Immigration, Wages, and Education: A Labor Market Equilibrium Structural Model

Immigration, Wages, and Education:

A Labor Market Equilibrium Structural Model

Joan Llull

MOVE, UAB, and Barcelona GSE

joan.llull [at] movebarcelona [dot] eu

X Barcelona GSE Trobada

Barcelona, October 2012

Immigration, Wages and Education 1

Motivation


Research questions

A large literature has analyzed the eect of immigration onwages. However,

How do human capital investment and labor supply ofnatives react to immigration?

How important are these adjustments to understand theeect of immigration on wages?

These adjustments are crucial, but omitted in the literature


Contribution

Estimate labor market equilibrium structural model allowingnatives to react to the higher competition induced by immigration

Labor supply: forward looking agents decide on education, par-ticipation, and occupation

Labor demand: an aggregate rm combines blue-collar andwhite-collar labor with capital to produce a single output

Equilibrium: channels the eect of immigration on incentives toinvest in human capital through relative wages

Wage eects of immigration are quantied by comparing data andcounterfactual simulations of a world w/o mass immigration


Literature

Literature does not establish a consensus about wage eects ofimmigration.

Two dierent approaches:

Spatial correlations: Grossman (1982), Borjas (1983, 1985,1995), Card (1990, 2001), Altonji and Card (1991), LaLondeand Topel (1991), Lewis (2010), Dustman et al (2012)...

Factor proportions: Borjas, Freeman, and Katz (1992,1997), Borjas(2003), Borjas and Katz (2007), Borjas, Grog-ger, and Hanson (2010), Ottaviano and Peri (2012), Dustmanet al (2012)...

Other labor market equilibrium models: Heckman, Lochner, &Taber (1998); Lee (2005); Lee & Wolpin (2006)


Factor proportions approach (e.g. Borjas QJE'03)

Compare wages across dierent skill groups that receiveddierent amounts of immigrants:

Reduced form: before-after and across groups comparison

Structural: production function with the dierent skillgroups and use it to simulate the eect

However, natives may react by moving from less skilledgroups to more skilled:

Reduced form ⇒ still relatively small eects (althoughlarger than spatial correlations)

Structural ⇒ wrong counterfactuals

Do not allow for skill-biased technical change




















Preview of the main results

Immigration reduces wages importantly

Labor market equilibrium adjustments compensate partially theeect on impact

Individuals adjust by switching occupations, exiting the labormarket, increasing education and changing experience accumu-lation proles

Important eects over the distribution of wages

It is very important to take into account individuals that leavethe market when looking at eects over the distribution


Outline

1 Motivation

2 The model

3 Methodology

4 Data

5 Results

6 Conclusion


The model


Individuals decide yearly on participation, education andoccupation from age 16 (or upon entry) to 65

Immigrants enter the country exogenously and with agiven skill endowment

An aggregate rm combines labor skill units with capitalto produce a single output

Labor skill rental prices are determined in equilibrium.The wage of an individual i at time t in occupation j:

wji,t = rjt × si ≡ pricejt × skill unitsi


Labor supply

From age a = 16 to 65 years old, individuals choose amongfour alternatives:

Working in a blue-collar job (da = B)

Working in a white-collar job (da = W )

Attending school (da = S)

Staying at home (da = H)

They are not allowed to save, so they consume all theirnet income each period

This discrete choice dynamic programming problem buildson Keane-Wolpin (1994,1997), and Lee-Wolpin (2006,2010)


Individuals solve the following dynamic programming problem:

Va,t,l(Ωa,t) = maxda

Ua,l(Ωa,t, da) + βE [Va+1,t+1,l(Ωa+1,t+1) | Ωa,t, da, l]

U ja,t,l = wja,t,l+δBWg 1da−1 6= B,W, wja,t,l = rjt × s

ja,l, j = B,W

wja,t,l = rjt expωj0,l + ωj1,isEa + ωj2XBa + ωj3X2Ba + ωj4XWa + ωj5X

2Wa + ωj6XFa + εja

(εBa

εWa

)∼ i.i.N

([0

0

],

[(σBg )2 ρBWσBg σ

Wg

ρBWσBg σWg (σWg )2

])

