Figure 1
Figure 2
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 |
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 |
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) | ||
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 |
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/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 |