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)