USa,l = δS0,l − δS1,g1da−1 6= S − τ11Ea ≥ 12 − τ21Ea ≥ 16+ σSg εSa

UHa,t,l = δH0,l + δH1,gna + δH2,gt+ σHg εHa

Notation: a ≡ age; l ≡ ability type (gender×region of origin); t ≡ time;g ≡ gender; is ≡ immigrant/native





ja,l, j = B,W



(εBa

εWa

)∼ i.i.N

([0

0

],


Wg


])








ja,l, j = B,W



(εBa

εWa

)∼ i.i.N

([0

0

],


Wg


])








ja,l, j = B,W



(εBa

εWa

)∼ i.i.N

([0

0

],


Wg


])








ja,l, j = B,W



(εBa

εWa

)∼ i.i.N

([0

0

],


Wg


])








ja,l, j = B,W



(εBa

εWa

)∼ i.i.N

([0

0

],


Wg


])








ja,l, j = B,W



(εBa

εWa

)∼ i.i.N

([0

0

],


Wg


])








ja,l, j = B,W



(εBa

εWa

)∼ i.i.N

([0

0

],


Wg


])








ja,l, j = B,W



(εBa

εWa

)∼ i.i.N

([0

0

],


Wg


])








ja,l, j = B,W



(εBa

εWa

)∼ i.i.N

([0

0

],


Wg


])








ja,l, j = B,W



(εBa

εWa

)∼ i.i.N

([0

0

],


Wg


])








ja,l, j = B,W



(εBa

εWa

)∼ i.i.N

([0

0

],


Wg


])








ja,l, j = B,W



(εBa

εWa

)∼ i.i.N

([0

0

],


Wg


])








ja,l, j = B,W



(εBa

εWa

)∼ i.i.N

([0

0

],


Wg


])



Notation: a ≡ age; l ≡ ability type (gender×region of origin);t ≡ time; g ≡ gender; is ≡ immigrant/native





ja,l, j = B,W



(εBa

εWa

)∼ i.i.N

([0

0

],


Wg


])








ja,l, j = B,W



(εBa

εWa

)∼ i.i.N

([0

0

],


Wg


])








ja,l, j = B,W



(εBa

εWa

)∼ i.i.N

([0

0

],


Wg


])








ja,l, j = B,W



(εBa

εWa

)∼ i.i.N

([0

0

],


Wg


])








ja,l, j = B,W



(εBa

εWa

)∼ i.i.N

([0

0

],


Wg


])








ja,l, j = B,W



(εBa

εWa

)∼ i.i.N

([0

0

],


Wg


])








ja,l, j = B,W



(εBa

εWa

)∼ i.i.N

([0

0

],


Wg


])








ja,l, j = B,W



(εBa

εWa

)∼ i.i.N

([0

0

],


Wg


])








ja,l, j = B,W



(εBa

εWa

)∼ i.i.N

([0

0

],


Wg


])








ja,l, j = B,W



(εBa

εWa

)∼ i.i.N

([0

0

],


Wg


])




Labor demand

Aggregate rm combines blue- andwhite-collar skill units (SB , SW )with capital structures and equipment (KS ,KE) to produce asingle output (Y ) with the following technology:

Yt = ztKλStαS

ρBt + (1− α)[θSγWt + (1− θ)Kγ

Et]ρ/γ(1−λ)/ρ

Two types of labor: blue- and white-collar. Workers within anoccupation are also heterogeneous in skills

The nested CES is included to capture the capital-skill com-plementarity and SBTC (Krusell et al., 2000)


No savings: equilibrium capital and output taken fromdata

zt is an aggregate productivity shock (identied as theresidual of the production function)

It is assumed to evolve according to:

ln zt+1 − ln zt = φ0 + φ1(ln zt − ln zt−1) + εzt+1

εzt+1 ∼ N (0, σz)


Equilibrium

Demands of skill units are given by the rst order conditionson rm's problem

The aggregate supply of skill units is given by:

Sjt =

65∑a=16

N∑i=1

sja,i1da,i = j j = B,W

⇒ The equilibrium is given by the skill prices that equate thesupply and the demand of skill units (market clearing)

Expectations are approximated with a rule in line with LeeandWolpin (2006,2010), and in the same spirit of Krusell andSmith (1998)


Methodology


Estimating dierent pieces of the model separately is notfeasible:

Aggregate skill units are not observable

Occupation-specic work experience is not available in CPS

NLSY cohorts are not refreshed with new immigrants

Internal consistency of the model is crucial for counterfactu-als

Available data does not allow Maximum Likelihood

The model is estimated by Simulated Minimum Distance

using a two step nested algorithm


Θ1 ≡ all fundamental parameters except aggregate shock process

Θ2 ≡ expectation parameters and aggregate shock process

Solve optimization prob.

