Substitution between Immigrant and Native Farmworkers in the United States: Does Legal Status Matter?

Xuan Wei; Gülcan Önel; Zhengfei Guan; Fritz Roka

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Substitution between Immigrant and Native Farmworkers in the United States: Does Legal Status Matter?

| 27 jul 2019

IZA Journal of Development and Migration

Volumen 10 (2019): Edición 1 (June 2019)

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Publicado en línea: 27 jul 2019

Páginas: -

DOI: https://doi.org/10.2478/izajodm-2019-0007

Palabras clave
elasticity of substitution, immigration, legal status, agricultural labor, nested CES framework

© 2019 Xuan Wei, Gülcan Önel, Zhengfei Guan and Fritz Roka, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 Public License.

Nested CES Model A: Skill is approximated by task type

Nested CES Model B: Skill is approximated by farmwork experience

Nested constant elasticity of substitution (CES) Model A: Estimated elasticities of substitution by immigration status, age, and task groups

Nested CES Model A: Skill is approximated by task type
	Step 1 Estimation:Three immigration groups (Citizens, authorized immig., unauthorized immig.)	Step 2 Estimation:Four age groups (14–19, 20–39, 40–59, and ≥60 yrs.)	Step 3 Estimation:Two-task groups (Less-skilled manual vs. semi-skilled and skilled)

Variable:	Major coefficients of interest
Citizen vs. Authorized immigrants vs.	Unauthorized immig. (by	age and task)
Coefficient (-1/σ_I)	−0.475^*** (0.038)	−0.606^*** (0.038)	−0.619^*** (0.029)
Elasticity (σ_I)	2.11
Less-skilled Manual vs. semi-skilled	and skilled (by age)
Coefficient (-1/σ_I)		−0.383^*** (0.100)	−0.351^*** (0.063)
Elasticity (σ_A)		2.61
Less-skilled manual vs.
semi-skilled and Skilled (aggregate)
Coefficient (-1/σ_I)			−0.208^*** (0.044)
Elasticity (σ_I)			4.81

		Other coefficients

Task type dummies:
Semi-skilled and skilled	Base
Less-skilled manual	−0.005 (0.048)
Age group dummies:
14–19	Base	Base	Base
20–39	−0.019 (0.071)	0.059^*** (0.058)	0.037 (0.030)
40–59	0.282^*** (0.082)	0.069 (0.080)	0.032 (0.038)
≥60	0.425^*** (0.101)	0.115 (0.087)	0.066 (0.044)
Immigration status dummies: Citizens		Base	Base
Authorized immigrants		0.156 (0.050)	−0.101 (0.047)
Unauthorized immigrants		−0.149^*** (0.048)	0.766^*** (0.069)
Recovered a_sa in step 2:
α₁₁		1.000
α₁₂		2.321
α₁₃		2.406
α₁₄		1.502
α₂₁		1.725
α₂₂		3.866
α₂₃		3.783
α₂₄		2.175
Estimated k₁in Step 3:
k₁			0.017^*** (0.002)

No. of observations	373	255	414
R²	0.714	0.735	0.676

Nested constant elasticity of substitution (CES) Model B: Estimated elasticities of substitution by immigration status, age, and experience groups

Nested CES Model B: Skill is approximated by farmwork experience
	Step 1 Estimation: Three immigration groups (Citizens, authorized immig., unauthorized immig.)	Step 2 Estimation: Four age groups (14–19, 20–39, 40–59, and ≥60 yrs.)	Step 3 Estimation: Two experience groups less than 10 yrs. ≥10 yrs.

Variable:	Major coefficients of interest
Citizen vs. authorized immigrants vs. unauthorized immig. (by age		and experience)
Coefficient (-1/σ_I)	−0.454^*** (0.031)	−0.443^*** (0.053)	−0.450^*** (0.037)
Elasticity (σ_I)	2.2
Less-experienced vs. more-experienced	(by age)
Coefficient (-1/s)		−0.569^*** (0.124)	−0.575^*** (0.086)
_AElasticity (σ_A)		1.76
Less-experienced vs.
more-experienced (aggregate)
Coefficient (-1/σ_S)			−0.706^*** (0.079)
Elasticity (σ_S)			1.42

Other coefficients

Experience dummies:
More experienced (≥10 years)	Base
Less experienced (≥10 years)	−0.191^*** (0.055)
Age group dummies:
14–19	Base	Base	Base
20–39	−0.082 (0.082)	1.768^*** (0.372)	1.739^*** (0.258)
40–59	0.12 (0.082)	2.725^*** (0.622)	2.705^*** (0.434)
≥60	0.138 (0.101)	2.900^*** (0.750)	2.864^*** (0.529)
Immigration status dummies:
Citizens		Base	Base
Authorized immigrants		0.095 (0.069)	0.101 (0.047)
Unauthorized immigrants		−0.756^*** (0.098)	−0.766^*** (0.069)
Recovered α_sa in Step 2:
α₁₁		1
α₁₂		3.499
α₁₃		7.168
α₁₄		5.791
α₂₁		3.957
α₂₂		6.233
α₂₃		2.99
α₂₄		1.862
Estimated k₁in Step 3:
k₁			−0.022^*** (0.003)

