Immigration, Wages, and Education:        A Labor Market Equilibrium Structural Model                                     ...
MotivationImmigration, Wages and Education            2
Research questions     A large literature has analyzed the eect of immigration on     wages. However,         How do human...
Contribution           Estimate labor market equilibrium structural model allowing           natives to react to the highe...
Literature           Literature does not establish a consensus about wage eects of           immigration.           Two di...
Factor proportions approach (e.g. Borjas QJE03)           Compare wages across dierent skill groups that received         ...
Factor proportions approach (e.g. Borjas QJE03)           Compare wages across dierent skill groups that received         ...
Factor proportions approach (e.g. Borjas QJE03)           Compare wages across dierent skill groups that received         ...
Preview of the main results           Immigration reduces wages importantly           Labor market equilibrium adjustments...
Outline      1   Motivation      2   The model      3   Methodology      4   Data      5   Results      6   ConclusionImmi...
The modelImmigration, Wages and Education           9
Individuals decide yearly on participation, education and           occupation from age 16 (or upon entry) to 65          ...
Labor supply           From age a = 16 to 65 years old, individuals choose among           four alternatives:             ...
Individuals solve the following dynamic programming problem:  Va,t,l (Ωa,t ) = max Ua,l (Ωa,t , da ) + βE [Va+1,t+1,l (Ωa+...
Individuals solve the following dynamic programming problem:  Va,t,l (Ωa,t ) = max Ua,l (Ωa,t , da ) + βE [Va+1,t+1,l (Ωa+...
Individuals solve the following dynamic programming problem:  Va,t,l (Ωa,t ) = max Ua,l (Ωa,t , da ) + βE [Va+1,t+1,l (Ωa+...
Individuals solve the following dynamic programming problem:  Va,t,l (Ωa,t ) = max Ua,l (Ωa,t , da ) + βE [Va+1,t+1,l (Ωa+...
Individuals solve the following dynamic programming problem:  Va,t,l (Ωa,t ) = max Ua,l (Ωa,t , da ) + βE [Va+1,t+1,l (Ωa+...
Individuals solve the following dynamic programming problem:  Va,t,l (Ωa,t ) = max Ua,l (Ωa,t , da ) + βE [Va+1,t+1,l (Ωa+...
Individuals solve the following dynamic programming problem:        Va,t,l (Ωa,t ) = max Ua,l (Ωa,t , da ) + βE [Va+1,t+1,...
Individuals solve the following dynamic programming problem:        Va,t,l (Ωa,t ) = max Ua,l (Ωa,t , da ) + βE [Va+1,t+1,...
Individuals solve the following dynamic programming problem:        Va,t,l (Ωa,t ) = max Ua,l (Ωa,t , da ) + βE [Va+1,t+1,...
Individuals solve the following dynamic programming problem:        Va,t,l (Ωa,t ) = max Ua,l (Ωa,t , da ) + βE [Va+1,t+1,...
Individuals solve the following dynamic programming problem:        Va,t,l (Ωa,t ) = max Ua,l (Ωa,t , da ) + βE [Va+1,t+1,...
Individuals solve the following dynamic programming problem:        Va,t,l (Ωa,t ) = max Ua,l (Ωa,t , da ) + βE [Va+1,t+1,...
Individuals solve the following dynamic programming problem:        Va,t,l (Ωa,t ) = max Ua,l (Ωa,t , da ) + βE [Va+1,t+1,...
Individuals solve the following dynamic programming problem:        Va,t,l (Ωa,t ) = max Ua,l (Ωa,t , da ) + βE [Va+1,t+1,...
Individuals solve the following dynamic programming problem:        Va,t,l (Ωa,t ) = max Ua,l (Ωa,t , da ) + βE [Va+1,t+1,...
Individuals solve the following dynamic programming problem:        Va,t,l (Ωa,t ) = max Ua,l (Ωa,t , da ) + βE [Va+1,t+1,...
Individuals solve the following dynamic programming problem:        Va,t,l (Ωa,t ) = max Ua,l (Ωa,t , da ) + βE [Va+1,t+1,...
Individuals solve the following dynamic programming problem:        Va,t,l (Ωa,t ) = max Ua,l (Ωa,t , da ) + βE [Va+1,t+1,...
Individuals solve the following dynamic programming problem:        Va,t,l (Ωa,t ) = max Ua,l (Ωa,t , da ) + βE [Va+1,t+1,...
Individuals solve the following dynamic programming problem:        Va,t,l (Ωa,t ) = max Ua,l (Ωa,t , da ) + βE [Va+1,t+1,...
Individuals solve the following dynamic programming problem:        Va,t,l (Ωa,t ) = max Ua,l (Ωa,t , da ) + βE [Va+1,t+1,...
Individuals solve the following dynamic programming problem:        Va,t,l (Ωa,t ) = max Ua,l (Ωa,t , da ) + βE [Va+1,t+1,...
Individuals solve the following dynamic programming problem:        Va,t,l (Ωa,t ) = max Ua,l (Ωa,t , da ) + βE [Va+1,t+1,...
Individuals solve the following dynamic programming problem:        Va,t,l (Ωa,t ) = max Ua,l (Ωa,t , da ) + βE [Va+1,t+1,...
Labor demand           Aggregate rm combines blue- and white-collar skill units (SB , SW )           with capital structur...
No savings: equilibrium capital and output taken from           data           zt is an aggregate productivity shock (iden...
Equilibrium           Demands of skill units are given by the rst order conditions           on rms problem           The ...
MethodologyImmigration, Wages and Education         16
Estimating dierent pieces of the model separately is not           feasible:                 Aggregate skill units are not...
Θ1 ≡   all fundamental parameters except aggregate shock process     Θ2   ≡ expectation parameters and aggregate shock pro...
DataImmigration, Wages and Education          19
Data           I need a suciently large variation in the data to identify the           57 parameters of the structural mo...
List of statistics       Description                                                       Source                         ...
Career transitions...                                                                         14,154         By year and s...
Identication           Identication is a matter of uniqueness of the global min and curva-           ture around it.      ...
ResultsImmigration, Wages and Education             24
Estimation results           Parameter estimates in reasonable values:       Parameter estimates                 ρ  γ ⇒ Sk...
Counterfactual           Simulations of a world without large scale immigration           Wage eect of immigration: dieren...
Average eects and the role of equilibrium                                                Wages        Skill prices:       ...
Labor supply adjustments                                             Choice with immigration                              ...
Education adjustments                                                   i.     BC to BC                                   ...
Blue collar experience adjustments                         vii.    BC to BC                                               ...