Estimate processes foraggr. shock & prices Θ2

Simulate statistics andcompare to data

Iterate Θ1

Iterate Θ2

Guess &Θ1 Θ2

Lee and Wolpin (2006)This paper

Guess &Θ1 Θ2

Simulate statistics andcompare to data

Estimate processes foraggr. shock & prices Θ2

Iterate Θ1

Iterate Θ2

Simulate the economySimulate the economy

Solve optimization prob.

Detailed algorithm


Data


Data

I need a suciently large variation in the data to identify the57 parameters of the structural model plus additional 8 for skillprice expectation rules.

Moreover, I also need some macro data for the exogenous vari-ables to be introduced in the solution of the model:

outputcapitalnative and immigrant cohort sizesfertility processage at entryinitial schoolingregion of origin

I t the model to statistics which I calculate with US micro-data (CPS, NLSY79,NLSY97) for 1967-2007


List of statistics

Description Source Number of statistics

TOTAL 30,012

Proportion of individuals choosing each alternative... 5,074

By year, sex, and 5-year age group CPS 41× 2× 10× (4− 1) 2,460By year, sex, and educational level CPS 41× 2× 4× (4− 1) 984By year, sex, and preschool children CPS 41× 2× 3× (4− 1) 738By year, sex, and region of origin CPS 15× 2× 4× (4− 1) 360Immigrants, by year, sex, and foreign potential experience CPS 15× 2× 5× (4− 1) 450By sex and experience in each occupation NLSY 2× (5× 5 + 4× 4)× (2− 1) 82

Wages: 6,404

Mean log hourly real wage... 3,000

By year, sex, 5-year age group, and occupation CPS 41× 2× 10× 2 1,640By year, sex, educational level, and occupation CPS 41× 2× 4× 2 656By year, sex, region of origin, and occupation CPS 15× 2× 4× 2 240Immigrants, by year, sex, fpx, and occupation CPS 15× 2× 5× 2 300By sex, experience in each occupation, and occupation NLSY 2× (5× 5 + 4× 4)× 2 164

Mean 1-year growth rates in log hourly real wage... 2,508

By year, sex, previous, and current occupation Matched CPS 41× 2× 2× 2 328By year, sex, 5-year age group, and current occupation Matched CPS 41× 2× 10× 2 1,640By year, sex, region of origin, and current occupation Matched CPS 15× 2× 4× 2 240Immigrants, by year, sex, years in the U.S., and occupation Matched CPS 15× 2× 5× 2 300

Variance in the log hourly real wages... 896

By year, sex, educational level, and occupation CPS 41× 2× 4× 2 656By year, sex, region of origin, and occupation CPS 15× 2× 4× 2 240


Career transitions... 14,154

By year and sex Matched CPS 41× 2× 4× (4− 1) 984By year, sex, and age Matched CPS 41× 2× 10× 4× (4− 1) 9,840By year, sex, and region of origin Matched CPS 15× 2× 4× 4× (4− 1) 1,440New entrants taking each choice by year and sex CPS 15× 2× (4− 1) 90Immigrants, by year, sex, and years in the U.S. Matched CPS 15× 2× 5× 4× (4− 1) 1,800

Distribution of highest grade completed... 4,260

By year, sex, and 5-year age group CPS 41× 2× 10× (4− 1) 2,460By year, sex, 5-year age group, and immi-

grant/nativeCPS 15× 2× 10× 2× (4− 1) 1,800

Distribution of experience... 120

Blue collar, by sex NLSY 2× (13 + 7) 40White collar, by sex NLSY 2× (13 + 7) 40Home, by sex NLSY 2× (13 + 7) 40


Identication

Identication is a matter of uniqueness of the global min and curva-ture around it.

As common in non-linear models of this kind, no formal proof.

Uniqueness is checked starting from dierent initial guesses.

Curvature is checked with partial di. and small s.e.

