Queuing to leave: A new approach to immigration

Nayantara Sarma

doi:10.2478/izajodm-2021-0007

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Queuing to leave: A new approach to immigration

IZA Journal of Development and Migration

Volume 12 (2021): Issue 1 (January 2021)

By: Nayantara Sarma

Open Access

|Jul 2021

Figures & Tables

Migration Queuing System (Cases I and II).

Expected utility from legal immigration at different acceptance rates. Parameter values: *R_l* = 1000, C =10, α = 0.05, 〈*W_l*〉 = 4, T = 30.

Expected utility from legal immigration at different discount rates. Parameter values: *R_l* = 1000, C =10, ν = 0.3, 〈*W_l*〉 = 4, T = 30.

Vertical axis shows steady state relative shares of legal and illegal migration flows and horizontal axis shows time for different patience parameters and critical waiting times.
**Source:** Simulations using Anylogic Parameter values: λ_o= 1, μ_l= 1.4, μ_i= 1.9 and a) W_l^c*= 18, P= 4 (top panel) b) W_l^c*= 40, P= 1 (bottom panel).

Steady state legal queue content and horizontal axis shows time.
**Source:** Simulations using Anylogic Parameter values: λ_o= 1, μ_j= 1.4, μ_i= 1.9, W_l^c*= 18, P= 4.

Countries with the highest illegal border crossings over the 5-year period 2010–2014 according to Frontex data.

Migration Queue (Case III).
**Source:** Author's representation.

Table 1

Summary statistics

Variable name	Category	Mean	Standard deviation	N	AR(1) Coefficient	$\frac{σ_{α}^{2}}{σ_{ε}^{2}}$
Log legal inflow	Overall	5.808	2.888	1,744	0.177	0.97
	Between		2.854	218
	Within		0.478	8
Log illegal inflow	Overall	3.479	3.257	1,096	0.296	0.81
	Between		3.092	137
	Within		1.052	8
Log CD	Overall	1.115	2.466	1,768	0.309	0.68
	Between		2.241	221
	Within		1.039	8
Log CD difference	Overall	0.800	2.025	1,768	0.230	0.71
	Between		1.800	221
	Within		0.934	8
Log GNI per capita	Overall	9.871	1.246	1,274	0.781	0.96
	Between		1.211	188
	Within		0.077	6.8
Log population density	Overall	5.097	1.567	1,644	0.965	0.98
	Between		1.568	206
	Within		0.046	8
Institutions score	Overall	−0.033	0.995	1,592	0.636	0.91
	Between		0.990	200
	Within		0.138	8

[i] Note: AR(1) coefficients and the relative variance explained by fixed effects $(\frac{σ_{α}^{2}}{σ_{ε}^{2}})$ are calulated by estimating y_it = ρy_it₋₁ + α_i + ɛ_it.

[ii] CD, conflict deaths.

Table 2

Pooled OLS and within-estimator dependent variable: Illegal inflow

	OLS	Within	Within	Within
	All	All	All	Restricted sample
	(1)	(2)	(3)	(4)
Log CD_t−1	0.306^*** (0.035)	0.094^** (0.040)	0.082^** (0.038)	0.071^* (0.036)
Log population density	0.244^*** (0.050)		6.761^*** (2.571)	4.234 (3.394)
Institutions	−1.390^*** (0.095)		−0.813 (0.579)	−1.419^** (0.672)
Constant	0.887^*** (0.336)	2.987^*** (0.130)	−29.881^** (12.270)	−17.052 (15.764)
Year fixed effects	Yes	Yes	Yes	Yes
Country fixed effects		Yes	Yes	Yes
Adjusted R²	0.273	0.130	0.171	0.246
Number of observations	920	959	920	497
Number of countries		137	132	71

Note:

* p < 0.10,

** p < 0.05,

*** p < 0.01.

Standard errors, given below coefficients in parentheses, are clustered at the country level.

CD, conflict deaths.

Table 3

Pooled OLS and within-estimator dependent variable: Legal inflow

	OLS	Within	Within	Within
	All	All	All	Restricted sample
	(1)	(2)	(3)	(4)
Log CD_t−l	0.302^*** (0.016)	0.033 (0.034)	−0.000 (0.011)	−0.009 (0.012)
Log population density	−0.231^*** (0.056)		0.648 (0.562)	0.599 (0.685)
Institutions	0.268^*** (0.071)		0.000 (0.196)	−0.450^** (0.176)
Constant	6.905^*** (0.321)	5.556^*** (0.062)	2.943 (2.796)	4.008 (3.306)
Year fixed effects	Yes	Yes	Yes	Yes
Country fixed effects		Yes	Yes	Yes
Adjusted R²	0.101	0.039	0.054	0.142
Number of observations	1,364	1,526	1,364	532
Number of countries		218	196	76

Note:

* p < 0.10,

** p < 0.05,

*** p < 0.01.

Standard errors, given below coefficients in parentheses, are clustered at the country level.