White collar experience adjustments                     xiii.        BC to BC                                             ...
Distributional adjustments                                      xxi.   Natives, stayers                                   ...
Distributional adjustments                                       xxiii.     Natives, all                                  ...
ConclusionImmigration, Wages and Education            33
Conclusions           This paper quanties the eect of immigration on wages taking into           account human capital and...
Appendix Index  1. Skill composition of immigra-       10. Skill-biased technical change     tion                         ...
Skill Composition of Immigration         Table: Share of Immigrants in the Workforce (%)                                  ...
Skill Composition of Immigration         Table: Share of Immigrants in the Workforce (%)                                  ...
Skill Composition of Immigration         Table: Share of Immigrants in the Workforce (%)                                  ...
Skill Composition of Immigration         Table: Share of Immigrants in the Workforce (%)                                  ...
Table: Education of Natives and Immigrants (%)                                       1970 1980 1990 2000 2008           A....
Table: Share of Immigrants among Workers in each Occupation (%)                                      1970 1980 1990 2000 2...
Back
Some motivating correlationsBorjas(2003,s.II-VI): reduced form version of factorproportionsCompares dierent penetration of...
Figure: Immigration and Wages (1960-2008)Note: Each obs. is an education-experience-year cell. Both variables are plotted ...
Figure: Immigration and School Enrollment (1960-2008)Note:      Each obs. is an education-year cell. Both variables plotte...
Figure: Immigration and Occupation Transitions (1970-2008)Note:   Each obs. is an education-experience-year cell. Both var...
Figure: Immigration Policies and the Origin of Immigrants(1875-2007)Note:  The black solid line represents the share of th...
Skill-biased technical changeRelative skill prices from the rst order conditions of rms prob-lem:      W                  ...
Demands for skillsDemands of skills are derived from the rst order conditions ofrms problem:                              ...
ExpectationsIndividuals forecast future state variables Ω        usingthe current state Ω                                 ...
Θ1 ≡all fundamental parameters except aggregate shock processΘ2 ≡expectation parameters and aggregate shock process 1. Cho...
Back
Table: Production FunctionElasticity of substitution:Blue vs Equipment/White (ρ)          0.334 (0.001)White vs Equipment ...
Table: Wages                                            Blue-collar        White-collarReturns:  Education (ω ):    Native...
Table: Utility Parameters                                            Male   FemaleA. School:   Heterogeneity parameters (δ...
Figure: Actual vs Predicted Wages            i. Log hourly wages                       ii. College-high school wage gapNot...
Immigration, Wages, and Education: A Labor Market Equilibrium Structural Model
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Immigration, Wages, and Education: A Labor Market Equilibrium Structural Model

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Barcelona GSE Trobada X

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

  1. 1. 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 2012Immigration, Wages and Education 1
  2. 2. MotivationImmigration, Wages and Education 2
  3. 3. Research questions A large literature has analyzed the eect of immigration on wages. However, How do human capital investment and labor supply of natives react to immigration? How important are these adjustments to understand the eect of immigration on wages? These adjustments are crucial, but omitted in the literatureImmigration, Wages and Education 3
  4. 4. Contribution Estimate labor market equilibrium structural model allowing natives 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 and white-collar labor with capital to produce a single output Equilibrium: channels the eect of immigration on incentives to invest in human capital through relative wages Wage eects of immigration are quantied by comparing data and counterfactual simulations of a world w/o mass immigrationImmigration, Wages and Education 4
  5. 5. Literature Literature does not establish a consensus about wage eects of immigration. Two dierent approaches: Spatial correlations: Grossman (1982), Borjas (1983, 1985, 1995), Card (1990, 2001), Altonji and Card (1991), LaLonde and 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), Dustman et al (2012)... Other labor market equilibrium models: Heckman, Lochner, Taber (1998); Lee (2005); Lee Wolpin (2006)Immigration, Wages and Education 5
  6. 6. Factor proportions approach (e.g. Borjas QJE03) Compare wages across dierent skill groups that received dierent amounts of immigrants: Reduced form: before-after and across groups comparison Structural: production function with the dierent skill groups and use it to simulate the eectImmigration, Wages and Education 6