Heuristically, identication is a combination of functional form as-

sumptions and exclusion restrictions:

Synthetic cohort panel data

Variables that aect wages but not utilities (experience)

Variables that aect utility but not wages (children)

Production function: functional form (skills), aggregate data (capi-tal, output), and instruments for skills (cohort sizes)


Results


Estimation results

Parameter estimates in reasonable values: Parameter estimates

ρ > γ ⇒ Skill-biased technical change

Blue-collar return to education 5.7%, white-collar 12.3%

Immigrants relatively more productive in blue-collar

Return to foreign experience lower than to U.S. experience⇒ assimilation

Very small standard errors

Good t of the model in predicting main variables Model t


Counterfactual

Simulations of a world without large scale immigration

Wage eect of immigration: dierence between baseline andcounterfactual average log wages.

Stock of immigrants increased to keep immigrant/native ratioconstant to baseline year

All exogenous variables and shocks kept constant to baseline

Two scenarios for capital:

Fixed capital stock (max negative eects)

Fixed return to capital (min negative eects)

Additional counterfactuals (not reported): 1980-2000 and 1990-2007 → comparability with the literature


Average eects and the role of equilibrium

WagesSkill prices:

BC WCAverage

No capital adjustment (∂K/∂m = 0):

Total eect -8.28 -3.64 -2.71 -2.43

No labor market adjustment -8.96 -11.05 -0.95 -4.57

Equilibrium eect 0.68 7.41 -1.76 2.14

Full capital adjustment (∂rK/∂m = 0):

Total eect -4.62 -1.01 0.37 0.39

No labor market adjustment -4.99 -8.57 3.65 -0.72

Equilibrium eect 0.37 7.56 -3.28 1.12


Labor supply adjustments

Choice with immigration

No capital adjustment (∂K/∂m = 0)

AdjustOf which adjust to:

Choice w/oimmigration

Bluecollar

Whitecollar

School Home

Blue collar 0.085 0.378 0.022 0.600

White collar 0.035 0.102 0.064 0.834

School 0.115 0.155 0.163 0.683

Home 0.008 0.046 0.662 0.293

Full capital adjustment (∂rK/∂m = 0)

AdjustOf which adjust to:

Choice w/oimmigration

Bluecollar

Whitecollar

School Home

Blue collar 0.053 0.587 0.029 0.384

White collar 0.003 0.163 0.202 0.635

School 0.015 0.152 0.293 0.554

Home 0.016 0.038 0.897 0.066


Education adjustments

i. BC to BC 0

0.0

03

0.0

06

0.0

09

0.0

12

0.0

15

-12 -9 -6 -3 0 3 6 9 12

Fract

ion

Years of education

Adjusting education: • If ∂K/∂m=0: 3.8% • If ∂rK /∂m=0: 1.3%

ii. BC to WC

0 0

.00

72 0

.01

44 0

.02

16 0

.02

88

0.0

36

-12 -9 -6 -3 0 3 6 9 12

Fract

ion

Years of education


iii. Home to Work

0 0

.02

6 0

.05

2 0

.07

8 0

.10

4 0

.13

-12 -9 -6 -3 0 3 6 9 12

Fract

ion

Years of education


iv. WC to BC

0 0

.05

0.1

0.1

5 0

.2 0

.25

-12 -9 -6 -3 0 3 6 9 12

Fract

ion

Years of education


No capital adjust. (∂K/∂m=0)

v. WC to WC 0

0.0

06

0.0

12

0.0

18

0.0

24

0.0

3

-12 -9 -6 -3 0 3 6 9 12

Fract

ion

Years of education


vi. Work to Home

0 0

.02

0.0

4 0

.06

0.0

8 0

.1

-12 -9 -6 -3 0 3 6 9 12Fr

act

ion

Years of education


Full capital adjust. (∂rK /∂m=0)


