Asylum seekers in Europe: the warm glow of a hot potato

Abstract

The Common European Asylum System calls for increased coordination of the European Union (EU) countries’ policies towards asylum seekers and refugees. In this paper, we provide a formal analysis of the effects of coordination, explicitly modelling the democratic process through which policy is determined. In a symmetric, two-country citizen-candidate setup, in which accepting asylum seekers in one country generates a cross-border externality in the other, we show that coordination is desirable. Internalizing the externality leads to a welfare improvement over the non-cooperative outcome. However, contrary to suggestions by many observers, we show that allowing for cross-country transfers in the cooperative outcome leads to a welfare inferior outcome because the possibility of compensation exacerbates strategic delegation effects.

Appendix

1.1 Symmetric case

This appendix derives $dm_i^B/d\hat{\alpha}_i$ and $dm_{-i}^B/d\hat{\alpha}_i$ for the bargaining equilibrium without side payments. The first-order condition for $m_i^B$ as given by Eq. 14 is $N_{m_i}=0$. The first-order condition for $m_{-i}^B$ is $N_{m_{-i}}=0$. By totally differentiating these equations, we obtain

$$\eqalign{ \frac{dm_i^B}{d\hat{\alpha}_i} = \frac{-N_{m_i\hat{\alpha}_i}N_{m_{-i} m_{-i}}+N_{m_{-i}\hat{\alpha}_i}N_{m_i m_{-i}}}{N_{m_im_i}N_{m_{-i}m_{-i}}-N_{m_i m_{-i}}N_{m_{-i} m_i}}, }$$

(42)

$$\eqalign{ \frac{dm_{-i}^B}{d\hat{\alpha}_i} = \frac{-N_{m_{-i}\hat{\alpha}_i}N_{m_i m_i}+N_{m_i\hat{\alpha}_i}N_{m_{-i} m_i}}{N_{m_im_i}N_{m_{-i}m_{-i}}-N_{m_i m_{-i}}N_{m_{-i} m_i}}. }$$

(43)

Departing from the symmetric equilibrium ($\hat{\alpha}_i=\hat{\alpha}_{-i}$ and $s_i=s_{-i}$), the respective terms in Eqs. 42 and 43 can be derived as

$$ N_{{m_{i} m_{i} }} = - 2{\left[ {1 + \widehat{\alpha }_{i} } \right]}^{2} {\left\{ {2s_{i} {\left[ {1 - 2\lambda + 2\lambda ^{2} } \right]} + {\left[ {1 - 2\lambda } \right]}^{2} } \right\}} = N_{{m_{i} m_{i} }} $$

(44)

$$ N_{{m_{i} m_{{ - i}} }} = - 2{\left[ {1 + \widehat{\alpha }_{i} } \right]}^{2} {\left\{ {4s_{i} \lambda {\left[ {1 - \lambda } \right]} - {\left[ {1 - 2\lambda } \right]}^{2} } \right\}} = N_{{m_{{ - i}} m_{i} }} , $$

(45)

$$\eqalign{ N_{m_i \hat{\alpha}_i} = s_i + 2\left[1+\hat{\alpha}_i\right]\left[2\lambda-1\right]\left[m_i^B(\hat{\alpha})-m_i^N(\hat{\alpha}^N)\right], }$$

(46)

$$\eqalign{ N_{m_{-i} \hat{\alpha}_i} = s_i - 2\left[1+\hat{\alpha}_i\right]\left[2\lambda-1\right]\left[m_i^B(\hat{\alpha})-m_i^N(\hat{\alpha}^N)\right]. }$$

(47)

Inserting these equations into Eqs. 42 and 43 and rearranging yields

$$\eqalign{ \frac{dm_i^B}{d\hat{\alpha}_i} = \frac{\left[1+s_i\right]\left[2\lambda-1\right]+2\left[1+\hat{\alpha}_i\right]\left[m_i^B(\hat{\alpha})-m_i^N(\hat{\alpha}^N)\right]}{4\left[2\lambda-1\right]\left[1+\hat{\alpha}_i\right]^2\left[1+s_i\right]}, }$$

(48)

$$\eqalign{ \frac{dm_{-i}^B}{d\hat{\alpha}_i} = \frac{\left[1+s_i\right]\left[2\lambda-1\right]-2\left[1+\hat{\alpha}_i\right]\left[m_i^B(\hat{\alpha})-m_i^N(\hat{\alpha}^N)\right]}{4\left[2\lambda-1\right]\left[1+\hat{\alpha}_i\right]^2\left[1+s_i\right]}. }$$

(49)

1.2 Asymmetric case

As in the symmetric case, the equations determining the marginal influence of $\hat{\alpha}_i$ on the immigration levels can be derived from the first-order conditions and are identical to Eqs. 42 and 43 above,with $N_{m_i}=0$ given by Eq. 34. From Eq. 34 the following equations can be derived:

$$\eqalign{ N_{m_i m_i} = -\frac{s_{-i}}{\left[1-m_i\right]^2}-2 \left[1+\hat{\alpha}_{-i}\right]^2 s_i/s_{-i}, }$$

(50)

$$\eqalign{ N_{m_i m_{-i}} = 2\left[1+\hat{\alpha}_i\right]\left[1+\hat{\alpha}_{-i}\right], }$$

(51)

$$\eqalign{ N_{m_{-i} m_{-i}} = -\frac{s_{i}}{\left[1-m_{-i}\right]^2}-2 \left[1+\hat{\alpha}_{i}\right]^2s_{-i}/s_{i}, }$$

(52)

$$\eqalign{ N_{m_i \hat{\alpha}_i} = s_{-i} + \left[ 1+\hat{\alpha}_{-i}\right] Δ m^B, }$$

(53)

$$\eqalign{ N_{m_{-i} \hat{\alpha}_i} = s_{-i} - \left[1+\hat{\alpha}_i\right]Δ m^B s_{-i}/s_i . }$$

(54)

Inserting these equations, employing Eq. 34, and rearranging yields Eqs. 35 and 36, with $\mid H\mid \equiv N_{m_im_i}N_{m_{-i}m_{-i}}-N_{m_i m_{-i}}N_{m_{-i} m_i}>0$.