  7. 7. Factor proportions approach (e.g. Borjas QJE03) Compare wages across dierent skill groups that received dierent amounts of immigrants: Reduced form: before-after and across groups comparison Structural: production function with the dierent skill groups and use it to simulate the eect However, natives may react by moving from less skilled groups to more skilled: Reduced form ⇒ still relatively small eects (although larger than spatial correlations) Structural ⇒ wrong counterfactualsImmigration, Wages and Education 6
  8. 8. Factor proportions approach (e.g. Borjas QJE03) Compare wages across dierent skill groups that received dierent amounts of immigrants: Reduced form: before-after and across groups comparison Structural: production function with the dierent skill groups and use it to simulate the eect However, natives may react by moving from less skilled groups to more skilled: Reduced form ⇒ still relatively small eects (although larger than spatial correlations) Structural ⇒ wrong counterfactuals Do not allow for skill-biased technical changeImmigration, Wages and Education 6
  9. 9. Preview of the main results Immigration reduces wages importantly Labor market equilibrium adjustments compensate partially the eect on impact Individuals adjust by switching occupations, exiting the labor market, 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 leave the market when looking at eects over the distributionImmigration, Wages and Education 7
  10. 10. Outline 1 Motivation 2 The model 3 Methodology 4 Data 5 Results 6 ConclusionImmigration, Wages and Education 8
  11. 11. The modelImmigration, Wages and Education 9
  12. 12. Individuals decide yearly on participation, education and occupation from age 16 (or upon entry) to 65 Immigrants enter the country exogenously and with a given skill endowment An aggregate rm combines labor skill units with capital to produce a single output Labor skill rental prices are determined in equilibrium. The wage of an individual i at time t in occupation j: wi,t = rt × si ≡ pricej × skill unitsi j j tImmigration, Wages and Education 10
  13. 13. Labor supply From age a = 16 to 65 years old, individuals choose among four 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 their net income each period This discrete choice dynamic programming problem builds on Keane-Wolpin (1994,1997), and Lee-Wolpin (2006,2010)Immigration, Wages and Education 11
  14. 14. Individuals solve the following dynamic programming problem: Va,t,l (Ωa,t ) = max Ua,l (Ωa,t , da ) + βE [Va+1,t+1,l (Ωa+1,t+1 ) | Ωa,t , da , l] da Notation: a ≡ age; l ≡ ability type (gender×region of origin); t ≡ time; g ≡ gender; is ≡ immigrant/native
  15. 15. Individuals solve the following dynamic programming problem: Va,t,l (Ωa,t ) = max Ua,l (Ωa,t , da ) + βE [Va+1,t+1,l (Ωa+1,t+1 ) | Ωa,t , da , l] daUa,t,l = wa,t,l +δg 1{da−1 = {B, W }}, j j BW j j wa,t,l = rt × sj , a,l j = B, W Notation: a ≡ age; l ≡ ability type (gender×region of origin); t ≡ time; g ≡ gender; is ≡ immigrant/native
  16. 16. Individuals solve the following dynamic programming problem: Va,t,l (Ωa,t ) = max Ua,l (Ωa,t , da ) + βE [Va+1,t+1,l (Ωa+1,t+1 ) | Ωa,t , da , l] daUa,t,l = wa,t,l +δg 1{da−1 = {B, W }}, j j BW j j wa,t,l = rt × sj , a,l j = B, W Notation: a ≡ age; l ≡ ability type (gender×region of origin); t ≡ time; g ≡ gender; is ≡ immigrant/native
  17. 17. Individuals solve the following dynamic programming problem: Va,t,l (Ωa,t ) = max Ua,l (Ωa,t , da ) + βE [Va+1,t+1,l (Ωa+1,t+1 ) | Ωa,t , da , l] daUa,t,l = wa,t,l +δg 1{da−1 = {B, W }}, j j BW j j wa,t,l = rt × sj , a,l j = B, W Notation: a ≡ age; l ≡ ability type (gender×region of origin); t ≡ time; g ≡ gender; is ≡ immigrant/native
  18. 18. Individuals solve the following dynamic programming problem: Va,t,l (Ωa,t ) = max Ua,l (Ωa,t , da ) + βE [Va+1,t+1,l (Ωa+1,t+1 ) | Ωa,t , da , l] daUa,t,l = wa,t,l +δg 1{da−1 = {B, W }}, j j BW j j wa,t,l = rt × sj , a,l j = B, W Notation: a ≡ age; l ≡ ability type (gender×region of origin); t ≡ time; g ≡ gender; is ≡ immigrant/native
  19. 19. Individuals solve the following dynamic programming problem: Va,t,l (Ωa,t ) = max Ua,l (Ωa,t , da ) + βE [Va+1,t+1,l (Ωa+1,t+1 ) | Ωa,t , da , l] daUa,t,l = wa,t,l +δg 1{da−1 = {B, W }}, j j BW j j wa,t,l = rt × sj , a,l j = B, W Notation: a ≡ age; l ≡ ability type (gender×region of origin); t ≡ time; g ≡ gender; is ≡ immigrant/native
  20. 20. Individuals solve the following dynamic programming problem: Va,t,l (Ωa,t ) = max Ua,l (Ωa,t , da ) + βE [Va+1,t+1,l (Ωa+1,t+1 ) | Ωa,t , da , l] da Ua,t,l = wa,t,l +δg 1{da−1 = {B, W }}, j j BW j j wa,t,l = rt × sj , a,l j = B, W j jwa,t,l = rt exp{ω0,l + ω1,is Ea + ω2 XBa + ω3 XBa + ω4 XW a + ω5 XW a + ω6 XF a + εj } j j j j 2 j j 2 j a Notation: a ≡ age; l ≡ ability type (gender×region of origin); t ≡ time; g ≡ gender; is ≡ immigrant/native
  21. 21. Individuals solve the following dynamic programming problem: Va,t,l (Ωa,t ) = max Ua,l (Ωa,t , da ) + βE [Va+1,t+1,l (Ωa+1,t+1 ) | Ωa,t , da , l] da Ua,t,l = wa,t,l +δg 1{da−1 = {B, W }}, j j BW j j wa,t,l = rt × sj , a,l j = B, W j jwa,t,l = rt exp{ω0,l + ω1,is Ea + ω2 XBa + ω3 XBa + ω4 XW a + ω5 XW a + ω6 XF a + εj } j j j j 2 j j 2 j a Notation: a ≡ age; l ≡ ability type (gender×region of origin); t ≡ time; g ≡ gender; is ≡ immigrant/native