Blue collar experience adjustments

vii. BC to BC 0

0.0

3 0

.06

0.0

9 0

.12

0.1

5

-30 -20 -10 0 10 20 30

Fract

ion

Years of experience

Adjust BC experience: • If ∂K/∂m=0: 28.2% • If ∂rK /∂m=0: 18.6%

viii. BC to WC

0 0

.04

0.0

8 0

.12

0.1

6 0

.2

-30 -20 -10 0 10 20 30Fr

act

ion

Years of experience


ix. Home to Work

0 0

.04

0.0

8 0

.12

0.1

6 0

.2

-30 -20 -10 0 10 20 30

Fract

ion

Years of experience


x. WC to BC

0 0

.03

0.0

6 0

.09

0.1

2 0

.15

-30 -20 -10 0 10 20 30

Fract

ion

Years of experience



xi. WC to WC 0

0.0

2 0

.04

0.0

6 0

.08

0.1

-30 -20 -10 0 10 20 30

Fract

ion

Years of experience


xii. Work to Home

0 0

.05

0.1

0.1

5 0

.2 0

.25

-30 -20 -10 0 10 20 30Fr

act

ion

Years of experience




White collar experience adjustments

xiii. BC to BC 0

0.0

1 0

.02

0.0

3 0

.04

0.0

5

-30 -20 -10 0 10 20 30

Fract

ion

Years of experience

Adjust WC experience: • If ∂K/∂m=0: 15.3% • If ∂rK /∂m=0: 12.0%

xiv. BC to WC

0 0

.04

0.0

8 0

.12

0.1

6 0

.2

-30 -20 -10 0 10 20 30Fr

act

ion

Years of experience


xv. Home to Work

0 0

.03

0.0

6 0

.09

0.1

2 0

.15

-30 -20 -10 0 10 20 30

Fract

ion

Years of experience


xvi. WC to BC

0 0

.04

0.0

8 0

.12

0.1

6 0

.2

-30 -20 -10 0 10 20 30

Fract

ion

Years of experience



xvii. WC to WC 0

0.0

2 0

.04

0.0

6 0

.08

0.1

-30 -20 -10 0 10 20 30

Fract

ion

Years of experience


xviii. Work to Home

0 0

.03

0.0

6 0

.09

0.1

2 0

.15

-30 -20 -10 0 10 20 30Fr

act

ion

Years of experience




Distributional adjustments

xix. Natives, all

-0.1

6-0

.12

-0.0

8-0

.04

0 0

.04

0 25 50 75 100

Perc

enta

ge c

hange

Percentile

xx. Immigrants, all

-0.1

6-0

.12

-0.0

8-0

.04

0 0

.04

0 25 50 75 100

Perc

enta

ge c

hange

Percentile

xxi. Natives, stayers

-0.1

6-0

.12

-0.0

8-0

.04

0 0

.04

0 25 50 75 100

Perc

enta

ge c

hange

PercentileNo capital adjust. (∂K/∂m=0) ±2 s.e.

xxii. Immigrants, stayers

-0.1

6-0

.12

-0.0

8-0

.04

0 0

.04

0 25 50 75 100Pe

rcenta

ge c

hange

PercentileFull capital adjust. (∂rK /∂m=0) ±2 s.e.


Distributional adjustments

xxiii. Natives, all

-0.1

6-0

.12

-0.0

8-0

.04

0 0

.04

0 25 50 75 100

Perc

enta

ge c

hange

Percentile

xxiv. Immigrants, all

-0.1

6-0

.12

-0.0

8-0

.04

0 0

.04

0 25 50 75 100

Perc

enta

ge c

hange

Percentile

xxv. Natives, stayers

-0.1

6-0

.12

-0.0

8-0

.04

0 0

.04

0 25 50 75 100

Perc

enta

ge c

hange

PercentileNo capital adjust. (∂K/∂m=0) ±2 s.e.

xxvi. Immigrants, stayers

-0.1

6-0

.12

-0.0

8-0

.04

0 0

.04

0 25 50 75 100Pe

rcenta

ge c

hange

PercentileFull capital adjust. (∂rK /∂m=0) ±2 s.e.