No. of observations	344	207	414
R²	0.698	0.586	0.554

Estimated elasticities of substitution by birthplace, age, and skill (approximated by task type, experience in farming, and education level)

	Step 1 Estimation: Two immigration groups by birthplace (U.S.-born and foreign-born)	Step 2 Estimation: Four age groups (14–19, 20–39, 40–59, and ≥60 yrs.)	Step 3 Estimation: Two skill groups (varies, see below)
Coefficient	1. Skill groups approximated by task type

U.S.-born vs. foreign-born (by age and task)
Coefficient (-1/σ_I)	−0.447^*** (0.049)	−0.479^*** (0.032)	−0.467^*** (0.039)
Less-skilled manual vs. semiskilled and skilled tasks (by age)
Coefficient (-1/σ_A)		−0.348^*** (0.071)	−0.354^*** (0.077)
Less-skilled manual vs. semiskilled and skilled tasks (aggregate)
Coefficient (-1/σ_s)			−0.033 (0.058)

2. Skill groups approximated by experience in farming

U.S.-born vs. foreign-born (by age and experience)
Coefficient (-1/σ_I)	−0.443^*** (0.037)	−0.440^*** (0.028)	−0.452^*** (0.029)
Less-experienced vs. more experienced (by age)
Coefficient (-1/σ_A)		−0.510^*** (0.050)	−0.476^*** (0.047)
Less-experienced vs. more experienced (aggregate)
Coefficient (-1/σ_s)			−0.597^*** (0.094)

3. Skill groups approximated by education

U.S.-born vs. foreign-born (by age and education)
Coefficient (-1/σ_I)	−0.497^*** (0.055)	−0.584^*** (0.048)	−0.588^*** (0.049)
Primary education and less vs. secondary education and above (by age)
Coefficient (-1/σ_A)		−0.563^*** (0.078)	−0.529^*** (0.064)
Primary education and less vs. secondary education and m(aggregate)
Coefficient (-1/σ_S)			−0.478^*** (0.060)

Distribution of individual and aggregated observations by legal status, age, and skill groups (1989-2012)

	U.S. citizen				Authorized immigrant				Unauthorized immigrant
Skill and age groups	14-19	20-39	40-59	≥60	14-19	20-39	40-59	≥60	14-19	20-39	40-59	≥60	Total^a

Number of individual farmworkers within each immigration status, age, and skill cell
Skill proxy: Task type
Less-skilled manual	1.114	4.219	3.348	670	298	6.135	4.405	598	2.174	13.607	2.593	194	39.355
Semi-skilled and skilled	337	1.352	1.276	246	82	2.475	2.170	291	473	3.658	763	49	13.172
Total	1.451	5.571	4.624	916	380	8.610	6.575	889	2.647	17.265	3356	243	52.527
Skill proxy: Experience
Less than 10-year experience	1.388	2.980	826	106	368	3.758	845	75	2.635	13.747	1.679	88	30.174
More than 10-year experience	63	2.570	3.773	803	10	4.809	5.679	805	11	3.441	1.652	153	25.273
Total	1.451	5.550	4.599	909	378	8.567	6.524	880	2.646	17.188	3.331	241	52.264

Number of aggregated observations/cells generated from individual observations
Skill proxy: Task type
Less-skilled manual	24	24	24	24	22	24	24	24	24	24	24	24	286
Semi-skilled and skilled	24	24	24	24	21	24	24	24	24	24	24	18	279
Total	48	48	48	48	43	48	48	48	48	48	48	42	565
Skill proxy: Experience
Less than 10-year experience	24	24	24	24	24	24	24	22	24	24	24	22	284
More than 10-year experience	18	24	24	24	8	24	24	24	8	24	24	24	250
Total	42	48	48	48	32	48	48	46	32	48	48	46	534

Average hourly wage rates by age groups and legal status

Immigration status	U.S. citizen				Authorized immigrant				Unauthorized immigrant
Age group	14–19	20–39	40–59	≥60	14–19	20–39	40–59	≥60	14–19	20–39	40–59	≥60
1989	$4.00	$4.81	$4.99	$4.82	$4.50	$4.82	$4.87	$4.46	$4.57	$4.86	$4.69	$2.70
1990	$4.33	$5.22	$5.17	$4.86	$4.83	$5.32	$5.19	$4.46	$4.82	$4.87	$4.71	$3.60
1995	$5.04	$6.04	$6.35	$5.79	$5.70	$5.87	$5.65	$5.25	$5.29	$5.42	$5.47	$5.62
2000	$6.32	$7.48	$7.26	$7.50	$6.72	$7.13	$6.85	$6.57	$6.13	$6.46	$6.62	$6.57
2005	$7.06	$8.48	$8.45	$8.38	$7.38	$8.07	$8.13	$7.29	$7.06	$7.33	$7.32	$7.73
2010	$8.39	$9.85	$10.39	$9.81	$8.43	$9.34	$9.46	$8.86	$8.04	$8.65	$8.78	$8.41
2012	$8.77	$10.50	$11.17	$10.47	$9.58	$9.94	$10.00	$9.77	$8.26	$8.96	$8.96	$8.81

