American Political Science Review Vol.104,No.1 FIGURE 3.Support for Highly Skilled and Low-skilled Immigration by Respondents'Skill Level Allow more low-skilled immigration? Allow more highly skilled immigration? ngly agree Agre er agree nor dsagree ther agree nor disagree Upper 95%confidence bound Upper 95%%confdence bound -a 0.0 0.2 0.4 0.6 0.8 0.0 0.2 0.4 0.6 0.8 Fraction Fraction Formal Tests of the Labor Market who did not finish high school),we expect strong sup- Competition Model port for highly skilled over low-skilled immigration,so We created a binary indicator variable,HSKFRAME, that y+8.1>0.For the most highly skilled respon- dents with EDUCATION =4 (those with a bache- coded one if the respondent i received the question about highly skilled immigrants and zero if he or she lor's degree or higher),we expect the exact opposite, y+8.4 <0.In other words,low-skilled immigration received the question about low-skilled immigrants. is preferred over highly skilled immigration.Taken to- The observed support for immigration is measured by the categorical variable PROIMIG,which takes on the gether this implies that 8 is negative,fairly large in integer value associated with one of the five answer magnitude(lyl>8/4),and statistically significant. In our second test specification we relax the assump- categories j=(1,2,...,5)from "strongly disagree" to“strongly agree.”We model PROIMIG using an tion of linearity in the premium for highly skilled im- migration and estimate ordered probit model with poststratification weights. For all uncertainty estimates we employ the robust lin- earized variance estimator that yields the valid design i=a+yHSKFRAME+8x(HSKFRAME based inferences.20 k∈{1,2.4 To explicitly test the labor market competition ar- gument,we estimate the systematic component of the 1EDUCATION;=))+> ordered probit model with the specification. ke{1,2,4) i=a+yHSKFRAME;+8(HSKFRAME 1 EDUCATION;=k+Z攻. EDUCATION)+EDUCATION;+Zi This specification allows a different premium con- ditional on each of the four skill categories HS where the parameter y is the lower-order term on the DROPOUT.HIGH SCHOOL.SOME COLLEGE. treatment indicator that identifies the premium that and BA DEGREE.Notice that we use SOME COL- natives attach to highly skilled immigrants relative to low-skilled immigrants.The parameter 8 captures how LEGE(respondents who have some college education the premium for highly skilled immigration varies con- but did not graduate)as our reference category,so that y identifies the premium estimated for this skill ditional on the skill level of the respondent. The key predictions based on the standard model of level.Accordingly,y+81,y+82,and y+84 identify the premia estimated for those respondents in the cat- labor market competition are as follows:For the least egories HS DROPOUT,HIGH SCHOOL,and BA skilled respondents with EDUCATION;=1 (those DEGREE.The key prediction is that y+81 is positive and significant whereas y+84 should be negative and 20 Let S(B)=be the score function where B is estimated by significant. solving S(B)=0.Following a first-order Taylor series expansion,the We also enter a basic set of sociodemographic linearized variance estimator is given by V(B)=DV(S(B)=D. covariates Z including the respondent's age (in seven where D=()1. age brackets),gender (female =1,male =0),and race 69American Political Science Review Vol. 104, No. 1 FIGURE 3. Support for Highly Skilled and Low-skilled Immigration by Respondents’ Skill Level HS DROPOUT HIGH SCHOOL SOME COLLEGE BA, MA, PHD Allow more highly skilled immigration? Fraction 0.0 0.2 0.4 0.6 0.8 Strongly agree Agree Neither agree nor disagree Disagree Strongly disagree Upper 95% confidence bound HS DROPOUT HIGH SCHOOL SOME COLLEGE BA, MA, PHD Allow more low-skilled immigration? Fraction 0.0 0.2 0.4 0.6 0.8 Strongly agree Agree Neither agree nor disagree Disagree Strongly disagree Upper 95% confidence bound Formal Tests of the Labor Market Competition Model We created a binary indicator variable, HSKFRAME, coded one if the respondent i received the question about highly skilled immigrants and zero if he or she received the question about low-skilled immigrants. The observed support for immigration is measured by the categorical variable PROIMIG, which takes on the integer value associated with one of the five answer categories j = (1, 2,..., 5) from “strongly disagree” to “strongly agree.” We model PROIMIG using an ordered probit model with poststratification weights. For all uncertainty estimates we employ the robust lin￾earized variance estimator that yields the valid design based inferences.20 To explicitly test the labor market competition ar￾gument, we estimate the systematic component of the ordered probit model with the specification. µi = α + γ HSKFRAMEi + δ (HSKFRAMEi · EDUCATIONi) + θ EDUCATIONi + Ziψ, where the parameter γ is the lower-order term on the treatment indicator that identifies the premium that natives attach to highly skilled immigrants relative to low-skilled immigrants. The parameter δ captures how the premium for highly skilled immigration varies con￾ditional on the skill level of the respondent. The key predictions based on the standard model of labor market competition are as follows: For the least skilled respondents with EDUCATIONi = 1 (those 20 Let S(β) = ∂lnL ∂β be the score function where βˆ is estimated by solving Sˆ(β) = 0. Following a first-order Taylor series expansion, the linearized variance estimator is given by Vˆ (βˆ) = D V{Sˆ(β)}|β=βˆ D
, where D = { ∂Sˆ(β) ∂β }−1. who did not finish high school), we expect strong sup￾port for highly skilled over low-skilled immigration, so that γ + δ · 1 > 0. For the most highly skilled respon￾dents with EDUCATION = 4 (those with a bache￾lor’s degree or higher), we expect the exact opposite, γ + δ · 4 < 0. In other words, low-skilled immigration is preferred over highly skilled immigration. Taken to￾gether this implies that δ is negative, fairly large in magnitude (|γ| > δ/4), and statistically significant. In our second test specification we relax the assump￾tion of linearity in the premium for highly skilled im￾migration and estimate µi = α + γ HSKFRAMEi +
k∈{1,2,4} δk (HSKFRAMEi · 1 {EDUCATIONi = k}) +
k∈{1,2,4} θk 1 {EDUCATIONi = k} + Ziψ. This specification allows a different premium con￾ditional on each of the four skill categories HS DROPOUT, HIGH SCHOOL, SOME COLLEGE, and BA DEGREE. Notice that we use SOME COL￾LEGE (respondents who have some college education but did not graduate) as our reference category, so that γ identifies the premium estimated for this skill level. Accordingly, γ + δ1, γ + δ2, and γ + δ4 identify the premia estimated for those respondents in the cat￾egories HS DROPOUT, HIGH SCHOOL, and BA DEGREE. The key prediction is that γ + δ1 is positive and significant whereas γ + δ4 should be negative and significant. We also enter a basic set of sociodemographic covariates Z including the respondent’s age (in seven age brackets), gender (female = 1, male = 0), and race 69