Figure 1
Nested CES Model A: Skill is approximated by task type
Figure 2
Nested CES Model B: Skill is approximated by farmwork experience
Table 1
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 | Totala |
| 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 |
[i] Note: Not all survey participants answered all skill-related NAWS questions. Therefore, total number of observations when task type is used as skill proxy does not match under the alternative skill proxy (i.e., experience), leading to different sample sizes across alternative models. Without any missing observations, a sample size of 576 cells with 24 observations in each skill-age-immigration status cell would have been achieved.
Table 2
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 |
[i] Source: Authors’ calculation based on NAWS data, 1989–2012.
Table 3
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/σI) | −0.475*** (0.038) | −0.606*** (0.038) | −0.619*** (0.029) |
| Elasticity (σI) | 2.11 | ||
| Less-skilled Manual vs. semi-skilled | and skilled (by age) | ||
| Coefficient (-1/σI) | −0.383*** (0.100) | −0.351*** (0.063) | |
| Elasticity (σA) | 2.61 | ||
| Less-skilled manual vs. | |||
| semi-skilled and Skilled (aggregate) | |||
| Coefficient (-1/σI) | −0.208*** (0.044) | ||
| Elasticity (σI) | 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 asa 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 |
[i] Note: The table reports least squares estimates of Equations (4), (5), (6), and (7). Different combinations of experience, age, year, and immigration status fixed effects are applied in the model. Year dummies are included in all three steps but excluded from the table for the sake of brevity. The following notation is used for αsa that are recovered in Step 2: s = {1,2} represent “semi-skilled and skilled tasks” and “less-skilled manual tasks,” respectively; α = {1,2,3,4} represent age groups 14–19, 20–39, 40–59, and greater than 60. Standard errors are in parentheses.
***Denote significance at the 1% level.
Table 4
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/σI) | −0.454*** (0.031) | −0.443*** (0.053) | −0.450*** (0.037) |
| Elasticity (σI) | 2.2 | ||
| Less-experienced vs. more-experienced | (by age) | ||
| Coefficient (-1/s) | −0.569*** (0.124) | −0.575*** (0.086) | |
| AElasticity (σA) | 1.76 | ||
| Less-experienced vs. | |||
| more-experienced (aggregate) | |||
| Coefficient (-1/σS) | −0.706*** (0.079) | ||
| Elasticity (σS) | 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 αsa 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 |
[i] Note: The table reports least squares estimates of Equations (4), (5), (6), and (7). Different combinations of experience, age, year, and immigration status fixed effects are applied in the model. Year dummies are included in all three steps but excluded from the table for the sake of brevity. The following notation is used for αsa that are recovered in Step 2: s = {1,2} represent “experienced” and “less experienced,” respectively; α = {1,2,3,4} represent age groups 14–19, 20–39, 40–59, and greater than 60. Standard errors are in parentheses.
***Denote significance at the 1% level.
Table B1
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/σI) | −0.484*** (0.042) | −0.546*** (0.052) | −0.558*** (0.037) |
| Elasticity (σI) | 2.07 | ||
| Primary education and less vs. | secondary education and above ( | by age) | |
| Coefficient (-1/σA) | −0.653*** (0.154) | −0.591*** (0.085) | |
| Elasticity (σA ) | 1.53 | ||
| Primary education and less vs. | secondary education and above ( | aggregate) | |
| Coefficient (-1/σS) | −0.408*** (0.074) | ||
| Elasticity (σS) | 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 αsa 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 |
[i] Note: The table reports least squares estimates of Equations (4), (5), (6), and (7). Different combinations of experience, age, year, and immigration status fixed effects are applied in the model. Year dummies are included in all three steps, but excluded from the table for the sake of brevity. The following notation is used for αsa that are recovered in Step 2: s = {1,2} represent “secondary education and above” and “primary education and less,” respectively; α = {1,2,3,4} represent age groups 14–19, 20–39, 40–59, and greater than 60. Standard errors are in parentheses.
***Denote significance at the 1% level.
Table B2
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/σI) | −0.447*** (0.049) | −0.479*** (0.032) | −0.467*** (0.039) |
| Less-skilled manual vs. semiskilled and skilled tasks (by age) | |||
| Coefficient (-1/σA) | −0.348*** (0.071) | −0.354*** (0.077) | |
| Less-skilled manual vs. semiskilled and skilled tasks (aggregate) | |||
| Coefficient (-1/σs) | −0.033 (0.058) | ||
| 2. Skill groups approximated by experience in farming | |||
| U.S.-born vs. foreign-born (by age and experience) | |||
| Coefficient (-1/σI) | −0.443*** (0.037) | −0.440*** (0.028) | −0.452*** (0.029) |
| Less-experienced vs. more experienced (by age) | |||
| Coefficient (-1/σA) | −0.510*** (0.050) | −0.476*** (0.047) | |
| Less-experienced vs. more experienced (aggregate) | |||
| Coefficient (-1/σs) | −0.597*** (0.094) | ||
| 3. Skill groups approximated by education | |||
| U.S.-born vs. foreign-born (by age and education) | |||
| Coefficient (-1/σI) | −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/σA) | −0.563*** (0.078) | −0.529*** (0.064) | |
| Primary education and less vs. secondary education and m(aggregate) | |||
| Coefficient (-1/σS) | −0.478*** (0.060) | ||
[i] Note: The table reports estimated (negative inverse) substitution elasticities from Equations (4), (5), (6), and (7) using birthplace as an alternative measure of immigration status. Standard errors are in parentheses.
***Denote significance at the 1% level.