Estimated elasticities of substitution by immigration status, age, and skill (measured by education level)

Alternative Model: Education is used as skill proxy
	Step 1 Estimation: Three immigration groups (Citizens, authorized immig., unauthorized immig.)	Step 2 Estimation: Four age groups (14–19, 20–39, 40–59, and ≥60 yrs.)	Step 3 Estimation: Two education groups (≤6 yrs., and <6 yrs. of schooling)

Variable:	Major coefficients of interest
Citizen vs. authorized immigrants	vs. unauthorized immig. (by age	and education)
Coefficient (-1/σ_I)	−0.484^*** (0.042)	−0.546^*** (0.052)	−0.558^*** (0.037)
Elasticity (σ_I)	2.07
Primary education and less vs.	secondary education and above (	by age)
Coefficient (-1/σ_A)		−0.653^*** (0.154)	−0.591^*** (0.085)
Elasticity (σ_A )		1.53
Primary education and less vs.	secondary education and above (	aggregate)
Coefficient (-1/σ_S)			−0.408^*** (0.074)
Elasticity (σ_S)			2.45

Other coefficients

Education dummies:
Primary education and less	−0.704^*** (0.121)
Secondary education and above	Base
Age group dummies:
14–19	Base	Base	Base
20–39	−0.107 (0.071)	−0.575^*** (0.174)	−0.518^*** (0.116)
40–59	0.361^*** (0.090)	−1.263^*** (0.191))	−1.230^*** (0.135)
≥60	0.537^*** (0.108)	−1.541^*** (0.224)	−1.575^*** (0.164))
Legal status dummies:
Citizens		Base	Base
Authorized immigrants		−1.453*** (0.177)	−1.493*** (0.124)
Unauthorized immigrants		−1.551*** (0.201)	−1.595*** (0.140)
Recovered α_sa in Step 2:
α₁₁	1.000
α₁₂	1.966
α₁₃	2.112
α₁₄	1.598
α₂₁	0.723
α₂₂	1.414
α₂₃	1.967
α₂₄	1.514

Estimated κ₁in Step 3:
κ₁			0.020^*** (0.004)

No. of observations	340	207	414
R²	0.723	0.733	0.700

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Substitution between Immigrant and Native Farmworkers in the United States: Does Legal Status Matter?

Publicado en línea: 27 jul 2019

Páginas: -

DOI: https://doi.org/10.2478/izajodm-2019-0007

Palabras clave
elasticity of substitution, immigration, legal status, agricultural labor, nested CES framework

© 2019 Xuan Wei, Gülcan Önel, Zhengfei Guan and Fritz Roka, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 Public License.

Figure 1

Figure 2

Nested constant elasticity of substitution (CES) Model A: Estimated elasticities of substitution by immigration status, age, and task groups

Nested constant elasticity of substitution (CES) Model B: Estimated elasticities of substitution by immigration status, age, and experience groups

Estimated elasticities of substitution by birthplace, age, and skill (approximated by task type, experience in farming, and education level)

Distribution of individual and aggregated observations by legal status, age, and skill groups (1989-2012)

Average hourly wage rates by age groups and legal status

Estimated elasticities of substitution by immigration status, age, and skill (measured by education level)

Substitution between Immigrant and Native Farmworkers in the United States: Does Legal Status Matter?

Publicado en línea: 27 jul 2019

Páginas: -

DOI: https://doi.org/10.2478/izajodm-2019-0007

Palabras claveelasticity of substitution, immigration, legal status, agricultural labor, nested CES framework

© 2019 Xuan Wei, Gülcan Önel, Zhengfei Guan and Fritz Roka, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 Public License.

Figure 1

Figure 2

Nested constant elasticity of substitution (CES) Model A: Estimated elasticities of substitution by immigration status, age, and task groups

Nested constant elasticity of substitution (CES) Model B: Estimated elasticities of substitution by immigration status, age, and experience groups

Estimated elasticities of substitution by birthplace, age, and skill (approximated by task type, experience in farming, and education level)

Distribution of individual and aggregated observations by legal status, age, and skill groups (1989-2012)

Average hourly wage rates by age groups and legal status

Estimated elasticities of substitution by immigration status, age, and skill (measured by education level)

Palabras clave
elasticity of substitution, immigration, legal status, agricultural labor, nested CES framework