ECON immigration

Age-earnings profile

The relationship between a worker's age and their earnings; typically, these profiles are upward-sloping and concave, meaning earnings rise over time but at a decreasing rate

Efficiency units

A measure of the units of skill a worker embodies, which is "rented" to the labor market at a specific dollar rate

Gini coefficient

A single number between 0 (perfect equality) and 1 (perfect inequality) used to summarize an entire income distribution; it increases as inequality increases

Human capital (HC

The stock of skills and knowledge a worker possesses, often acquired through education or training

Intergenerational correlation

The slope of the regression line between a child’s earnings and parental earnings; a slope of 1 indicates total persistence of parental earnings, while 0 indicates complete regression toward the mean

Lorenz curve

A graphical representation of income distribution where the ratio of the area between the "perfect-equality" line and the "actual" curve determines the Gini coefficient

Mincer earnings function

A mathematical formula—log(w)=a⋅s+b⋅t−c⋅t2—used to model earnings based on years of schooling (s) and labor market experience (t)

On-the-job training (OJT)

Training acquired after formal education; General OJT is useful at all firms (e.g., coding), while Specific OJT is only useful at the firm where it is acquired

Skill premium

The ratio of skilled to unskilled workers' wages (e.g., WS​/WU​); it represents the economic return to being skilled

Wage gap

The difference between wages at different percentiles of the distribution, often expressed as a percentage of the lower percentile wage (e.g., the 90–10 Wage Gap)

Asylee

An individual requesting protection from persecution while already inside the destination country or at a port of entry

Economic immigrant

A person who migrates specifically to seek better economic opportunities for themselves or their families

Emigrant

An individual who leaves their home country

Immigrant (Economist definition)

People who are not citizens at birth of the country in which they currently live

Immigrant share

The fraction of a country's population that is comprised of immigrants.

Nonimmigrant

An individual who enters a country temporarily with a visa, such as a student, tourist, or temporary worker

Refugee

An individual residing outside their country of nationality who is unable or unwilling to return due to a well-founded fear of persecution based on race, religion, nationality, or political opinion

Unauthorized immigrant

Foreign-born non-citizens who are not legal residents, including those who entered without inspection or overstayed a temporary visa

Gravity model of migration

A model based on Newton's law of gravity that predicts migration flows between two countries based on their "economic mass" (population and income) and the distance between them

Push factors

conditions that propel people to leave their origin country (e.g., poverty, war)

Pull factors

conditions that entice them to a destination (e.g., high wages, safety)

Return to skills (ϵ)

In the Roy model, this is the extra amount (positive or negative) paid for a worker's specific skill set in a given country

Roy model

A canonical framework used to examine how workers self-select into different markets or countries based on where their skills receive the highest return

Utility maximization model

A model where individuals decide to migrate if the utility (often based on wages minus costs) in the destination is higher than the utility in the origin

Brain-drain

A form of positive selection where highly skilled workers emigrate because the marginal return to skills is higher in the destination country

Intermediate selection

Occurs when immigrants are drawn from the middle of the skill distribution, often because low-skilled workers face liquidity constraints (cash-in-advance) and high-skilled workers have better returns at home

Negative selection

Occurs when immigrants have below-average skills relative to their origin country; this often happens if the destination country has lower income inequality (less reward for high skills) than the origin

Positive selection

Occurs when immigrants have above-average skills and earnings compared to the population in their origin country

Refugee sorting (inverse sorting)

A situation where immigrants are from the low end of the wage distribution in their origin but end up at the upper end in the destination country

Complements

Two groups of workers where hiring more of one increases the demand for the other (e.g., more immigrant programmers leading to a need for more native managers)

Derived demand

Labor demand that is "derived" from the demand for the goods and services those workers produce

Elasticity of substitution

A measure of the extent to which one type of worker (e.g., young/inexperienced) can be easily replaced by another (e.g., old/experienced) in the production process

Immigration surplus

The economic benefits that accrue to the native-born population (specifically owners of capital and other factors of production) as a result of immigration

Substitutes

Workers who are interchangeable; if immigrants and natives are substitutes, they compete for the same jobs, which can lead to lower wages for natives

Mincer Earnings Function

This models the relationship between schooling, experience, and log wages: log(w)=a⋅s+b⋅t−c⋅t2+Other variables, where s is years of schooling and t is years of labor market experience

90–10 Wage Gap

Measured as the difference between the 90th and 10th percentiles as a percent of the 10th percentile wage: (w90​−w10​)/w10​

50–10 Wage Gap

Measured as the difference between the 50th and 10th percentiles as a percent of the 10th percentile wage: (w50​−w10​)/w10

Skill Premium

Often expressed as the ratio of college-educated wages to high-school-educated wages: WCollege​/WHS

Simple Utility Maximization

A person chooses to migrate if the utility of the destination (minus costs) exceeds the utility of the origin: U(WD​−Migration costs)>U(WO​)

Linear Income Maximization

If utility depends only on income, the condition simplifies to: WD​−costs>WO

Neoclassical Migration Model (Present Value)

This accounts for probabil

ity of employment, cost of living, and discounted future earnings:

Basic Gravity Model

Predicts migration flows based on population and distance: Migration from origin to destination=c×DistancePopulationO​×PopulationD​​/distance

Expanded Gravity Model

Log Wage Equations

• Origin: ln(WO​)=μO​+εO​.

