Post on 22-Dec-2015
Ec-980u: Self-Selection of Immigrants
George J. BorjasFall 2010
2. Hourly wage differentials between immigrant and native men in 2000, by national origin
Country of origin % of immigrant workforce
Log wage gap
All immigrants New arrivals
Mexico 31.9 -0.485 -0.686
China 4.7 0.008 -0.180
India 4.4 0.303 0.226
Philippines 3.8 -0.010 -0.242
Vietnam 3.4 -0.194 -0.486
El Salvador 2.9 -0.420 -0.633
Cuba 2.8 -0.201 -0.525
United Kingdom 2.7 0.326 0.369
Canada 2.3 0.300 0.348
Korea 2.2 -0.006 -0.093
Russia 1.9 -0.007 -0.212
Dominican Republic 1.9 -0.376 -0.470
Guatemala 1.7 -0.461 -0.654
Germany 1.6 0.202 0.249
Jamaica 1.6 -0.130 -0.357
3. The migration decision
What determines whether to migrate or not? Basic economic model: person migrates if the income gain from migrating exceeds the migration cost
Let V1 be present value of earnings (income) if one migrates to, say, the US
Let V0 be the present value of earnings if one stays in the sending country
Migration occurs if V1 – V0 > C , where C measures the cost of migration
4. The selection problem
The immigrant flow is a non-random sample of the population from the countries of origin
The immigrant flow is self-selected: Not all persons from a particular source country wish to migrate to the United States
Which persons leave the country of origin and which persons stay there?
5. Ad hoc theories of selection
Benjamin Franklin, 1753: German immigrants are “the most stupid of their own nation.”
George Patton, 1943: “When we land, we will meet German and Italian soldiers whom it is our honor and privilege to attack and destroy. Many of you have in your veins German and Italian blood, but remember that these ancestors of yours so loved freedom that they gave up home and country to cross the ocean in search of liberty. The ancestors of the people we shall kill lacked the courage to make such a sacrifice and continued as slaves.”
6. More ad hoc theories of selection
Chiswick (1978): immigrants are “more able and more highly motivated” than natives.
Carliner (1980): immigrants “choose to work longer and harder than nonmigrants”
7. Types of selection
Positively-Selected Immigrant Flow
Frequency
Negatively-Selected ImmigrantFlow
SkillssPsN
8. Theory of selection: The Roy model
Two-country model: a sending country (0) and a receiving country (1); e.g., Mexico and the U.S.
Log earnings in the sending country are given by:
logw0 =μ0 + ε0 , with ε0 ~N(0,σ02 )
Think of ε0 as the de-meaned value of worker’s skills in the sending country.
If everyone from 0 were to migrate to 1, their log earnings distribution would be (ignoring any general equilibrium effects!):
logw1 =μ1 + ε1, with ε1 ~N(0,σ12 )
9. Migration costs
Assume the costs of migration are equal to C. Define “time-equivalent” migration costs as Π=C/w0. Suppose time-equivalent migration costs are constant.
A person chooses to migrate from country 0 to country 1 if:
I =logw1
w0 +C=log
w1
w0 (1+ π)> 0
I =logw1 −logw0 −π > 0I =μ1 + ε1 −μ0 −ε0 −π > 0OR : (μ1 −μ0 −π)+ (ε1 −ε0 ) > 0
10. Probability of migration
The random variable v is normal with standard deviation σv; Φ is the cumulative distribution function of the normal. Note that the larger z, the lower is the probability of migration. Hence:
Let v=ε1 −ε0 .
P =Pr[v> (μ0 −μ1 +π)] =Prvσv
>(μ0 −μ1 +π)
σ v
⎡
⎣⎢
⎤
⎦⎥
=1−Φ(μ0 −μ1 +π)
σ v
⎡
⎣⎢
⎤
⎦⎥=1−Φ(z).
∂P / ∂μ 0 < 0, ∂P / ∂μ1 > 0, ∂P / ∂π < 0.
11. A definition
The correlation between the ε component of sending and receiving country earnings is:
ρ=σ01
σ 0σ1
Where σ01 is the covariance between ε0 and ε1, and σj is the standard deviation of εj.
12. Self-selection
Question: how do the out-migrants do in the source country prior to migration?
This depends on mean earnings in the source country, on the ε error terms, and implicitly on the correlation between these error terms.
E(logw0 | immigrate) =μ0 +E(ε0 |vσv
> z)
=μ1 +σ0 E(ε0σ0
|vσv
> z)
13. A property of normal random variables
Suppose x and y are normal random variables. Then the conditional expectation is linear and the coefficient is the regression coefficient:
This implies we can write the “population” regression between standard normal random variables as:
E(y | x) =σxy
σx2 x→ E(
yσy
|x) =σxy
σyσx
xσx
=ρxy
xσx
y
σy
=ρxy
xσx
+ζ, whereζ is random noise.
14. Let’s use this property
The “*” denote standard normal random variables. Note that λ(z) must be a positive number.