  22. 22. Individuals solve the following dynamic programming problem: Va,t,l (Ωa,t ) = max Ua,l (Ωa,t , da ) + βE [Va+1,t+1,l (Ωa+1,t+1 ) | Ωa,t , da , l] da Ua,t,l = wa,t,l +δg 1{da−1 = {B, W }}, j j BW j j wa,t,l = rt × sj , a,l j = B, W j jwa,t,l = rt exp{ω0,l + ω1,is Ea + ω2 XBa + ω3 XBa + ω4 XW a + ω5 XW a + ω6 XF a + εj } j j j j 2 j j 2 j a Notation: a ≡ age; l ≡ ability type (gender×region of origin); t ≡ time; g ≡ gender; is ≡ immigrant/native
  23. 23. Individuals solve the following dynamic programming problem: Va,t,l (Ωa,t ) = max Ua,l (Ωa,t , da ) + βE [Va+1,t+1,l (Ωa+1,t+1 ) | Ωa,t , da , l] da Ua,t,l = wa,t,l +δg 1{da−1 = {B, W }}, j j BW j j wa,t,l = rt × sj , a,l j = B, W j jwa,t,l = rt exp{ω0,l + ω1,is Ea + ω2 XBa + ω3 XBa + ω4 XW a + ω5 XW a + ω6 XF a + εj } j j j j 2 j j 2 j a Notation: a ≡ age; l ≡ ability type (gender×region of origin); t ≡ time; g ≡ gender; is ≡ immigrant/native
  24. 24. Individuals solve the following dynamic programming problem: Va,t,l (Ωa,t ) = max Ua,l (Ωa,t , da ) + βE [Va+1,t+1,l (Ωa+1,t+1 ) | Ωa,t , da , l] da Ua,t,l = wa,t,l +δg 1{da−1 = {B, W }}, j j BW j j wa,t,l = rt × sj , a,l j = B, W j jwa,t,l = rt exp{ω0,l + ω1,is Ea + ω2 XBa + ω3 XBa + ω4 XW a + ω5 XW a + ω6 XF a + εj } j j j j 2 j j 2 j a Notation: a ≡ age; l ≡ ability type (gender×region of origin); t ≡ time; g ≡ gender; is ≡ immigrant/native
  25. 25. Individuals solve the following dynamic programming problem: Va,t,l (Ωa,t ) = max Ua,l (Ωa,t , da ) + βE [Va+1,t+1,l (Ωa+1,t+1 ) | Ωa,t , da , l] da Ua,t,l = wa,t,l +δg 1{da−1 = {B, W }}, j j BW j j wa,t,l = rt × sj , a,l j = B, W j jwa,t,l = rt exp{ω0,l + ω1,is Ea + ω2 XBa + ω3 XBa + ω4 XW a + ω5 XW a + ω6 XF a + εj } j j j j 2 j j 2 j a Notation: a ≡ age; l ≡ ability type (gender×region of origin); t ≡ time; g ≡ gender; is ≡ immigrant/native
  26. 26. Individuals solve the following dynamic programming problem: Va,t,l (Ωa,t ) = max Ua,l (Ωa,t , da ) + βE [Va+1,t+1,l (Ωa+1,t+1 ) | Ωa,t , da , l] da Ua,t,l = wa,t,l +δg 1{da−1 = {B, W }}, j j BW j j wa,t,l = rt × sj , a,l j = B, W j jwa,t,l = rt exp{ω0,l + ω1,is Ea + ω2 XBa + ω3 XBa + ω4 XW a + ω5 XW a + ω6 XF a + εj } j j j j 2 j j 2 j a Notation: a ≡ age; l ≡ ability type (gender×region of origin); t ≡ time; g ≡ gender; is ≡ immigrant/native
  27. 27. Individuals solve the following dynamic programming problem: Va,t,l (Ωa,t ) = max Ua,l (Ωa,t , da ) + βE [Va+1,t+1,l (Ωa+1,t+1 ) | Ωa,t , da , l] da Ua,t,l = wa,t,l +δg 1{da−1 = {B, W }}, j j BW j j wa,t,l = rt × sj , a,l j = B, W j jwa,t,l = rt exp{ω0,l + ω1,is Ea + ω2 XBa + ω3 XBa + ω4 XW a + ω5 XW a + ω6 XF a + εj } j j j j 2 j j 2 j a Notation: a ≡ age; l ≡ ability type (gender×region of origin); t ≡ time; g ≡ gender; is ≡ immigrant/native
  28. 28. Individuals solve the following dynamic programming problem: Va,t,l (Ωa,t ) = max Ua,l (Ωa,t , da ) + βE [Va+1,t+1,l (Ωa+1,t+1 ) | Ωa,t , da , l] da Ua,t,l = wa,t,l +δg 1{da−1 = {B, W }}, j j BW j j wa,t,l = rt × sj , a,l j = B, W j jwa,t,l = rt exp{ω0,l + ω1,is Ea + ω2 XBa + ω3 XBa + ω4 XW a + ω5 XW a + ω6 XF a + εj } j j j j 2 j j 2 j a Notation: a ≡ age; l ≡ ability type (gender×region of origin); t ≡ time; g ≡ gender; is ≡ immigrant/native
  29. 29. Individuals solve the following dynamic programming problem: Va,t,l (Ωa,t ) = max Ua,l (Ωa,t , da ) + βE [Va+1,t+1,l (Ωa+1,t+1 ) | Ωa,t , da , l] da Ua,t,l = wa,t,l +δg 1{da−1 = {B, W }}, j j BW j j wa,t,l = rt × sj , a,l j = B, W j jwa,t,l = rt exp{ω0,l + ω1,is Ea + ω2 XBa + ω3 XBa + ω4 XW a + ω5 XW a + ω6 XF a + εj } j j j j 2 j j 2 j a εB a 0 (σg )2 B ρBW σg σg B W ∼ i.i. N , εW a 0 ρBW σg σg B W (σg )2 W Notation: a ≡ age; l ≡ ability type (gender×region of origin); t ≡ time; g ≡ gender; is ≡ immigrant/native
  30. 30. Individuals solve the following dynamic programming problem: Va,t,l (Ωa,t ) = max Ua,l (Ωa,t , da ) + βE [Va+1,t+1,l (Ωa+1,t+1 ) | Ωa,t , da , l] da Ua,t,l = wa,t,l +δg 1{da−1 = {B, W }}, j j BW j j wa,t,l = rt × sj , a,l j = B, W j jwa,t,l = rt exp{ω0,l + ω1,is Ea + ω2 XBa + ω3 XBa + ω4 XW a + ω5 XW a + ω6 XF a + εj } j j j j 2 j j 2 j a εB a 0 (σg )2 B ρBW σg σg B W ∼ i.i. N , εW a 0 ρBW σg σg B W (σg )2 W Ua,l = δ0,l − δ1,g 1{da−1 = S} − τ1 1{Ea ≥ 12} − τ2 1{Ea ≥ 16} + σg εS S S S S a Notation: a ≡ age; l ≡ ability type (gender×region of origin); t ≡ time; g ≡ gender; is ≡ immigrant/native
  31. 31. Individuals solve the following dynamic programming problem: Va,t,l (Ωa,t ) = max Ua,l (Ωa,t , da ) + βE [Va+1,t+1,l (Ωa+1,t+1 ) | Ωa,t , da , l] da Ua,t,l = wa,t,l +δg 1{da−1 = {B, W }}, j j BW j j wa,t,l = rt × sj , a,l j = B, W j jwa,t,l = rt exp{ω0,l + ω1,is Ea + ω2 XBa + ω3 XBa + ω4 XW a + ω5 XW a + ω6 XF a + εj } j j j j 2 j j 2 j a εB a 0 (σg )2 B ρBW σg σg B W ∼ i.i. N , εW a 0 ρBW σg σg B W (σg )2 W Ua,l = δ0,l − δ1,g 1{da−1 = S} − τ1 1{Ea ≥ 12} − τ2 1{Ea ≥ 16} + σg εS S S S S a Notation: a ≡ age; l ≡ ability type (gender×region of origin); t ≡ time; g ≡ gender; is ≡ immigrant/native