Conclusion


Conclusions

This paper quanties the eect of immigration on wages taking intoaccount human capital and labor supply adjustments

Labor market equilibrium structural model with immigration

Endogenous participation, occupation, and education decisions +skill-biased technical change

Main results:

Immigration reduces wages importantly

Labor market equilibrium adjustments compensate partially theeect on impact

Individuals adjust by switching occupations, exiting the labormarket, increasing education and changing experience accumu-lation proles

Important eects over the distribution of wages

It is very important to take into account individuals that leavethe market when looking at eects over the distribution


Appendix Index

1. Skill composition of immigra-tion

2. Education of natives and immi-grants

3. Share of immigrants amongworkers in each occupation

4. Bias of the estimates of the lit-erature

5. Some motivating correlations

6. Immigration and wages

7. Immigration and school enroll-ment

8. Immigration and blue-collar towhite-collar transitions

9. Immigration policies

10. Skill-biased technical change

11. Demands for skills

12. Expectations

13. Algorithm

14. Sections of the objective func-tion

15. Production function estimates

16. Wage equations estimates

17. Utility function estimates

18. Actual and predicted wages

19. Actual and predicted humancapital and labor supply vari-ables

Skill Composition of Immigration

Table: Share of Immigrants in the Workforce (%)

1970 1980 1990 2000 2008

A. Working-age population 5.70 7.13 10.27 14.62 16.56

B. By education: more

Dropouts 6.84 9.60 17.93 29.02 33.73High school 4.32 5.14 7.94 12.04 13.27Some college 5.14 6.63 7.92 9.96 11.65College 6.48 8.02 10.60 14.59 16.92

C. In blue collar jobs:

more

All education levels

6.03 7.83 11.21 17.53 24.07


Note: Figures in each panel indicate the percentage of immigrants among the overallworking-age population, among workers in each education group, and among blue-collarworkers respectively. Sources: Census data (1970-2000) and ACS (2008).



1970 1980 1990 2000 2008





more

All education levels

6.03 7.83 11.21 17.53 24.07





1970 1980 1990 2000 2008





more

All education levels 6.03 7.83 11.21 17.53 24.07





1970 1980 1990 2000 2008




C. In blue collar jobs: more

All education levels 6.03 7.83 11.21 17.53 24.07



Table: Education of Natives and Immigrants (%)

1970 1980 1990 2000 2008

A. Natives


B. Immigrants

Dropouts 49.8 39.0 31.8 30.6 27.4High school 26.5 27.3 26.2 25.9 28.9Some college 12.1 16.9 21.8 20.5 17.4College 11.6 16.8 20.1 23.0 26.3a. Western Countries


b. Latin America


c. Asia and Africa


Note: Figures indicate the percentage of individuals from each origin in eacheducation group. Columns for each panel add to 100%. Western countries includeimmigrants from Canada, Europe and Oceania. Sources: Census data (1970-2000)and ACS (2008). Back

Table: Share of Immigrants among Workers in each Occupation (%)

1970 1980 1990 2000 2008

A. Blue-collar 6.03 7.83 11.21 17.53 24.08

Farm laborers 8.32 14.06 26.08 40.08 51.11Laborers 5.47 7.40 11.87 21.48 31.27Service workers 7.58 9.62 13.65 19.58 25.59Operatives 5.84 8.38 11.74 18.55 23.98Craftsmen 5.38 6.06 8.16 12.69 18.24

B. White-collar 4.96 5.76 7.70 10.78 13.34

Professionals 6.29 6.90 8.64 11.95 14.50Managers 5.02 5.93 7.76 10.75 13.37Clerical and kindred 4.27 5.17 7.14 9.97 12.47Sales workers 4.78 5.03 6.78 9.29 11.52Farm managers 1.52 1.56 2.87 4.87 6.38

Note: Figures indicate the share of immigrants among workers employed in eachoccupation. Sources: Census data (1970-2000) and ACS (2008).

Back

Back

Some motivating correlations

Borjas(2003,s.II-VI): reduced form version of factorproportions

Compares dierent penetration of immigrants acrosseducation-experience-time cells

Immigration and wages are negatively correlated graph

With the same approach I nd some motivating correlations

Immigration and school enrollment rates are positivelycorrelated (education-time cells) graph

Immigration and occupational switches from blue-collarto white-collar are also positively correlated graph

Figure: Immigration and Wages (1960-2008)

Note: Each obs. is an education-experience-year cell. Both variables are plotted net of xedeects. The plotted line is:

lnwijt = −0.394mijt + νi + ιj + δt + εijt.

(0.041)

where lnwijt is the log average hourly wage of individuals with education i and experience j,at census year t, and mijt is the share of immigrants in education-experience-period cell ijt.Regression tted to 240 observations. Standard error clustered by education-experience cell isin parenthesis. Sources: Census data (1960 to 2000) and ACS (2008).