• Destination: ln(WD​)=μD​+εD​

Migration Condition (Log)

ln(WO​WD​−Costs​/wO)>0

Approximated Migration Condition

(μD​−μO​)−costsmigration​+(εD​−εO​)>0.

Variance Explained

The relationship between correlation (ρ) and goodness of fit: ρ2×100=R2

Immigration Surplus (Area D)

The net gain to the destination country's native population: 1/2×(L∗−L1​)×(WD​−W∗)

Immigration Surplus as a Share of National Income (Y)

Immigsurplus/Y​=21​×%ΔL×%ΔW×YL∗W∗​, where %ΔL is employment growth, %ΔW is the percentage change in wages, and YL∗W/Y​ is labor's share of national income

Optimal Factor Adjustment

Firms adjust labor and capital until the ratio of marginal products equals the ratio of their prices: MPL/MPK=w/r

Elasticity of Substitution

Measured across groups (e.g., experience or education) using the formula: 1/(1−σ)

the age-earnings profile is

• upward-sloping and concave

• older workers earn more

• growth rate of earnings slows down over time

wage differentials exsit because

• human capital investments vary worker to worker

• age differences

the Gini Coefficient

• increases as inequlaity increases

• Summarizes the entire income distribution with a single number

  between 0 (perfect equality) and 1 (perfect inequality).

Immigrants

Those who enter the country

Emigrants

Those who leave the country

Migrants

Could be either

U.S. government definition of immigrant

Any foreign-born

person (alien) in the United States who

is not a U.S. citizen, U.S. national, or person

admitted under a nonimmigrant category.

Illegal immigrants

often interpreted as implying a permanent state of criminality.

Undocumented immigrants

uggests individuals lack official documentation, though they may possess some forms of ID.

Unauthorized immigrants

a term frequently used in U.S. government publications.

People residing in the U.S. illegally

a descriptive legal phrase without additional labels.

The Utility max setup is as follows

1. Utility depends only on their income (mainly wages).

2. Utility function is given by U;compares utility across two locations for simplicity

3. Destination (D) viewed as the best of all possible destinations

4. People move if:

𝑈(W𝑎𝑔𝑒𝐷 − 𝑀𝑖𝑔𝑟𝑎𝑡𝑖𝑜𝑛 𝑐𝑜𝑠𝑡𝑠) > 𝑈(W𝑎𝑔𝑒𝑂)

If utility increases linearly with and depends only on income, then:

W𝑎𝑔𝑒𝐷 − 𝑐𝑜𝑠𝑡𝑠 > W𝑎𝑔𝑒𝑂

This implies that:

• Increase in W𝑎𝑔𝑒𝐷 makes migration more likely, ceteris paribus.

• Increase in migration costs reduces the likelihood of migration, ceteris paribus.

• Increase in W𝑎𝑔𝑒𝑂 will make it less likely that a person migrates, all else constant.

Utility depends on

probabilityofemployment,wagesand cost ofliving:

THEGRAVITYMODELOFMIGRATION

• When the model is applied to data, GDP per capita is often used as a proxy for

income.

• Applications of the gravity model may also include variables that measure the

restrictiveness of immigration policy.

• Applies best to economic migrants and has limited applicability to

family-based migrants.

• Applies to both temporary and permanent migration

when do we use The utility model

or income-maximization model is used to estimate the

determinants of migration with individual-level data.

the gravity model is used

with aggregate data. There are more

available data on migration at the macro level. Therefore, the gravity

model is more commonly used.

The Roy model

xamined how self-selection into occupations affects the

distribution of income.

In Borjas’s version of the Roy model, workers earn the average

wage in their country plus a random term.

The larger |ρ|

stronger relationship between earnings in the

origin and the destination.

The more similar the two countries, the bigger ρ is likely to be.

▶ If skills that are valuable in the origin are also valuable in the

destination country (ρ > 0).

▶ If skills that are valuable in the origin are “downgraded” in the

destination country and vice versa (ρ < 0).

▶ Recall that ρ2 ∗ 100 = R2, i.e., variance explained (goodness of

fit)

The model assumes that ε is

normally distributed with mean 0

and variance σ2 because normal distributions have nice

properties that the model exploits.