  32. 32. Individuals solve the following dynamic programming problem: Va,t,l (Ωa,t ) = max Ua,l (Ωa,t , da ) + βE [Va+1,t+1,l (Ωa+1,t+1 ) | Ωa,t , da , l] da Ua,t,l = wa,t,l +δg 1{da−1 = {B, W }}, j j BW j j wa,t,l = rt × sj , a,l j = B, W j jwa,t,l = rt exp{ω0,l + ω1,is Ea + ω2 XBa + ω3 XBa + ω4 XW a + ω5 XW a + ω6 XF a + εj } j j j j 2 j j 2 j a εB a 0 (σg )2 B ρBW σg σg B W ∼ i.i. N , εW a 0 ρBW σg σg B W (σg )2 W Ua,l = δ0,l − δ1,g 1{da−1 = S} − τ1 1{Ea ≥ 12} − τ2 1{Ea ≥ 16} + σg εS S S S S a Notation: a ≡ age; l ≡ ability type (gender×region of origin); t ≡ time; g ≡ gender; is ≡ immigrant/native
  33. 33. Individuals solve the following dynamic programming problem: Va,t,l (Ωa,t ) = max Ua,l (Ωa,t , da ) + βE [Va+1,t+1,l (Ωa+1,t+1 ) | Ωa,t , da , l] da Ua,t,l = wa,t,l +δg 1{da−1 = {B, W }}, j j BW j j wa,t,l = rt × sj , a,l j = B, W j jwa,t,l = rt exp{ω0,l + ω1,is Ea + ω2 XBa + ω3 XBa + ω4 XW a + ω5 XW a + ω6 XF a + εj } j j j j 2 j j 2 j a εB a 0 (σg )2 B ρBW σg σg B W ∼ i.i. N , εW a 0 ρBW σg σg B W (σg )2 W Ua,l = δ0,l − δ1,g 1{da−1 = S} − τ1 1{Ea ≥ 12} − τ2 1{Ea ≥ 16} + σg εS S S S S a Notation: a ≡ age; l ≡ ability type (gender×region of origin); t ≡ time; g ≡ gender; is ≡ immigrant/native
  34. 34. Individuals solve the following dynamic programming problem: Va,t,l (Ωa,t ) = max Ua,l (Ωa,t , da ) + βE [Va+1,t+1,l (Ωa+1,t+1 ) | Ωa,t , da , l] da Ua,t,l = wa,t,l +δg 1{da−1 = {B, W }}, j j BW j j wa,t,l = rt × sj , a,l j = B, W j jwa,t,l = rt exp{ω0,l + ω1,is Ea + ω2 XBa + ω3 XBa + ω4 XW a + ω5 XW a + ω6 XF a + εj } j j j j 2 j j 2 j a εB a 0 (σg )2 B ρBW σg σg B W ∼ i.i. N , εW a 0 ρBW σg σg B W (σg )2 W Ua,l = δ0,l − δ1,g 1{da−1 = S} − τ1 1{Ea ≥ 12} − τ2 1{Ea ≥ 16} + σg εS S S S S a Ua,t,l = δ0,l + δ1,g na + δ2,g t + σg εH H H H H H a Notation: a ≡ age; l ≡ ability type (gender×region of origin); t ≡ time; g ≡ gender; is ≡ immigrant/native
  35. 35. Individuals solve the following dynamic programming problem: Va,t,l (Ωa,t ) = max Ua,l (Ωa,t , da ) + βE [Va+1,t+1,l (Ωa+1,t+1 ) | Ωa,t , da , l] da Ua,t,l = wa,t,l +δg 1{da−1 = {B, W }}, j j BW j j wa,t,l = rt × sj , a,l j = B, W j jwa,t,l = rt exp{ω0,l + ω1,is Ea + ω2 XBa + ω3 XBa + ω4 XW a + ω5 XW a + ω6 XF a + εj } j j j j 2 j j 2 j a εB a 0 (σg )2 B ρBW σg σg B W ∼ i.i. N , εW a 0 ρBW σg σg B W (σg )2 W Ua,l = δ0,l − δ1,g 1{da−1 = S} − τ1 1{Ea ≥ 12} − τ2 1{Ea ≥ 16} + σg εS S S S S a Ua,t,l = δ0,l + δ1,g na + δ2,g t + σg εH H H H H H a Notation: a ≡ age; l ≡ ability type (gender×region of origin); t ≡ time; g ≡ gender; is ≡ immigrant/native
  36. 36. Individuals solve the following dynamic programming problem: Va,t,l (Ωa,t ) = max Ua,l (Ωa,t , da ) + βE [Va+1,t+1,l (Ωa+1,t+1 ) | Ωa,t , da , l] da Ua,t,l = wa,t,l +δg 1{da−1 = {B, W }}, j j BW j j wa,t,l = rt × sj , a,l j = B, W j jwa,t,l = rt exp{ω0,l + ω1,is Ea + ω2 XBa + ω3 XBa + ω4 XW a + ω5 XW a + ω6 XF a + εj } j j j j 2 j j 2 j a εB a 0 (σg )2 B ρBW σg σg B W ∼ i.i. N , εW a 0 ρBW σg σg B W (σg )2 W Ua,l = δ0,l − δ1,g 1{da−1 = S} − τ1 1{Ea ≥ 12} − τ2 1{Ea ≥ 16} + σg εS S S S S a Ua,t,l = δ0,l + δ1,g na + δ2,g t + σg εH H H H H H a Notation: a ≡ age; l ≡ ability type (gender×region of origin); t ≡ time; g ≡ gender; is ≡ immigrant/native
  37. 37. Individuals solve the following dynamic programming problem: Va,t,l (Ωa,t ) = max Ua,l (Ωa,t , da ) + βE [Va+1,t+1,l (Ωa+1,t+1 ) | Ωa,t , da , l] da Ua,t,l = wa,t,l +δg 1{da−1 = {B, W }}, j j BW j j wa,t,l = rt × sj , a,l j = B, W j jwa,t,l = rt exp{ω0,l + ω1,is Ea + ω2 XBa + ω3 XBa + ω4 XW a + ω5 XW a + ω6 XF a + εj } j j j j 2 j j 2 j a εB a 0 (σg )2 B ρBW σg σg B W ∼ i.i. N , εW a 0 ρBW σg σg B W (σg )2 W Ua,l = δ0,l − δ1,g 1{da−1 = S} − τ1 1{Ea ≥ 12} − τ2 1{Ea ≥ 16} + σg εS S S S S a Ua,t,l = δ0,l + δ1,g na + δ2,g t + σg εH H H H H H a Notation: a ≡ age; l ≡ ability type (gender×region of origin); t ≡ time; g ≡ gender; is ≡ immigrant/native
  38. 38. Labor demand Aggregate rm combines blue- and white-collar skill units (SB , SW ) with capital structures and equipment (KS , KE ) to produce a single output (Y ) with the following technology: ρ γ γ Yt = zt KSt {αSBt + (1 − α)[θSW t + (1 − θ)KEt ]ρ/γ }(1−λ)/ρ λ Two types of labor: blue- and white-collar. Workers within an occupation are also heterogeneous in skills The nested CES is included to capture the capital-skill com- plementarity and SBTC (Krusell et al., 2000)Immigration, Wages and Education 13
  39. 39. No savings: equilibrium capital and output taken from data zt is an aggregate productivity shock (identied as the residual of the production function) It is assumed to evolve according to: ln zt+1 − ln zt = φ0 + φ1 (ln zt − ln zt−1 ) + εz t+1 εz ∼ N (0, σ z ) t+1Immigration, Wages and Education 14
  40. 40. Equilibrium Demands of skill units are given by the rst order conditions on rms problem The aggregate supply of skill units is given by: 65 N Sjt = sj 1{da,i = j} j = B, W a,i a=16 i=1 ⇒ The equilibrium is given by the skill prices that equate the supply and the demand of skill units (market clearing) Expectations are approximated with a rule in line with Lee and Wolpin (2006,2010), and in the same spirit of Krusell and Smith (1998)Immigration, Wages and Education 15
  41. 41. MethodologyImmigration, Wages and Education 16
  42. 42. Estimating dierent pieces of the model separately is not feasible: 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 algorithmImmigration, Wages and Education 17