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Figure: Immigration and School Enrollment (1960-2008)

Note: Each obs. is an education-year cell. Both variables plotted net of xed eects. The plottedline is:

sit = 0.458mit + νi + δt + εit.

(0.125)

where sit is the enrollment rate of individuals with completed education i at census year t, andmit is the share of immigrants in each education-experience-period cell. Regression tted to 24observations. Standard error clustered by education is in parenthesis. Sources: Census data (1960to 2000) and ACS (2008).

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Figure: Immigration and Occupation Transitions (1970-2008)

Note: Each obs. is an education-experience-year cell. Both variables are plotted net of xedeects. The plotted line is:pijt = 0.150mijt + νi + ιj + δt + εijt.

(0.044)where pijt is the blue-collar to white-collar transition probability of individuals with education iand experience j, at census year t, and mijt is the share of immigrants in education-experience-period cell ijt. Regression tted to 240 observations. Standard error clustered by education-experience cell is in parenthesis. Sources: Census data (1970 to 2000) and ACS (2008) forimmigrant shares. Matched March Supplements of CPS for occupation transitions (1970-71 to2007-2008 Supplements).

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Figure: Immigration Policies and the Origin of Immigrants(1875-2007)

Note: The black solid line represents the share of the population working-age which is foreignborn. The area below the dashed red line corresponds to the share of the working-age populationwhich was born in Western Countries (Canada, Europe, and Oceania). The area between thedashed and the dotted lines represents the corresponding share of Latin Americans. And thearea between the dotted and the solid lines represents the share of Asian and African. Sources:Census data (1870-2000) and ACS (2001-2008). Inter-Census interpolations based on the intensityof legal entry (Yearbook of Immigration Statistics 2009 U.S. Department of Homeland Security)excluding the legalization of illegal immigrants granted with an amnesty by IRCA 1986. Back

Skill-biased technical change

Relative skill prices from the rst order conditions of rm's prob-

lem:

ln

(rWtrWt

)= ln

(1− α)θ

α+(ρ−1) ln

(SWt

SBt

)+ρ− γγ

ln

(θ + (1− θ)

(KEt

SWt

)γ)

Skill-biased technical change embedded in capital equipment ac-

cumulation if (ρ > γ)

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Demands for skills

Demands of skills are derived from the rst order conditions of

rm's problem:

rBt = (1− λ)α(ztK

λSt

) ρ1−λ

Sρ−1Bt Y

1− ρ1−λ

t

rWt = (1− λ)(1− α)θ(ztK

λSt

) ρ1−λ

Sγ−1Wt KW

ρ−γt Y

1− ρ1−λ

t

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Expectations

Individuals forecast future state variables Ωt+1,a+1 usingthe current state Ωt,a

State variables: education, blue-collar and white-collarexperience, pot.exp.abroad, being at school in previousperiod, preschool children, idiosyncratic shock, current skillprices, calendar year, and known determinants of futureskill prices

Problem: future skill prices depend upon the currentdistrib of state variables across the whole population

Numerical solution: assume that equilibrium aggregateskill units are well represented by∆ ln rjt+1 = ηj0 + ηjB∆ ln rBt + ηjW∆ ln rWt + ηjz∆ ln zt+1

Θ1 ≡ all fundamental parameters except aggregate shock processΘ2 ≡ expectation parameters and aggregate shock process

1. Choose a set of parameters [Θ1]0 and [Θ2]0

2. Solve the optimization problem for each cohort that exists from t = 1to t = T (dynamic programming problem solved recursively by backwardinduction; interpolation method based on the one described in Keane andWolpin (1994,1997) with quadrature for integrals).

3. Find the equilibrium skill rental prices which clear the markets and theaggregate shock simulating the economy from t = 1 to t = T :

3.1 Guess the aggregate skill prices of period t = 1 (r0).

3.2 Obtain the aggregate supply of skill units given r0.

3.3 Plug the supply of skills into the production function and, togetherwith data on capital and output, recover the aggregate shock.

