Kahneman (1992) functional forms, condition on irregular migrant threshold (θ I ) yields: Predicting eviction prices • Compute the minimum retention share s using an iterative solver on SE applied to θ = 0: • variation in share of migrants: Detail on variation in share F (θ L )−F(θ I )