  43. 43. Θ1 ≡ all fundamental parameters except aggregate shock process Θ2 ≡ expectation parameters and aggregate shock process This paper Lee and Wolpin (2006) Guess Θ1 Θ2 Guess Θ1 Θ2 Solve optimization prob. Solve optimization prob. Simulate the economy Simulate the economy Iterate Θ1 Iterate Θ2 Simulate statistics and Estimate processes for compare to data aggr. shock prices Θ2 Estimate processes for Simulate statistics and aggr. shock prices Θ2 compare to data Iterate Θ2 Iterate Θ1 Detailed algorithmImmigration, Wages and Education 18
  44. 44. DataImmigration, Wages and Education 19
  45. 45. Data I need a suciently large variation in the data to identify the 57 parameters of the structural model plus additional 8 for skill price expectation rules. Moreover, I also need some macro data for the exogenous vari- ables to be introduced in the solution of the model: output capital native and immigrant cohort sizes fertility process age at entry initial schooling region of origin I t the model to statistics which I calculate with US micro- data (CPS, NLSY79,NLSY97) for 1967-2007Immigration, Wages and Education 20
  46. 46. 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) 2,460 By year, sex, and educational level CPS 41 × 2 × 4 × (4 − 1) 984 By year, sex, and preschool children CPS 41 × 2 × 3 × (4 − 1) 738 By year, sex, and region of origin CPS 15 × 2 × 4 × (4 − 1) 360 Immigrants, by year, sex, and foreign potential experience CPS 15 × 2 × 5 × (4 − 1) 450 By sex and experience in each occupation NLSY 2 × (5 × 5 + 4 × 4) × (2 − 1) 82 Wages: 6,404 By year, sex, 5-year age group, and occupation CPS 1,640 Mean log hourly real wage... 3,000 41 × 2 × 10 × 2 By year, sex, educational level, and occupation CPS 41 × 2 × 4 × 2 656 By year, sex, region of origin, and occupation CPS 15 × 2 × 4 × 2 240 Immigrants, by year, sex, fpx, and occupation CPS 15 × 2 × 5 × 2 300 By sex, experience in each occupation, and occupation NLSY 2 × (5 × 5 + 4 × 4) × 2 164 By year, sex, previous, and current occupation Matched CPS 328 Mean 1-year growth rates in log hourly real wage... 2,508 41 × 2 × 2 × 2 By year, sex, 5-year age group, and current occupation Matched CPS 41 × 2 × 10 × 2 1,640 By year, sex, region of origin, and current occupation Matched CPS 15 × 2 × 4 × 2 240 Immigrants, by year, sex, years in the U.S., and occupation Matched CPS 15 × 2 × 5 × 2 300 By year, sex, educational level, and occupation CPS 656 Variance in the log hourly real wages... 896 41 × 2 × 4 × 2 By year, sex, region of origin, and occupation CPS 15 × 2 × 4 × 2 240Immigration, Wages and Education 21
  47. 47. Career transitions... 14,154 By year and sex Matched CPS 41 × 2 × 4 × (4 − 1) 984 By year, sex, and age Matched CPS 41 × 2 × 10 × 4 × (4 − 1) 9,840 By year, sex, and region of origin Matched CPS 15 × 2 × 4 × 4 × (4 − 1) 1,440 New entrants taking each choice by year and sex CPS 15 × 2 × (4 − 1) 90 Immigrants, 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) 2,460 By year, sex, 5-year age group, and immi- CPS 15 × 2 × 10 × 2 × (4 − 1) 1,800 grant/native Distribution of experience... 120 Blue collar, by sex NLSY 2 × (13 + 7) 40 White collar, by sex NLSY 2 × (13 + 7) 40 Home, by sex NLSY 2 × (13 + 7) 40Immigration, Wages and Education 22
  48. 48. 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)Immigration, Wages and Education 23
  49. 49. ResultsImmigration, Wages and Education 24
  50. 50. 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 tImmigration, Wages and Education 25
  51. 51. Counterfactual Simulations of a world without large scale immigration Wage eect of immigration: dierence between baseline and counterfactual average log wages. Stock of immigrants increased to keep immigrant/native ratio constant 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 literatureImmigration, Wages and Education 26
  52. 52. Average eects and the role of equilibrium Wages Skill prices: BC WC Average 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 1.12Immigration, Wages and Education 27
  53. 53. Labor supply adjustments Choice with immigration No capital adjustment (∂K/∂m = 0) Adjust Of which adjust to: Choice w/o Blue White School Home immigration collar collar 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) Adjust Of which adjust to: Choice w/o Blue White School Home immigration collar collar 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 Immigration, Wages and Education 28
  54. 54. Education adjustments i. BC to BC ii. BC to WC iii. Home to Work 0.003 0.006 0.009 0.012 0.015 0.00720.01440.02160.0288 0.036 0.026 0.052 0.078 0.104 0.13 Adjusting education: • If ∂K/∂m=0: 3.8% Adjusting education: • If ∂K/∂m=0: 11.6% Adjusting education: • If ∂K/∂m=0: 34.2% • If ∂rK /∂m=0: 1.3% • If ∂rK /∂m=0: 11.7% • If ∂rK /∂m=0: 22.4% Fraction Fraction Fraction 0 0 0 -12 -9 -6 -3 0 3 6 9 12 -12 -9 -6 -3 0 3 6 9 12 -12 -9 -6 -3 0 3 6 9 12 Years of education Years of education Years of education iv. WC to BC v. WC to WC vi. Work to Home 0.25 0.03 0.1 Adjusting education: • If ∂K/∂m=0: 80.5% Adjusting education: • If ∂K/∂m=0: 6.6% Adjusting education: • If ∂K/∂m=0: 28.9% • If ∂rK /∂m=0: 76.3% • If ∂rK /∂m=0: 1.7% • If ∂rK /∂m=0: 8.2% 0.006 0.012 0.018 0.024 0.08 0.2 0.15 0.06 Fraction Fraction Fraction 0.04 0.1 0.05 0.02 0 0 0 -12 -9 -6 -3 0 3 6 9 12 -12 -9 -6 -3 0 3 6 9 12 -12 -9 -6 -3 0 3 6 9 12 Years of education Years of education Years of education No capital adjust. (∂K/∂m=0) Full capital adjust. (∂rK /∂m=0)Immigration, Wages and Education 29