3.4 Find skill rental prices with the demand equations.

3.5 If xed point in skill prices, done. Otherwise, repeat steps 3.2 to 3.4till reaching convergence

3.6 Repeat steps 3.1 to 3.5 for t = 2, ..., T .

4. Compare simulated data with their observed counterparts. Update Θ1 withsimplex iterations and repeat steps 2 and 3 with [Θ1]1 to nd the min

Θ1([Θ2]0)

5. Given Θ1([Θ2]0), update Θ2 solving for the xed point in expectation rules

(repeat steps 2 and 3 with Θ1 and [Θ2]0 and t OLS regressions forprocesses)

6. Iterate to nd a xed point Θ2(Θ1)Back

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Table: Production Function

Elasticity of substitution:

Blue vs Equipment/White (ρ) 0.334 (0.001)

White vs Equipment (γ) -0.402 (0.001)

Factor share paramameters:

Structures (λ) 0.118 (0.002)

Blue-collar (α) 0.748 (0.001)

White-collar (θ) 0.067 (0.001)

Aggregate shock process:

Constant (φ0) 0.001 (0.001)

Autorregressive term (φ1) 0.384 (0.028)

St. dev. of innivations (σz) 0.022 (0.006)

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Table: Wages

Blue-collar White-collar

Returns:

Education (ω1,i):

Natives 0.057 (0.000) 0.123 (0.000)Immigrants 0.063 (0.001) 0.093 (0.000)

BC experience (ω2) 0.106 (0.000) 0.001 (0.000)BC experience2 (ω3) -0.0020 (0.0009) 0.0000 (0.0000)WC experience (ω4) 0.001 (0.000) 0.061 (0.000)WC experience2 (ω5) 0.0000 (0.0000) -0.0006 (0.0000)Foreign experience (ω6) -0.008 (0.000) 0.032 (0.001)

Heterogeneity parameters (ω0,l):

Western countries 0.055 (0.005) -0.027 (0.005)Latin America 0.057 (0.007) -0.233 (0.008)Asia and Africa 0.032 (0.009) -0.052 (0.010)Female -0.144 (0.002) -0.119 (0.002)

Standard deviations of transitory shocks:

Male 0.384 (0.003) 0.479 (0.002)Female 0.286 (0.005) 0.383 (0.002)

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Table: Utility Parameters

Male Female

A. School:

Heterogeneity parameters (δS0,l):

Natives -2,635 (79) 6,544 (72)Western countries 220 (149) 9,399 (172)Latin America -3,388 (518) 5,791 (517)Asia and Africa 3,109 (244) 12,287 (246)

Tuition fees:Undergraduate (τ1) 17,325 (144)Graduate (τ1 + τ2) 33,446 (273)

Reentering disutility (δS1 ) 21,505 (142) 47,250 (268)Variance (σS) 5,971 (42) 1,718 (8)

Heterogeneity parameters (δH0,l):

B. Home:

Heterogeneity parameters (δH0,l):

Natives 13,875 (54) 15,633 (41)Western countries 15,525 (598) 17,283 (599)Latin America 18,306 (137) 20,064 (131)Asia and Africa 13,640 (638) 15,398 (636)

Children (δH1 ) 3,580 (64) 11,211 (127)Trend (δH2 ) 88.28 (0.10) 55.43 (0.02)Variance (σH) 4,945 (38) 9,436 (32)

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Figure: Actual vs Predicted Wages

i. Log hourly wages ii. College-high school wage gap

Note: Solid lines are data; dashed are simulations. Black lines are for males; gray for females.Wages: average real log hourly wage. College-high school wage gap: dierence in average reallog hourly wage of college workers (more than 12 years of education) and high school workers(12 or less years of education). Data sources: March Supplements of CPS for survey dates from1968 to 2008.

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Table: Actual and Predicted Human Capital and Labor SupplyVariables

Male Female

Actual Predicted Actual Predicted

Participation rate 63.50 62.45 40.93 36.94Share of workers in blue-collar 49.83 54.10 27.38 30.93Share of dropouts 23.67 31.17 22.38 32.67Increase in average years of education 2.12 1.85 2.39 1.56

Note: Predicted data are computed with the estimated parameters. All gures butthe increase in average years of education are in percentages. Data sources: MarchSupplements of CPS for survey dates from 1968 to 2008.

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Immigration, Wages, and Education: A Labor Market Equilibrium Structural Model

Documents

rst order conditions

dynamic programming problem

received dierent amounts

standard error clustered

groups comparison structural

aggregate shock process

factor proportions approach

dierent skill groups