CD, conflict deaths.

Table 4

Two-Stage Least Squares (2SLS) estimator

Part A	Legal inflow			Illegal Inflow
	All	All	Restricted sample	All	All	Restricted sample
	(1)	(2)	(3)	(4)	(5)	(6)
Log CD_t−1	0.042^* (0.022)	−0.000 (0.013)	−0.010 (0.013)	0.120^*** (0.039)	0.120^*** (0.041)	0.106^** (0.041)
Log population density		0.648 (0.410)	0.600 (0.499)		6.783^*** (1.610)	4.162^** (2.111)
Institutions		−0.000 (0.154)	−0.453^*** (0.130)		−0.724^* (0.371)	−1.288^*** (0.458)
Year fixed effects	Yes	Yes	Yes	Yes	Yes	Yes
Country fixed effects	Yes	Yes	Yes	Yes	Yes	Yes
Part B	First stage dependent variable: Log CD
Log CD difference	0.828^*** (0.041)	0.800^*** (0.044)	0.782^*** (0.045)	0.824^*** (0.040)	0.789^*** (0.043)	0.779^*** (0.043)
Log population density		0.628 (0.796)	3.522^* (1.944)		1.133 (1.130)	3.289^* (1.995)
Institutions		−0.576^*** (0.178)	−1.831^*** (0.454)		−1.096^*** (0.316)	−1.811^*** (0.462)
Number of observations	1,526	1,364	532	959	920	497
Number of Countries	218	196	76	137	132	71
Kleibergen-Paap F-stat	405.913	327.501	302.436	430.805	340.704	322.067

Note:

* p < 0.10,

** p < 0.05,

*** p < 0.01.

Standard errors, given below coefficients in parentheses, are clustered at the country level.

CD, conflict deaths.

Table 5

GMM estimates

	Difference GMM		System GMM		Common factor
	Illegal	Legal	Illegal	Legal	Illegal	Legal
	(1)	(2)	(3)	(4)	(5)	(6)
Log illegal inflow_t−1	0.103 (0.085)	−0.030 (0.030)	0.752^*** (0.047)	0.018 (0.012)	0.806^*** (0.047)	−0.008 (0.016)
Log illegal inflow_t−2						0.027 (0.016)
Log legal inflow_t−1	−0.105 (0.152)	−0.140^* (0.074)	0.266^*** (0.085)	0.899^*** (0.031)	0.050 (0.088)	0.903^*** (0.027)
Log legal inflow_t−2					0.163^** (0.081)
Log CD_t−1	0.010 (0.059)	−0.009 (0.020)	0.071^** (0.034)	0.013 (0.011)	0.063^** (0.032)	0.002 (0.013)
Log CD_t−2					0.015 (0.031)	0.008 (0.015)
Year fixed effects			Yes	Yes	Yes	Yes
Number of observations	804	804	938	938	804	804
Number of countries	134	134	134	134	134	134
Number of instruments	46	46	71	71	73	73
AR(1) p-stat	0.0004	0.1682	0.0000	0.0000	0.0000	0.0000
AR(2) p-stat	0.1811	0.7931	0.3345	0.0821	0.4006	0.1477
Hansen p-statistic	0.0004	0.0574	0.0194	0.0645	0.0085	0.0601

Note:

* p < 0.10,

** p < 0.05,

*** p < 0.01.

Standard errors, given below the coefficient in parentheses, are clustered by country. Columns 1–4 use the two-step and Columns 5 and 6 use the one-step co-variance matrix estimations.

CD, conflict deaths; GMM, generalized method of moments.

Table 6

Within and 2SLS estimators dependent variable: Log of resettled persons

	Within	Within	Within	Within	2SLS	2SLS
	(1)	(2)	(3)	(4)	(5)	(6)
Log CD_t−1	0.072 (0.048)
Log CD_t−2		0.072 (0.045)
Log CD_t−3			0.130^*** (0.048)	0.077^* (0.046)	0.143^** (0.066)	0.068 (0.066)
Log population density				−1.059 (2.129)		−1.085 (2.131)
Institutions				−0.400 (0.328)		−0.407 (0.332)
Constant	0.617^*** (0.102)	0.674^*** (0.087)	0.464^*** (0.096)	5.755 (10.530)	0.445^*** (0.118)	5.896 (10.538)
Year fixed effects	Yes	Yes	Yes	Yes	Yes	Yes
Country fixed effects	Yes	Yes	Yes	Yes	Yes	Yes
Adjusted R²	0.013	0.012	0.036	0.017
Number of observations	1,576	1,379	1,182	952	1,182	952
Number of groups	197	197	197	192	197	192