  55. 55. Blue collar experience adjustments vii. BC to BC viii. BC to WC ix. Home to Work 0.15 0.2 0.2 Adjust BC experience: • If ∂K/∂m=0: 28.2% Adjust BC experience: • If ∂K/∂m=0: 77.4% Adjust BC experience: • If ∂K/∂m=0: 88.3% • If ∂rK /∂m=0: 18.6% • If ∂rK /∂m=0: 72.6% • If ∂rK /∂m=0: 59.6% 0.12 0.16 0.16 0.09 0.12 0.12 Fraction Fraction Fraction 0.06 0.08 0.08 0.03 0.04 0.04 0 0 0 -30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30 Years of experience Years of experience Years of experience x. WC to BC xi. WC to WC xii. Work to Home 0.15 0.25 0.1 Adjust BC experience: • If ∂K/∂m=0: 80.8% Adjust BC experience: • If ∂K/∂m=0: 17.5% Adjust BC experience: • If ∂K/∂m=0: 44.1% • If ∂rK /∂m=0: 93.3% • If ∂rK /∂m=0: 14.1% • If ∂rK /∂m=0: 60.9% 0.12 0.08 0.2 0.09 0.06 0.15 Fraction Fraction Fraction 0.06 0.04 0.1 0.03 0.02 0.05 0 0 0 -30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30 Years of experience Years of experience Years of experience No capital adjust. (∂K/∂m=0) Full capital adjust. (∂rK /∂m=0)Immigration, Wages and Education 30
  56. 56. White collar experience adjustments xiii. BC to BC xiv. BC to WC xv. Home to Work 0.05 0.15 0.2 Adjust WC experience: • If ∂K/∂m=0: 15.3% Adjust WC experience: • If ∂K/∂m=0: 67.6% Adjust WC experience: • If ∂K/∂m=0: 87.0% • If ∂rK /∂m=0: 12.0% • If ∂rK /∂m=0: 67.6% • If ∂rK /∂m=0: 72.6% 0.04 0.16 0.12 0.03 0.12 0.09 Fraction Fraction Fraction 0.02 0.08 0.06 0.01 0.04 0.03 0 0 0 -30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30 Years of experience Years of experience Years of experience xvi. WC to BC xvii. WC to WC xviii. Work to Home 0.15 0.2 0.1 Adjust WC experience: • If ∂K/∂m=0: 90.0% Adjust WC experience: • If ∂K/∂m=0: 21.7% Adjust WC experience: • If ∂K/∂m=0: 40.3% • If ∂rK /∂m=0: 95.4% • If ∂rK /∂m=0: 15.7% • If ∂rK /∂m=0: 35.7% 0.16 0.08 0.12 0.12 0.06 0.09 Fraction Fraction Fraction 0.08 0.04 0.06 0.04 0.02 0.03 0 0 0 -30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30 Years of experience Years of experience Years of experience No capital adjust. (∂K/∂m=0) Full capital adjust. (∂rK /∂m=0)Immigration, Wages and Education 31
  57. 57. Distributional adjustments xxi. Natives, stayers xxii. Immigrants, stayers 0.04 0.04 0 0 Percentage change Percentage change 0 25 50 75 100 0 25 50 75 100 -0.04 -0.04 -0.08 -0.08 -0.12 -0.12 -0.16 -0.16 Percentile Percentile No capital adjust. (∂K/∂m=0) ±2 s.e. Full capital adjust. (∂rK /∂m=0) ±2 s.e.Immigration, Wages and Education 32
  58. 58. Distributional adjustments xxiii. Natives, all xxiv. Immigrants, all 0.04 0.04 0 0 Percentage change Percentage change 0 25 50 75 100 0 25 50 75 100 -0.04 -0.04 -0.08 -0.08 -0.12 -0.12 -0.16 -0.16 Percentile Percentile xxv. Natives, stayers xxvi. Immigrants, stayers 0.04 0.04 0 0 Percentage change Percentage change 0 25 50 75 100 0 25 50 75 100 -0.04 -0.04 -0.08 -0.08 -0.12 -0.12 -0.16 -0.16 Percentile Percentile No capital adjust. (∂K/∂m=0) ±2 s.e. Full capital adjust. (∂rK /∂m=0) ±2 s.e.Immigration, Wages and Education 32
  59. 59. ConclusionImmigration, Wages and Education 33
  60. 60. Conclusions This paper quanties the eect of immigration on wages taking into account 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 the eect on impact Individuals adjust by switching occupations, exiting the labor market, 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 leave the market when looking at eects over the distributionImmigration, Wages and Education 34
  61. 61. Appendix Index 1. Skill composition of immigra- 10. Skill-biased technical change tion 11. Demands for skills 2. Education of natives and immi- grants 12. Expectations 3. Share of immigrants among 13. Algorithm workers in each occupation 14. Sections of the objective func- 4. Bias of the estimates of the lit- tion erature 15. Production function estimates 5. Some motivating correlations 16. Wage equations estimates 6. Immigration and wages 7. Immigration and school enroll- 17. Utility function estimates ment 18. Actual and predicted wages 8. Immigration and blue-collar to 19. Actual and predicted human white-collar transitions capital and labor supply vari- 9. Immigration policies ables
  62. 62. 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 16.56Note: 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).
  63. 63. 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 33.73 High school 4.32 5.14 7.94 12.04 13.27 Some college 5.14 6.63 7.92 9.96 11.65 College 6.48 8.02 10.60 14.59 16.92Note: 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).
  64. 64. 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 33.73 High school 4.32 5.14 7.94 12.04 13.27 Some college 5.14 6.63 7.92 9.96 11.65 College 6.48 8.02 10.60 14.59 16.92 C. In blue collar jobs: All education levels 6.03 7.83 11.21 17.53 24.07Note: 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).