People will likely migrate if:

▶ μD ↑ (conversely, less likely to migrate if μO increases)

▶ migration costs decrease

▶ εD is larger

▶ ρ ↑ (As skills become more transferrable)

Borjas developed the selection model to examine

where immigrants

are likely to be in the distributions of wages in the origin and

destination countries, i.e., the direction of selection.

Assumptions of Borjas’s model:

Return to skill is related to income inequality

– Higher income inequality, higher return to skill

– Depends on technology, international trade, and institutions.

▶ Extent of income inequality is measured by the variance in

wages, σ2

– If σ2

D > σ2

O → return to skill is higher in the destination.

– Relative income inequality affects the direction of selection.

Positive selection occurs when

immigrants have above-average

earnings in both the source and host country.

1. Marginal return to skills higher in destination (highly-skilled

emigrates → “brain-drain”)

2. ρ is high enough, and inequality is higher in the destination

mmigrants are negatively selected when

he receiving country

taxes “high-skilled” workers and subsidizes “low-skilled workers”.

– Marginal return to skills higher in origin (more skilled people

stay)

– ρ is high enough, but inequality is lower in the destination

(low-skilled are penalized less in the destination)

Refugee sorting” or “inverse sorting

mmigrants are from the low end of the wage distribution in

the origin but are at the upper end of the wage distribution in

the destination country (ρ < 0).

– Occurred in Eastern Europe, Cuba, and parts of Latin America

in the 20th century when these governments transitioned to

Communism.

If migration costs depend on skill

Intermediate selection may

occur instead of positive or negative selection

Intermediate selection is when immigrants are from the middle

of the skill (and wage) distribution.

Intermediate selection

Reasons why migration costs might decrease as skills increase:

• People with low skills and income may face “cash-in-advance”

or liquidity constraints.

• immigration policies that favor skilled migrants may make

migration costs lower for skilled migrants than for unskilled

migrants.

Three key insights to the selection model :

1. Mean incomes and migration costs affect the size of migration

flows.

▶ They do not determine where on the skill distribution

immigrants are drawn from.

2. Selection is determined by the variances of those incomes in

the origin and the destination (i.e., the relative return to skill).

3. Estimates of the returns to migration that do not account for

selection may overestimate the returns to migration

The Roy model predicts that immigrants will be:

positively selected on skill if the return to skill is higher in the

destination than in the origin

▶ negatively selected if returns to skill is lower

A country with high σ2

pays skilled workers a lot more than

unskilled workers.

country with low σ2

pays everyone about the same amount,

regardless of skill.

Need to control for other aspects when estimating selection:

• Poverty: Belot and Hatton (2012) - poverty prevents

low-skilled from migrating; selection is more positive as

destination inequality grows.

• Liquidity constraints: Grogger and Hanson (2011) - poor/low

skilled cannot afford to cover migration costs.

Estimates of immigration surplus for the destination depend on:

1. the magnitude of the wage response;

▶ If the change in wage is smaller, the immigration surplus is

smaller, all else constant.

2. the amount of immigration and;

▶ If there is more immigration, the immigration surplus is bigger,

all else constant.

3. labor’s share of national income

When migration costs are added to the model, the net gain to

migration is

smaller.

▶ The immigration surplus is smaller when there are migration

costs.

When immigrants and natives are perfect substitutes

• Assume that labor supply has some elasticity—some workers

They are no longer willing to work if wages fall

• In the case of a perfectly inelastic supply, all native workers are

willing to work at the lower wage → immigration does not

lead to a change in the number of natives employed.

▶ Elasticity of labor has welfare implications.

In addition to increasing labor supply, immigrants buy goods

and services in the destination country →

ncreases

aggregate demand

➥ Firms increase production to meet the increase in AD

➥ Output prices increase

➥ This makes it profitable for firms to hire more workers

➥ Labor demand increases (“derived demand”)

Under diminishing marginal returns, an increase in the supply

of less-skilled workers will

Reduce less-skilled workers’ wages

and raise the relative wages of more-skilled workers

Ottaviano & Peri (2012): Central Question

What are the wage effects of immigration using a structural production

framework?

Borjas, Grogger & Hanson (2012): Central Question

Same question, but challenges how it is empirically answered.

Ottaviano & Peri (2012): Key Assumption

Imperfect substitutes (finite σ).

Borjas, Grogger & Hanson

(2012): Key Assumption

Near-perfect substitutes (very large σ).

Ottaviano & Peri (2012): Role of σ

Moderate σ → small wage

effects.

Borjas, Grogger & Hanson

(2012): Role of σ

Large σ → larger wage

competition.

Ottaviano & Peri (2012) Methodology

Nested CES + wage

regression.

Methodology Borjas, Grogger & Hanson

(2012)

Re-estimation with

alternative specifications.

Ottaviano & Peri (2012) Data Choices

Education/experience cells;

employment weights

Borjas, Grogger & Hanson

(2012) Data Choices

Alternative weights;

critiques grouping.