E(logw0 | immigrate) =μ0 +σ0Eε0σ0
|vσv
> z⎛
⎝⎜⎞
⎠⎟
=μ0 +σ0E ε0* |v* > z( ) =μ0 +σ0E (ρ0vv
* +ζ) |v* > z( )
=μ0 +σ0Eσ0v
σ0σv
v* |v* > z⎛
⎝⎜⎞
⎠⎟
=μ0 +σ0v
σv
E v* |v* > z( ) =μ0 +σ0v
σv
λ(z)
15. And to simplify further:
E(logw0 | immigrate) =μ0 +σ0v
σv
λ(z)
=μ0 +(σ01 −σ0
2 )σv
λ(z)
=μ0 +σ0σ1
σv
ρ−σ0
σ1
⎛
⎝⎜⎞
⎠⎟λ(z) =μ0 +Q0
16. Self-selection, part 2
Question: how do the immigrants do in the receiving country after migration?
E(logw1 | immigrate) =μ1 +E(ε1 |vσ v
> z)
=μ1 +σ1 E(ε1σ1
|vσ v
> z)
=μ1 +σ1E (ρ1vv* +ζ) |v* > z( )
=μ1 +σ0σ1
σv
σ1
σ0
−ρ⎛
⎝⎜⎞
⎠⎟λ(z) =μ1 +Q1
17. Types of selection
Suppose μ0 = μ1, so that we can isolate the selection in the distribution of skills, as measured by Q0 and Q1. There are four possibilities:
Case 1: Q0>0 and Q1>0. Case 2: Q0<0 and Q1<0. Case 3: Q0<0 and Q1>0. Case 4: Q0>0 and Q1<0.
18. Case 1: Positive selection
Q0>0 and Q1>0. Since λ(z) is always a positive number this
requires that:
19. Case 2: Negative selection
Q0<0 and Q1<0. This requires that:
20. Case 3: Refugee sorting
Q0<0 and Q1>0. This requires that:
21. Case 4: Impossible
Q0>0 and Q1<0. This requires that:
This type of selection requires that the correlation coefficient exceeds 1, which is impossible. The reason is that income maximization would never lead to an outcome where high-income people migrate to become low-income people.
22. A graphical version of the Roy model
There is a linear relationship between wages and “skills” in each country:
log wagej = aj + rj S The intercept aj gives the earnings of a person
with little (zero) skills; the slope rj gives the rate of return to skills in country j.
“Skills” increase earnings in both the country of origin and in the United States.
There are no migration costs
23. Positive selection
Skills
Log wage
Do Not Move
Move
aS
aUS
sP
Source Country
U.S.
24. Negative selection
Skills
Log wage
Do Not Move
Move
sN
aS
aUS
Source Country
U.S.
26. Impact of a decline in U.S. incomes (with positive selection)
Skills
Log wage
aS
aUS
sP
Source Country
U.S.
s*
27. Impact of a decline in U.S. incomes (with negative selection)
Skills
Log wage
sN
aS
aUS
Source Country
U.S.
s*
28. Adjusted entry wage of immigrants and per-capita GDP in source country
-0.8
0.6
-2 0 2
Measure of per-capita GDP (in logs)
En
try
wag
e (i
n lo
gs)
Each point represents a national origin group
Regression line indicates that a doubling of the source country's per-capita GDP raises the entry wage of the immigrant group by 15 percent
Mexico
Haiti
India
CanadaItaly
Australia
Laos
New Zealand
Malaysia
IrelandIsrael
Sw itzerland
Hong Kong
Japan
Trinidad
Belgium
29. Entry wage of immigrants and income inequality in the source country
-0.8
0.8
-23 5 33
Measure of wage inequality (Gini coefficient)
En
try
wa
ge
(in
log
s)
Each point represents a national origin group
Regression line indicates that a 25-unit increase in the Gini coeff icient--roughly the difference betw een the UK and Mexico--low ers the w age by 30 percent
Mexico
UK
Poland
France
Iraq
South Africa
Turkey
Netherlands
Spain
Canada
Belgium
Sw eden
China Honduras
Brazil
Australia
Sw itzerland
Japan
Malaysia
30. Trends in emigrant share, by education, Mexico (Chiquiar-Hanson)
0
0.1
0.2
0.3
1960 1965 1970 1975 1980 1985 1990 1995 2000
Year
Emig
rant
sha
re
High school graduates
Some college
High school dropouts, 0-8
College graduates
High school dropouts, 8-11
31. Chiquiar-Hanson and Fernandez-Huertas
Chiquiar-Hanson use Census data Fernandez-Huertas uses the ENET: “The ENET is the household survey…used to calculate
the official employment statistics for Mexico from the second quarter of 2000 until the end of 2004…The ENET is very similar to the Current Population Survey in the United States…Since every household is interviewed five times, with one of the five panels dropping out of the sample each quarter, a researcher can match the data on wages or schooling of an individual in a quarter in which she lives in Mexico with the migration behavior of that individual in the following quarter.”
32. Wage distributions of migrants and non-migrants (Fernandez-Huertas, 2009)
33. Degree of selection (diff in wages) (Fernandez-Huertas, 2009)