  65. 65. 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 33.73 High school 4.32 5.14 7.94 12.04 13.27 Some college 5.14 6.63 7.92 9.96 11.65 College 6.48 8.02 10.60 14.59 16.92 C. In blue collar jobs: more Dropouts 7.18 12.18 23.75 41.03 55.45 All education levels 6.03 7.83 11.21 17.53 24.07 High school 4.19 4.94 7.57 12.47 17.30 Some college 5.95 6.14 7.26 9.82 14.07 College 9.53 9.52 12.14 17.89 23.82Note: 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).
  66. 66. Table: Education of Natives and Immigrants (%) 1970 1980 1990 2000 2008 A. Natives Dropouts 41.0 28.2 16.7 12.8 10.7 High school 35.5 38.7 34.8 32.4 37.5 Some college 13.5 18.2 29.0 31.7 26.2 College 10.1 14.8 19.4 23.0 25.6 B. Immigrants Dropouts 49.8 39.0 31.8 30.6 27.4 High school 26.5 27.3 26.2 25.9 28.9 Some college 12.1 16.9 21.8 20.5 17.4 College 11.6 16.8 20.1 23.0 26.3 Dropouts 49.1 32.2 18.7 11.6 7.7 a. Western Countries High school 28.8 33.7 31.2 27.6 29.8 Some college 11.9 17.9 27.1 28.1 24.1 College 10.2 16.3 23.1 32.7 38.4 Dropouts 61.4 56.4 49.4 47.6 42.7 b. Latin America High school 21.8 22.4 25.8 28.1 32.2 Some college 10.0 13.1 16.7 15.7 14.2 College 6.9 8.1 8.2 8.6 10.9 Dropouts 31.5 22.6 16.4 13.2 10.9 c. Asia and Africa High school 22.4 22.8 22.3 21.2 22.6 Some college 16.9 21.5 25.0 23.9 19.6 College 29.2 33.1 36.3 41.7 46.9Note: 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
  67. 67. 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 51.11 Laborers 5.47 7.40 11.87 21.48 31.27 Service workers 7.58 9.62 13.65 19.58 25.59 Operatives 5.84 8.38 11.74 18.55 23.98 Craftsmen 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 14.50 Managers 5.02 5.93 7.76 10.75 13.37 Clerical and kindred 4.27 5.17 7.14 9.97 12.47 Sales workers 4.78 5.03 6.78 9.29 11.52 Farm managers 1.52 1.56 2.87 4.87 6.38Note: Figures indicate the share of immigrants among workers employed in eachoccupation. Sources : Census data (1970-2000) and ACS (2008). Back
  68. 68. Back
  69. 69. Some motivating correlationsBorjas(2003,s.II-VI): reduced form version of factorproportionsCompares dierent penetration of immigrants acrosseducation-experience-time cellsImmigration and wages are negatively correlated graphWith the same approach I nd some motivating correlations Immigration and school enrollment rates are positively correlated (education-time cells) graph Immigration and occupational switches from blue-collar to white-collar are also positively correlated graph
  70. 70. 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: ln wijt = −0.394mijt + νi + ιj + δt + ijt . Back (0.041)where ln wijt 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).
  71. 71. 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 + it . (0.125) Backwhere 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).
  72. 72. 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: ijt = 0.150mijt + νi + ιj + δt + ijt . p (0.044) Backwhere 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 to
  73. 73. 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 intensity
  74. 74. Skill-biased technical changeRelative skill prices from the rst order conditions of rms prob-lem: W γ rt (1 − α)θ SW t ρ−γ KEtln W = ln +(ρ−1) ln + ln θ + (1 − θ) rt α SBt γ SW tSkill-biased technical change embedded in capital equipment ac-cumulation if (ρ γ) Back
  75. 75. Demands for skillsDemands of skills are derived from the rst order conditions ofrms problem: ρ ρ B λ 1−λ ρ−1 1− 1−λ rt = (1 − λ)α zt KSt SBt Yt ρ ρ 1− 1−λ SW t KWtρ−γ Yt γ−1 W λ 1−λ rt = (1 − λ)(1 − α)θ zt KSt Back
  76. 76. ExpectationsIndividuals forecast future state variables Ω usingthe current state Ω t+1,a+1 t,aState 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 pricesProblem: future skill prices depend upon the currentdistrib of state variables across the whole populationNumerical solution: assume that equilibrium aggregateskill units are well represented by j j j B j W j∆ ln rt+1 = η0 + ηB ∆ ln rt + ηW ∆ ln rt + ηz ∆ ln zt+1
  77. 77. 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 = 1 to t = T (dynamic programming problem solved recursively by backward induction; interpolation method based on the one described in Keane and Wolpin (1994,1997) with quadrature for integrals). 3. Find the equilibrium skill rental prices which clear the markets and the aggregate 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, together with 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 3.4 till 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 with simplex 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 for processes)
  78. 78. Back
  79. 79. Table: Production FunctionElasticity 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 (φ ) 0.001 (0.001)Autorregressive term (φ ) 0.384 (0.028) 0St. dev. of innivations (σ ) 0.022 (0.006) 1 z Back
  80. 80. Table: Wages Blue-collar White-collarReturns: Education (ω ): Natives 0.057 (0.000) 0.123 (0.000) 1,i Immigrants 0.063 (0.001) 0.093 (0.000) BC experience (ω ) 0.106 (0.000) 0.001 (0.000) BC experience (ω ) -0.0020 (0.0009) 0.0000 (0.0000) 2 2 WC experience (ω ) 0.001 (0.000) 0.061 (0.000) 3 WC experience (ω ) 0.0000 (0.0000) -0.0006 (0.0000) 4 2 Foreign experience (ω ) -0.008 (0.000) 0.032 (0.001) 5 6Heterogeneity parameters(ω ): Western countries 0.055 (0.005) -0.027 (0.005) 0,l 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) Back
  81. 81. Table: Utility Parameters Male FemaleA. School: Heterogeneity parameters (δ ): S Natives -2,635 (79) 6,544 (72) 0,l 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 (τ ) 17,325 (144) Graduate (τ + τ ) 33,446 (273) 1 Reentering disutility (δ ) 21,505 (142) 47,250 (268) 1 2 S Variance (σ ) S 1 5,971 (42) 1,718 (8)Heterogeneity parameters (δ ): H 0,lB. Home: Heterogeneity parameters (δ ): H Natives 13,875 (54) 15,633 (41) 0,l 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 (δ ) H 3,580 (64) 11,211 (127) Trend (δ ) H 1 88.28 (0.10) 55.43 (0.02) Variance (σ ) 2 H 4,945 (38) 9,436 (32) Back
  82. 82. Figure: Actual vs Predicted Wages i. Log hourly wages ii. College-high school wage gapNote: 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. Back

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